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Stable32 User Manual - Hamilton Technical Services

1. Control Type Description Scale Max Edit Enter y axis scale maximum Sigma Min Text Display minimum sigma value Scale Min Edit Enter y axis scale minimum Options Groupbox Plot options Date Checkbox Show date on plot Box 1 Checkbox Draw box around plot Bars 2 Checkbox _ Show error bars on plot Table 3 Checkbox Show stability data table on plot Fit 4 Checkbox Show fit parameters at bottom of plot Wide Checkbox Use wide lines for stability data plot Plot File Edit Enter plot filename Read Config Pushbutton Read plot configuration data from STABLE32 INI Save Config Pushbutton Save plot configuration data in STABLE32 INI Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke this help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort The plot defaults may be restored with the Reset All button and the plot options may be saved and recalled in the STABLE32 INI configuration file between program runs with the Save Config and Read Config buttons These configuration data contain additional parameters such as axis labels and scale factors for each plot type The configuration file is read and saved automatically if the corresponding box is checked in the Conf
2. Control Type Description Mu Text Display estimated m value Dead Time Groupbox Dead time controls T Tau Edit Enter dead time ratio B2 Text Display B2 bias ratio B3 Text Display B3 bias ratio Confidence Limits Groupbox Confidence limit controls Analysis Pts Text Display analysis points Chi Sqr DF Text Display chi squared degrees of freedom Single Radio Button Select single sided confidence interval Double Radio Button Select double sided confidence interval Conf Factor Edit Enter desired confidence factor Max Sigma Text Display maximum sigma value Min Sigma Text Display minimum sigma value ACF Noise ID Groupbox Autocorrelation noise identification results rl Text Lag 1 autocorrelation value Alpha Text Estimated alpha value Apply Checkbox Use ACF noise ID in analysis Show Details Checkbox Deselect detailed Sigma dialog box format Set Noise Checkbox Set noise to user selected type Noise Combo Select noise type when Set Noise is checked Copy Pushbutton Copy results to clipboard Variance Parameters l Confidence Limits Variance Type overtap Allan j Analysis Pts 998 f 1 Avg Factor ChiSqrDF 781248 BW Factor Not Applicable 6 Single C Double Sided cl Help Tead 1 000000e 00 Cont Factor fo 950 Iv Show Details Sigma Results X 717 533 F SetNoise Sigma 2 921983e 01 Max ADEV 3 048956
3. Control Type Description Average Data Radiobutton Average the data as it is read First Portion Radiobutton Use the first portion of the data Last Portion Radiobutton Use the last portion of the data Read All Radiobutton Read all data with AF 1 Points Text Display the of points in the data file Avg Factor Edit Enter the averaging factor to be used to read the data file OK Pushbutton Accept selected option amp continue with Open Cancel Pushbutton Abort the Open operation Help Pushbutton Invoke the Large Data File help topic e Operation Choose one of the Average First Last or All options and press OK or press Cancel to abort the Open operation With the Average option the minimum Avg Factor required to read the entire data file is displayed It may be increased if another larger averaging factor is desired The Avg Factor is always 1 for the First Last and All options 135 STABLE32 USER MANUAL e Averaging Averaging of phase data is accomplished by simply eliminating the intermediate data points while averaging of frequency data uses the mean value of the points being averaged In either case the averaging factor is displayed as the default t value e Limits The maximum size data file that can be read is set by the Max Data File Size item in the Configure function The purpose of this setting is to automatically activate the data averaging dialog box when a large
4. Control Type Description Data Range Group Controls for entering data range to select Point Static Start and end point s Start Edit Start data point Pushbuttons Increment decrement start point End Edit End data point Pushbuttons Increment decrement end point Timetag Static Start and end timetag data Timetag Type Combo Choose timetag type OK Pushbutton Perform the Part function amp close dialog box Cancel Pushbutton Abort the Part function amp close dialog box Help Pushbutton Invoke the Part help topic e Operation Enter the Start and End data points to be selected If timetags are available choose the desired Timetag Type to help select the desired data points Use the Press OK to delete the data outside these limits or Cancel to abort e Timetag Display Timetags can be displayed for the start and end data points in MJD DOY Date or general exponential format 183 STABLE32 USER MANUAL 184 ANALYSIS FUNCTIONS Filter Function e Purpose Use the Filter function to filter the current phase or frequency data Low pass filtration can be useful for removing high frequency noise that may otherwise obscure underlying variations in the data Its effect is similar to data averaging but does not lengthen the sampling interval or reduce the number of data points High pass filtration can be useful for removing large amplitude low frequency fluctuation in the data due
5. 30 E 70 Largest Jump 5 037542e 01 ot Point 49 eie E H f E ZA sala i EI ION soll Ti FR con d Iii ir FETTE 40 Hi T 2 J File NEW FRD 2 20r SEOAVG Jump Detection Results Ea E 3 Window Length 10 1O0klump Threshold 3 507280e 01 4 EET i ji of Lorgest Jump 5 037542e 01 J Jn Point Jump Size a 49 5 037541e 01 10 EScaled Cumulative Sum Results 4 Min 2 021790e 004 at Point 100 20 Max 1 277337e 003 at Point 49 i i Single Jump Estimate Jump 5 174156e 001 at Point 49 30 Confidence Factor gt 99 9 4 40 i i i i Li i i i i 0 10 20 30 40 50 60 70 80 90 Data Point SEGAVG Freq Jump Detection Window Length 10 Window Offset 0 Jump Threshold 3 507280e 01 3 000 sigma 4 Jumps 1 100 Stables e CUSUM Frequency Jump Detection The Cumulative Sum CUSUM is a classic change point analysis technique that uses the cumulative sum of the differences between the current value and the overall average It is identical to the corresponding normalized mean removed phase data where a sharp slope change denotes a frequency jump Starting with So 0 S S diy P The CUSUM slope indicates the value of the data with respect to the overall average A flat cumulative sum indicates that the data is near the average value a straight cumulative sum indicates a period of constant data values and most importantly a sudden change in the CUSUM direction indicates a
6. Keyword Description Default Part Show Part function toolbutton 0 Help Show Help function toolbutton 0 Pad Show Notepad function toolbutton 0 DVAR Show DAVAR function toolbutton 0 Autol Show Autol function toolbutton 0 Auto2 Show Auto2 function toolbutton 0 Auto3 Show Auto3 function toolbutton 0 ACF Show ACF function toolbutton 0 Conf Show Configure function toolbutton 0 File Show Filenames function toolbutton 0 Comm Show 5110Comm program toolbutton 0 DBase Show Database function toolbutton 0 Tab Show Tab function toolbutton 0 Vibra Show Vibra function toolbutton 0 e Inputs The Inputs section of the STABLE32 INI file can contain several read only items that serve as user selectable default values for the following parameters Keyword Description Default PhaseTau Tau value for phase data 1 0 FreqTau Tau value for frequency data 1 0 PhaseAddend Default value to be added to phase data in Scale function 0 0 FreqAddend Default value to be added to freq data in Scale function 0 0 PhaseMultiplier Default factor to multiply phase data by in Scale function 1 0 FreqMultiplier Default factor to multiply freq data by in Scale function 1 0 PhaseTagScale Timetag scale multiplier for phase data 1 0 FregTagScale Timetag scale multiplier for freg data 1 0 PhaseTagOffset Timetag scale multiplier for phase data 1 0 FreqTagOffset Timetag scale multiplier for freq data 1 0 If there is no cor
7. e MVAR EDF The edf for the modified Allan variance MVAR is determined by the same expression as the overlapping Hadamard variance see below with the arguments changed as follows valid for 2 lt a lt 2 MVAR and TVAR edf for N m and a MVAR edf for N 1 m and a 2 e TOTVAR EDF The edf for the total variance TOTVAR is given by the formula b T t c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table Power Law TOTVAR edf Noise Type coefficients b c W FM 1 50 0 FFM 1 17 0 22 RW FM 0 93 0 36 e TOTMVAR EDF The edf for the total modified variance TOTMVAR is given by the same formula b T t c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table 91 STABLE32 USER MANUAL Power Law TOTMVAR edf Noise Type coefficients b c W PM 1 90 2 10 FPM 1 20 1 40 W FM 1 10 1 20 FFM 0 85 0 50 RW FM 0 75 0 31 e HVAR EDF The edf for the fully overlapping Hadamard variance HVAR can be found by an algorithm developed by C A Greenhall based on its generalized autocovariance function The HVAR edf is found either as a summation for small m cases with a small number of terms or from a limiting form for large m where 1 edf 1 p a0 a1 p wi
8. Copy Command Properties Function Information Format Remarks Statistics Basic statistics Bitmap Check Freq outliers Text OEM text Drift Drift data Text Sigma Sigma data Text OEM text PSD plot Metafile fF o ee renga pene bem meses pem All the data formats can be displayed with the Clipboard Viewer while the screen dump bitmaps can also be displayed with the Paint program The OEM text format should be used Be sure to use the Edit Metafile not Bitmap menu item for GraphiC plots 37 38 STABLE32 USER MANUAL GENERAL FrequenC FrequenC DLL The FrequenC dynamic link library DLL is a library of over 100 custom functions to support frequency stability analysis It is the basis of much of the underlying Stable32 functionality The following is a list of the functions in the FrequenC Library FrequenC Functions ACFNoiseID AddPSD AddSigma AutocorrelationCalc AverageFreqData AveragePhaseData BasScale BreakDate Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Ca Ca Ca Ca Cal Cal lcBiasl LcBias2 LcBias3 LcBias LcBisectionDrift LcChiSgrProb LcDegFree LcDiffusionFregDrift LcDomain LcFastMTIE LcFastModSigma lcFirstDiff LcFregHadamardDev LcFregModSigma lcFreqOffset lcFreqOverlapHadamardDev LcFregOverlapSigma LcFregSigma LcFregStdDev LcGreenhal1ModSigma
9. O o fln Wis O gt Q 2 T Omm OO K m e CO lt lt o 1 A S RS ER oo ca R a I R o c Sere oN XX Bee xs m 8 mo gt 9 0 gt 3 c O Os Oo Oo s tx e O I c N DO VOZZT FK a a o O 9 e 0 mo i c E C 8 Swiss Font Numeric Code 0201 a mM M 3 S 3 a y ZL m cC O Do M O pm o gt FB Ilo e 312 STABLE32 USER MANUAL e HSH x U N do Il m 2 gt N 65 66 eS n TJ lt 8 INM IV t n C co Mn 0 d w 80 87 4 8 8 pb e Dr ivman Id M oO 23 DR 08 K u v O T 0 P o T v R lt ei IR KR 39 na s a A IU J a GI 160 166 168 Newsgrm Font Numeric Code 0202 APPENDICES simplex fnt 3 lis 26 Class o Elm Vis Gi Y 16 fise x isa le Dies Uli flno wi ls Olio 17 36 53 917 o Ali Y 138 e 155 C 172 A 89 x Als Oln Glas o Ilim Z tu le l13 11190 36015 7172 He Yo J 123 luo 1157 174 3 91 39 s 3173 lle Z 107 kl 124 4 58 2 175 E 192 y 40 s Oi Jis lis lus Jim Als five 193 e gt 5 j 58 75 Kilo 109 MA 126 UR 3 Alto Qm Ow U 2 59 176 Lio Jimi nw 4 E list ili Elis Y sb n Mla O 23 C us e ms lis B 4 61 78
10. MM DD YY U S date format with 2 digit year MM DD YYYY U S date format with 4 digit year YYYY MM DD ISO date format UNIX UNIX DOS date time value the number of seconds since midnight January 1 1970 as returned by the C time function Lotus 1 2 3 and Microsoft Excel date time value the number of days Excel and fractional days since midnight January 1 1900 It is valid only after March 1 1900 because it incorrectly treats 1900 as a leap year HH MM Time in hours and minutes HH MM SS Time in hours minutes and seconds 132 FILE FUNCTIONS e MJD Timetags MJD timetags may be generated for equally spaced data without missing points by using the supported date and time format conversions with the Timetags function First perform the appropriate date time to MJD conversion for the first line of data and copy the resulting MJD value to the Windows clipboard Then after reading the data without timetags open the Timetags function and paste the MJD value into the Start box Finally choose units of Days Tau 86400 and press OK MJD timetags will be generated for the data e Line Rejection Data file lines are rejected for the following reasons 1 Lines that are blank 2 Lines that begin with the UNIX style comment symbol unless a UnixComment 0 statement is included as a read only item in the Preferences section of the Stable32 ini configuration file 3 Lines that do not have any numeric 0 9
11. e Frequency Jump Detection Stable32 has a choice of two methods for frequency jump detection block averaging BLKAVG or sequential averaging SEQAVG plus the classic cumulative sum CUSUM method The BLKAVG method has two detection window parameters the window length and offset while the SEQAVG method has only the window length The default analysis length is one tenth of the record length and the BLKAVG window offset can have a value between zero and the record length modulo the window size For both methods the jump threshold can be based on either an absolute fractional frequency or relative sigma factor limit Frequency Jump Detection Parameters x r Detection Method C BLKAVG SEQAVG m Detection Window Beset Window Length 100 Cancel Window Offset Help m Jump Limits Fractional Freq fa 724029e 13 F Conf Factor Sigma Factor 2 000 Alt Color FREE e Controls The Frequency Jump Detection Parameters dialog box contains the following controls Control Type Description Detection Method Groupbox Jump detection method BLKAVG Radiobutton Block average method SEQAVG Radiobutton Sequential average method Detection Window Groupbox Detection window parameters Window Length Edit Enter analysis window length Window Offset Edit Enter analysis window offset Jump Limits Groupbox Jump limit parameters Fractional Freq
12. Direction Group Search direction controls Up Radiobutton Search upwards Down Radiobutton Search downwards Find Next Pushbutton Perform a Find operation Close Pushbutton Abort the Find function amp close dialog box Help Pushbutton Invoke the Find help topic e Operation Select the search criterion with the two Find What controls The numeric value also determines the search precision Set the search direction with the Up and Down buttons and press the Find Next button The result of a successful search is displayed in the Edit dialog box Additional search may be conducted with the Find Next button The Find dialog box can be closed with the Cancel button or by closing the Edit dialog box 169 STABLE32 USER MANUAL 170 EDITING FUNCTIONS Replace Function e Purpose The Replace function is a Detailed Search sub function of the Edit function Use the Replace function to find and replace data phase or frequency data points that meet a particular criterion The Find function is also available to simply find certain phase or frequency data values Find What x y 8 5e 02 Eind Next Replace With o o Replace Next Iv Confirm Replacements Direction Replace All Up Close Note The of digits entered determines the search precision C Down Help n Controls The Replace function uses a modeless dialog box that can remain open while the Edit function is active It contains the following contr
13. Filter Filter time domain phase or frequency data Clear Clear phase or frequency data Analysis Statistics Calculate basic statistics for phase or frequency data Check Check frequency data for outliers Drift Calculate drift for phase or frequency data Sigma Calculate Allan deviation for phase or frequency data Run Calculate stability statistics DAVAR Perform a dynamic stability analysis Power Plot power spectrum of phase or frequency data Histogram Plot histogram for phase or frequency data Autocorrelation Plot autocorrelation for phase or frequency data 3 Cornered Hat Use the 3 cornered hat method to separate variances Plot Phase Plot phase data Frequency Plot frequency data STABLE32 USER MANUAL Generate Noise Timetags Utility Calendar Domain Inputs Play TSC 5110A Stable ini Log Pad Audio Vibra Autol Auto2 Auto3 Tabs Show Tabs Auto File Tabs Auto Change Tabs Auto Edit Tabs Auto Noise Tabs Save Current Data Rename Selected Tab Write Selected Tab Close Selected Tab Close AII Tabs Options Configure Filenames Status Bar Help About Index Using Help Stable on the Web Feedback 10 Generate simulated power law clock noise Generate timetag data Display a DOY MJD calendar Perform frequency time domain conversions Set input file scaling values Replay a TKF plot file Invoke the 5110Comm applet Open Stable32 INI f
14. Invoke the Configure help topic t Toolbuttons Plots Data Inputs Options Audio Run xj Plots Data Inputs Options Audio Run r General Settings r Select Active Toolbuttons IV Write Sigma File AutoCale Open 4 v Autoinc Filename Ext AutcPlot i IV Show File Opened IV Show Status Plots No Greek Plot Labels Iv Show Splash Screen Text Editor Notepad Motepad exe p Printer Point Size 9 v Default 9 pt Select the toolbuttons you prefer The number shown will depend on the width of your screen Select general Stable32 settings All are recommended except No Greek Plot Labels AutoCalc and AutoPlot are Page 1 General Page 2 Toolbuttons e General Page Controls The General property sheet page contains the following controls Control Type Description General Settings Groupbox General program flag settings Write Sigma File Checkbox Check to write stability file after run Autoinc Filename Checkbox Check to increment filename extension when data changes Show File Opened Checkbox Check to show data plot and info when phase or freq file opened No Greek Labels Checkbox Don t use Greek axis labels on plots AutoCalc Checkbox Check to automatically calculate AutoPlot Checkbox Check to automatically plot when function opened Show Status Plots Checkbox Show mini data plots in status ba
15. Multicolumn Data XI Columns t Columns 16 Taas 1 Cancel Data 2 Help More than 8 columns detected in input file uc Me Choose timetag amp data columns A 0 for Tags prevents reading timetags Press Details to see column values Then press DK to read data or Cancel to abort e Controls The alternate Multicolumn Data dialog box contains the following controls Control Type Description Columns Group Column selection section Columns Text Number of columns in data file Tags Radiobutton Choose column of timetag data to be read Data Radiobutton Choose column of phase or frequency data to be read OK Pushbutton Perform the read operation amp close dialog box Cancel Pushbutton Abort the read function amp close dialog box Help Pushbutton Invoke Multicolumn Read help topic Details Pushbutton Open Multicolumn Details dialog box None Text Brief instructions for Multicolumn Data dialog e Operation Select the desired column for the optional Timetags and Data and then press OK to read the data or Cancel to abort Press the Details button to see detailed information about the data file e No Timetags Timetag reading can be suppressed in the standard multicolumn dialog by deselecting all timetag choices select the current timetag column as the data column to do so Timetag reading can be suppressed in the alternative dialog box by entering a value o
16. TKF filename Null Position Message position 0 X Div x axis divisions 5 Y Div y axis divisions 5 Y Tic y axis tics 5 Line Line type 0 Mouse Mouse flag 0 318 APPENDICES Keyword Description Default Date Data annotation flag 0 Box Draw box around plot flag 0 JumpMethod Code for freq jump detection method 1 Wide Use wide plot line flag 0 X Offset X axis scale offset 0 0 FPlotX Frequency data plot x axis label 0 X Mult X axis scale multiplier 1 0 Y Offset Y axis scale offset 0 0 Y Mult Y axis scale multiplier 1 0 Y Min Y axis scale minimum value 0 0 Y Max Y axis scale maximum value 1 0 Fit Draw fit line flag 0 FXDefault Flag to set x axis scale to default 1 e PhasePlot The PhasePlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null X Label X axis time label text Null Y Label Y axis phase label text Null PlotFile TKF filename Null Position Message position 0 X Div x axis divisions 5 Y Div y axis divisions 3 Y Tic y axis tics 5 Line Line type 0 Mouse Mouse flag 0 Date Date annotation flag 0 Box Draw box around plot flag 0 Wide Use wide plot line flag 0 Fit Draw fit line flag 0 X Offset X axis scale offset 0 0 X Mult X axis scale
17. Th oBR m 7 N for 0 E lt m lt N I m even To where k is the largest available 7 lt 20 T e Th o1 Bias Reference 2 also includes an improved expression for the Th ol bias as a function of both noise type and averaging factor Bias AVAR Th ol a b m where m is the averaging factor and the constants a b and c are given in the table below Note that the effective tau for a Th ol estimation is t 0 75 m to where to is the measurement interval Noise Alpha a b c RW FM 2 2 70 1 53 0 85 F FM 1 1 87 1 05 0 79 W FM 0 1 00 0 00 0 00 F PM 1 0 14 0 82 0 30 W PM 2 0 09 0 74 0 40 80 TIME DOMAIN STABILITY This bias factor is applied to the Stable32 Th ol results e Th ol EDF Empirical formulae for the Th ol EDF as used in Stable32 will be found in Reference 1 below e Th ol Confidence Intervals A detailed discussion of the confidence intervals for Th ol is given in Reference 4 The Th ol confidence intervals are narrower and less skewed more symmetric than those based on chi square and Th ol therefore provides the highest confidence in estimating stability at large averaging factors Stable32 sets the Th ol error bars based on a chi square distribution and the Th ol equivalent X degrees of freedom as given in Reference 1 References The following references apply to the Th ol statistic 1 D A Howe and T K Peppler Very Long Term Frequency Stabilit
18. X Axis Groupbox X axis parameters 201 STABLE32 USER MANUAL Control Type Description Label Text X axis label FFT Points Text of FFT time domain data points PSD Points Text PSD frequency domain points Fourier Interval Text Spacing between Fourier freq points Max Fourier Freq Text Highest Fourier frequency Y Axis Groupbox Y axis parameters PSD Type List Select PSD type Label Text Y axis label Windowing Type List Select FFT windowing type Windowings or Select of windowings or Spurs From Data 7 Windows Select multitaper windows Avg Factor 4 List Select averaging factor or Auto or BW J Factor List Select multitaper J factor PSD Std Dev Text Standard deviation of PSD PSD Max Text Maximum PSD data value PSD Min Text Minimum PSD data value Scale Max Edit Maximum PSD plot scale Scale Min Edit Minimum PSD plot scale Smooth Checkbox Apply smoothing to PSD Max AF Text Maximum applicable averaging factor PSD File Edit Enter PSD data filename Options Groupbox Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Cursor Checkbox Activate mouse cursor for plot Fit 5 Checkbox Draw PSD line fit Points Checkbox Draw FFT points on plot Info Checkbox Show windowing amp carrier freq on plot Wide Checkbox Use wide l
19. e Controls The Normalize dialog box contains the following controls e Operation Press OK To abort press Cancel Control Type Description Average Text Display the mean value OK Pushbutton Perform the normalize function amp close dialog box Cancel Pushbutton Abort the normalize function amp close dialog box Help Pushbutton _ Invoke the Normalize help topic 175 STABLE32 USER MANUAL 176 EDITING FUNCTIONS Average Function e Purpose Use the Average function to combine groups of phase or frequency data into values corresponding to a longer averaging time t Note The entire phase or frequency data array is averaged regardless of the analysis limits Avg Factor 10 OK Cancel zi Press OKto average data by combining points for longer tau Help e Controls The Average dialog box contains the following controls Control Type Description Avg Factor Edit Enter averaging factor default 1 OK Pushbutton Perform the Average function amp close dialog box Cancel Pushbutton Abort the Average function amp close dialog box Help Pushbutton Invoke the Average help topic e Operation Enter the desired Avg Factor and press OK To abort press Cancel or OK with default averaging factor 1 e Phase Averaging Phase data averaging decimation which is done by simply eliminating the intermediate data points to form data a
20. for more divergent noise types such as flicker noise of converging to a value that is not dependent on the number of samples The confidence interval of an Allan deviation estimate is also dependent on the noise type but is often estimated as 0 1 NN A 61 62 STABLE32 USER MANUAL TIME DOMAIN STABILITY Overlapping Allan Variance e Overlapping Allan Variance The overlapping Allan variance is a version of the Allan variance o 1 AVAR that makes maximum use of a data set by forming all possible fully overlapping samples at each averaging time v It can be estimated from a set of M frequency measurements for averaging time tT mto where m is the averaging factor and ty is the basic measurement interval by the expression 2 1 M 2m 1 j m 1 2 o r 2m M 2m 1 2 2 Des y 2 In terms of phase data the overlapping Allan variance can be estimated from a set of N M 1 time measurements as N 2m O e Im y NE Xuam 2 Ki 2 The result is usually expressed as the square root o t the Allan deviation ADEV The confidence interval of an overlapping Allan deviation estimate is better than that of a non overlapping Allan variance estimation because even though the additional overlapping differences are not all statistically independent they nevertheless increase the number of degrees of freedom and thus improve the confidence in the estimation Analytical methods are available for calculating the number of de
21. 1 to M and the extended data for j 1 to M 1 is equal to y y and y m 1 yw The result is usually expressed as the square root Owau t the total Allan deviation TOTADEV When calculated using the doubly reflected method described above the expected value of TOTAVAR is the same as AVAR for white and flicker PM or white FM noise Bias corrections of the form 1 1 a t T where T is the record length need to be applied for flicker and random walk FM noise where a 0 481 and 0 750 respectively 69 STABLE32 USER MANUAL The number of equivalent X degrees of freedom for TOTAVAR can be estimated for white FM flicker FM and random walk FM noise by the expression b T t c where b 1 500 1 168 and 0 927 and c 0 0 222 and 0 358 respectively For white and flicker PM noise the edf for a total Allan deviation estimate is the same as that for the overlapping ADEV with the number of X degrees of freedom increased by 2 Stable32 supports the calculation of TOTADEV from phase or freguency data with the Total option under the Sigma and Run menus The calculation is always done from phase data by the doubly reflected method that does not reguire endpoint matching The Stable32 implementation follows the recipe described by D A Howe and C A Greenhall in Eg 3 of Reference 5 below e References The following references trace the development of the TOTVAR statistic 1 D A Howe An Extension of the Allan Variance with Increased Confiden
22. 52617 52618 52619 52620 52621 Today 18 2 3 16 350 17 351 352 19 353 20 354 7 52624 52625 52626 52627 52628 Copy EEE 23 1357 24 358 25 359 26 360 27 361 Close 52631 52632 52633 52634 52635 30 364 31365 52638 52639 e Controls The Calendar dialog box contains the following controls Control Type Description Year Up Autobutton Advance the calendar by 1 year Year Down Autobutton Retard the calendar by 1 year Month Up Autobutton Advance the calendar by 1 month Month Down Autobutton Retard the calendar by 1 month Today Pushbutton Go to current month amp highlight current day Copy Pushbutton Copy calendar to clipboard Close Pushbutton Close the Calendar dialog box Help Pushbutton Invoke this help topic e Operation The calendar opens to the current month with the current day highlighted Use the Year Up Year Down Month Up and Month Down auto repeating buttons to move to the month desired Use the Today button to return to the current month When finished Close the calendar dialog box 275 STABLE32 USER MANUAL e MJD The Modified Julian Date MJD is based on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 it starts at midnight on November 17 1858 MJD 50 000 was on October 10 1995 e GPS Week The GPS week number is displayed at the t
23. E Te pee ANR v Efe pee ceo E T s Open Save Add Read Prnt Eat Conv Nom Avg FW Scale Gear Part Stats Check Dan Soma Run Power Histo Piot Tag Reg Noise Cal Dom Cont Fie Play Pad Help felcome to the Stable32 program for frequency stability analysis Date 05 04 98 MID 50937 C Phase Data Total Freq Data Total i _ No Phase Data File No Freq Data Tau Start End Tau Start End Stable32 file manipulations include entering and opening phase and freguency files combining data files and storing all or a portion of a data array Data is stored in space or comma delimited multicolumn ASCII format with gaps denoted by a value of zero Editing features include displaying printing changing correcting converting scaling inserting or deleting data or removing outliers filling gaps and adding timetags STABLE32 USER MANUAL Plotting can be done for all or a portion of the data with automatic or user defined scales titles and annotations Stable32 includes provisions for the generation of simulated power law clock noise with the desired offset stability and drift It also has a function for the conversion between time and frequency domain measures of frequency stability e License A license is hereby granted to the purchaser for the use of this program Stable32 ma
24. If status bar plots are enabled the corresponding plot is dynamically updated during editing and a small cursor appears above the plot to indicate the position of the currently selected point e Editing Data A new value can be entered directly into the selected cell with the numeric keys The existing data may be edited by first pressing the F2 key It is necessary to delete a portion of the existing data to make room for the new entries The usual editing keys apply The original value may be restored with the Esc key and the changes are accepted with the Enter key e Caution Editing changes in phase and frequency data must be made with discretion so that the integrity of the data is not lost 167 STABLE32 USER MANUAL 168 EDITING FUNCTIONS Find Function e Purpose The Find function is a Detailed Search sub function of the Edit function Use the Find function to find phase or frequency data points that meet a particular criterion The Replace function is also available to find and replace phase or frequency data values Find What x R 8 5e 02 Eind Next Note The of digits entered Direction determines the search Up C Down precision Help e Controls The Find function uses a modeless dialog box that can remain open while the Edit function is active It contains the following controls Control Type Description Find What Combo Search type Edit Search value
25. PSD results at low Fourier frequencies have relatively low accuracy because little or no averaging is possible and can impair even weighted noise line fitting The number of low frequency PSD points omitted from the plot can be set by the PSDLFSkip read only configuration file Preferences item default 1 The value of the data size dependent maximum auto AF periodogram averaging factor can be set by the PSDAvgSize read only configuration file Preferences item default 64 and the absolute maximum averaging factor can be set with the PSDAvgMax read only configuration file Preferences item default 256 They should both be a power of 2 Thus the maximum AF is the smaller of N PSDAvgSize or PSDAvgMax where N is the of phase or frequency data points raised to the next higher power of 2 Stable32 is intended primarily for time domain frequency stability analysis but the Power function is included to provide additional insight into the noise properties under investigation as well as to assist in the detection of discrete and or periodic components e Caution The PSD results are based on time units of seconds e References 1 W H Press B P Flannery S A Teukolsky and W T Vetterling Numercial Recipes in C Cambridge University Press 1988 ISBN 0 521 35465 X Chapter 12 2 D J Thomson Spectrum Estimation and Harmonic Analysis Proc IEEE Vol 70 No 9 Sept 1982 pp 1055 1096 3 D B Percival and A T Walden Spectral Anal
26. The simplest use is to just display the current phase or frequency data Check the Show Timetags control to also display the corresponding timetag data and use the vertical scroll bars to scroll through the data The data point s are shown in the left column of the data display Use the Go To Point controls to move to a particular data point Check the Color Gaps and or Color Outliers to highlight those data points The outlier criterion can be set with the Sigma Factor entry box The Color Gaps option highlights timetag intervals that differ by more than 1 from the starting value and data points with a value of zero except the Ist and last points of phase data The Previous and Next Gaps and Outliers can be found using the Find controls More elaborate searching is supported by the Find and Replace functions of the Detailed Search controls Simple editing can be done with the usual editing keys directly in the data display including changing adding and deleting data No adjustments are made in the timetags when data is added or deleted and the timetag column is not editable Insertion or Deletion of a certain of points is facilitated by the Edit After Highlighted Point controls The editing changes can be accepted with the OK button or aborted by pressing Cancel e Navigation A cell may be selected with a mouse click the scroll bars or the arrow keys A cell may also be selected by using one of the Go To Find or Search functions
27. Use the standard file open dialog box to open the stability file The stability filename and data will then be displayed 153 STABLE32 USER MANUAL Use the Plot or Print buttons to plot or print the stability data or the Close button to close the dialog box e Stability File Format The format of the stability files written after a Run operation and read by the Read function is slightly different from the screen display The screen columns are Tau Min Sigma Sigma and Max Sigma where is the number of analysis points Sigma is the nominal sigma value and the Min amp Max Sigma values are used to define the plot error bars The order of the stability file columns is Tau Sigma Min Sigma Max Sigma and DF The Min amp Max Sigma and DF number of X degrees of freedom columns are optional and if they are omitted the plot will show the Sigma values without error bars An example of a stability data file is shown below the column headings are not included in the file Tau Sigma Min Sigma Max Sigma DF 1 000e 01 999 2 922e 01 2 846e 01 3 005e 01 6 651e 02 2 000e 01 997 2 010e 01 1 953e 01 2 072e 01 5 693e 02 4 000e 01 993 1 448e 01 1 396e 01 1 506e 01 3 456e 02 8 000e 01 985 1 057e 01 1 006e 01 1 117e 01 1 818e 02 1 600e 02 969 6 191e 02 5 780e 02 6 706e 02 9 121e 01 3 200e 02 937 4 808e 02 4 372e 02 5 409e 02 4 478e 01 6 400e 02 873 3 624e 02 3 177e 02 4 334e 02 2 141e 01 1 280e 03 745 2 767e 02 2 3
28. at each window position MTIE is the overall maximum of this time interval error over the entire data set MTIE 7 Max gex n Max ajaks x Min jep x where n 1 2 N 1 and N phase data points MTIE is a measure of the peak time deviation of a clock and is therefore very sensitive to a single extreme value transient or outlier The time required for an MTIE calculation increases geometrically with the averaging factor n and can become very long for large data sets although faster algorithms are available see Reference 4 below The relationship between MTIE and Allan variance statistics is not completely defined but has been the subject of recent theoretical work see References 2 and 3 below Because of the peak nature of the MTIE statistic it is necessary to express it in terms of a probability level B that a certain value is not exceeded For the case of white FM noise important for passive atomic clocks such as the most common rubidium and cesium frequency standards MTIE can be approximated by the relationship MTIE t p kp V ho t kg V2 0 1 1 where kg is a constant determined by the probability level B as given in the table below and h is the white FM power law noise coefficient B kg 95 1 77 90 1 59 so 139 e References The following references apply to the MTIE statistic 1 S Bregni Clock Stability Characterization and Measurement in Telecommunications IEEE T
29. but the default values 1 s are usually OK Other initial values can be entered after the function is entered by pressing the small button labeled 0 immediately to the right of the function entry box to open the Function Fit Parameter Initialization dialog box e Frequency Jump Detection Stable32 has two methods for frequency jump detection that are invoked and controlled by the Frequency Jump Detection Parameters dialog box 220 ANALYSIS FUNCTIONS e Plot Messages Several standard messages such as the minimum maximum and average values the frequency drift and any offset removed or line fits are available by exposing the plot message drop down list e Plot Inserts Mini plots may be inserted at bottom left of phase data frequency data and stability plots These plots must have been generated previously and named p_insert tkf f insert tkf and s insert tkf respectively For example a small plot of the frequency data can be inserted into a stability plot as shown in the sample below Dole QNT Tiag 142578 Dele Pelei 1 thru 39157 of 39157 T FREQUENCY STABILITY GPS Block IIA RAFS S N 008 Flac anDde QO7 1072 Tou Sigmo 9 00e 02 9 99e 14 1 80e 03 102e 13 9 00 3 60e 03 1 03e 13 7 20e4 03 9 36e 14 1 44e 04 5128 14 1 2 88e 04 4 72e 14 5 76e 04 2738 14 1 15e 05 1B8te 14 2 30e 05 141e 14 4 61e 05 1 28e 14 9 22e 05 1172 14 L84e 08 1 43e 14 3 69e 06 15
30. ka Files A B CxProgram Files A C CAProgram Files B C CAProgram Files Browse 1 000e 01 2 000e 01 6 400e 02 1 280e 03 1 427e 11 1 031e 11 7 241e 12 5 606e 12 4 065e 12 2 699e 12 2 031e 12 1 37 e 12 1 443e 11 1 023e 11 7463e 12 4 692e 12 3 471e 12 1 851e 12 1 479e 12 6 038e 13 Read 1 291e 11 9 733e 12 Calc 7 113e 12 5 119e 12 Close 3 720e 12 E 2 895e 12 Help 2 217e 12 1 962e 12 Plot Options Lines ii Notes Enter filenames read stability data and press Calc The 3 Cornered Hat method requires 3 sets of stability data with the same sigma type amp tau range Plot Sigma Type Copy Copy Overlapping Unit fa gt Pritt OMM ODF i Control Type Description Stability Files Group Choose stability filenames A B Edit Enter A B stability data filename A C Edit Enter A C stability data filename B C Edit Enter B C stability data filename Browse Pushbutton Invoke file open dialog box to select data file Tau Sigma A B etc Table Table of tau and stability data Read Pushbutton Read stability data Calc Pushbutton Perform calculation to separate variances Close Pushbutton Close dialog box Help Pushbutton Invoke this help topic Plot Pushbutton Plot stability data Options Pushbutton Open Options dialog box Lines Pushbutton Open Lines dialog box Notes Pushbutton Open Not
31. parameters that define the three automation scripts Keyword Description Default FileOpen Flag to open data file 0 Convert Flag to convert data type 0 Outliers Flag to remove outliers 0 Average Flag to average data 0 Drift Flag to remove drift 0 PhaseDataPlot Flag to plot phase data 0 FreqDataPlot Flag to plot frequency data 0 Run Flag to run stability analysis 0 StabPlot Flag to print stability plot 0 StabTable Flag to print stability table 0 Close Flag to close Auto dialog box 0 DataPlot Flag to plot data 0 DataPrint Flag to print data 0 PrintOriginal Flag to print original data 0 PrintCorrected Flag to print corrected data 0 PrintSelected Flag to print selected data 0 PrintAveraged Flag to print averaged data 0 PrintResidual Flag to print residual data 0 RunPlot Flag to plot stability 0 Part Flag to use part of data 0 Delay Flag to add extra delay 0 Script Script name Script_ PhaseVariance Variance type for phase data Normal FreqVariance Variance type for freq data Normal Filename Data filename to open Null PhaseDriftType Drift fit type for phase data Quadratic FreqDriftType Drift fit type for freq data Linear AvgFactor Averaging factor 1 DataType Data type 0 Phase 1 Freq 0 AnalysisType Stability analysis type 0 SigmaFactor Outlier sigma factor 5 000 DelayTime Extra delay time in msec 0 Start Start data point 1 End End
32. sure to select the correct data type in the status bar or Open Data File dialog box The following options apply when a data file is opened e The Open Data File dialog box is invoked when the data filename and type is not known The data type may be defined with a phd or frd filename extension or a p or f command line option e The Multicolumn Data dialog box is invoked when multicolumn data is detected in the last numeric line of the data file e The Data File Opened dialog box is invoked unless it is disabled by the Show Data Opened configuration option or the o skip command line option e Tau Entry It is important that the correct tau value be entered for a data file This can be done by entering it in the Data File Opened or status bar by the t command line option by a Tau statement in a data file header by a PhaseTau or FreqTau statement in the Stable32 ini configuration file by the interval between the first two timetags or by using the default value of 1 0 seconds The precedence for setting the tau value is as follows 1 Manual entry 2 Command line 3 File header 4 INI Inputs 5 Timetag interval 6 Default e Reference W J Riley Launching and Opening Data Files in Stable32 Hamilton Technical Services 31 32 STABLE32 USER MANUAL GENERAL Command Line Options e Purpose Stable32 accepts several command line options These options allow phase frequency or archive data to be loaded
33. up and down viewpoint of the plot and the Reverse checkbox flips the horizontal plot orientation Changing these viewpoints can sometimes help to improve the visibility of the stability data Their default settings are in the middle of the sliders 256 ANALYSIS FUNCTIONS A dynamic stability analysis can be performed with either the overlapping Allan AVAR or overlapping Hadamard HVAR variance The latter is more appropriate when there is frequency drift in the data The resulting dynamic stability plot is saved as a tkf file with a filename entered in the Plot Filename edit box default DAVAR TKF The plot options provide choices to put the Date and other information at the top of the page draw a Box around the page and use multiple Colors for the 3D surface plot For color surface plots the Grid control selects the grid type 0 No Grid 1 Full Grid 2 9 of x and y mesh lines skipped The preferred Message Position is Top Right where there is the most space The character sequence n backslash and lower case n will insert a carriage return line feed into the message to allow a longer more vertical format The dynamic stability analysis options and settings can be saved in the STABLE32 INI configuration file with the Save Config button recalled with the Read Config button and restored to their default settings with the Reset button e Dynamic Stability Plot The dynamic stability plot is a 3D surface plot of ADEV or HDE
34. 000000e 000 1 422213e 001 5 000000e 000 1 000000e 000 1 354947e 001 258 ANALYSIS FUNCTIONS Regularize Function e Purpose Use the Regularize function to find interruptions and missing points in time tagged phase or frequency data and optionally insert gaps as required to provide a regular sequence of data points The regularize function is not available for data that does not have timetags Regularize EI Interruptions 1 OK Missing Pts 3 Data Interval 9 0000000000e 02 2 Press OK to use timetag info to insert gaps where data is missing Help e Controls The Regularize dialog box contains the following controls Control Type Description Interruptions Text Display of interruptions in the data Missing Pts Text Display total missing points in the data Data Interval Text Display time interval between data points OK Pushbutton Perform the Regularize function amp close dialog box Cancel Pushbutton Abort the Regularize function amp close dialog box Help Pushbutton Invoke this help topic e Operation Observe the Interruptions Missing Pts and Data Interval displays If there are missing points that you wish to remove verify that the Data Interval is correct Then press OK to regularize the data To abort press Cancel or OK if interruptions 0 e Caution The Data Interval must indicate the proper time spacing It is de
35. 001 0 8 600000e 001 6 100000e 001 6 671141e 002 6 043232e 002 7 546575e 002 7 120376e 002 4 117894e 001 0 16 200000e 001 3 000000e 001 5 049280e 002 4 413549e 002 6 073074e 002 5 296763e 002 2 029433e 001 0 32 400000e 001 1 400000e 001 3 240792e 002 2 699058e 002 4 334743e 002 3 188477e 002 9 560976e 000 0 64 280000e 002 6 000000e 000 3 442747e 002 2 692889e 002 5 668582e 002 2 786492e 002 4 235294e 000 0 128 Two sets of rows are included for the Overlap amp Mod and Th oH variance types e Notes Printing of the stability results is not available for the All Tau option The TIE rms MTIE Th ol and Th oH statistics are only available for phase data TIE rms and MTIE do not include confidence intervals 241 STABLE32 USER MANUAL e Calculation Times The time required for the Run calculations depends on the number of data points the variance type and the selected tau increment as well as the processor speed Typical Run calculation times for a reasonably fast 2 8 GHz Pentium D processor are shown in the following plot Stable32 Typical Run Calculation Time for Stability Statistics T 75 Octave Points Mod Time amp Hadamard Total 2 8 GHz A A Pentium D Th o1 8 Th oH Processar ADEV MDEV TDEV HDEV TOTDEV 60 45 30 Calculation Time seconds 5 10 10 10 10 of Data Points These approximate calculation times are used to determine when a dialog box automatical
36. 489368e 01 Minimum 1 371760e 03 2 545924e 01 4 533354e 01 Average 1 4 897745e 01 4 897745e 01 4 897745e 01 Median 4 798849e 01 5 047888e 01 4 807261e 01 Linear Slope 2 3 6 490910e 06 5 979804e 05 1 056376e 03 Intercept 3 4 865258e 01 4 867547e 01 4 839644e 01 Bisection Slope 2 6 104214e 06 6 104214e 05 6 104214e 04 Ist Difference Slope 2 1 517561e 04 9 648320e 04 1 011791e 03 Log Fit 2 4 a 5 577220e 03 5 248477e 03 7 138988e 03 y t a In bt 1 c b 9 737500e 01 4 594973e 00 1 420429e 02 y ab bt 1 c 4 570469e 01 4 631172e 01 4 442759e 01 Slope at end 5 571498e 06 5 237080e 05 7 133666e 04 Standard Deviation 5 2 884664e 01 9 296352e 02 3 206656e 02 Normal Allan Deviation 6 2 922319e 01 9 965736e 02 3 897804e 02 Overlap Allan Deviation 8 2 922319e 01 9 159953e 02 3 241343e 02 Mod Allan Deviation 7 8 2 922319e 01 6 172376e 02 2 170921e 02 Time Deviation 8 1 687202e 01 3 563623e 01 1 253382e 00 Hadamard Deviation 2 943883e 01 1 052754e 01 3 910861e 02 Overlap Had Deviation 2 943883e 01 9 581083e 02 3 237638e 02 Hadamard Total Deviation Total Deviation 2 943883e 01 2 922319e 01 9 614787e 02 9 134743e 02 3 058103e 02 3 406530e 02 Total modified Deviation 2 418528e 01 6 499161e 02 2 287774e 02 Time Total Devia
37. 6745 makes the MAD equal to the standard deviation for normally distributed data Each frequency data point y 1 is compared with the median value of the data set m plus or minus the desired multiple of the MAD e Limits The Check function does not work with phase data which must be converted to frequency data to apply the Check function e Auto Calc A check can be done automatically when the Check function is invoked by setting the AutoCalc item in the Configure function e Caution Judgment is required when removing outliers Automatic outlier removal is convenient for quickly obtaining meaningful results when plotting and analyzing frequency data While providing a degree of objectivity the analyst is still responsible for decisions regarding outlier removal It is particularly important to explain all phase discontinuities 190 ANALYSIS FUNCTIONS Drift Function e Purpose Use the Drift function to analyze phase or frequency data for frequency drift or find frequency offset in phase data It is common to remove the deterministic frequency drift from phase or frequency data before analyzing the noise with Allan variance statistics It is sometimes useful to remove only the frequency offset from phase data e Controls The basic Drift dialog box contains the following controls Drift Type Combo Select drift analysis type Slope or Noise Text Display slope value or noise type c A e di Ca
38. 77 RWFM 2 0 75 4 BW factor 2nf to 10 Applies only to F PM noise 5 Theoretical R n for W FM noise 0 500 and 0 262 for F PM noise 6 Double sided 68 confidence interval p 0 158 and 0 842 7 Single sided 95 confidence interval p 0 950 8 Double sided 95 confidence interval p 0 025 and 0 975 298 OTHER INFORMATION Analysis Procedure e Analysis Procedure The Stable32 functions can be used freely as the circumstances dictate Nevertheless the following list shows a typical analysis procedure 1 Open a phase data file from disk 2 Examine the phase data in the Data File Opened box and enter the averaging time tau value Convert the phase data to frequency data Check the frequency data for outliers Plot the frequency data Remove the frequency drift Plot the frequency residuals Run a stability analysis Plot the stability data AA ES The results of an analysis can be documented by printing a table plotting a graph copying values to the Windows clipboard reading a stability file replaying a plot or reading or pasting a converted plot into another application In addition a log file is produced that documents all the analysis steps performed e Data Precision There are relatively few numerical precision issues relating to the analysis of frequency stability data One exception however is phase data for a highly stable frequency source having a relatively lar
39. A Hadamard B1 ratio HVAR Total Allan Lag 1 ACF TOTEDF 4 x TOTVAR TOTAVAR B1 ratio Bias 6 Total Lag 1 ACF TOTMVAR x TOTMVAR Modified B1 plus R n EDF Bias 7 TOTMVAR for a 1 2 for m gt 8 else EDF 5 Total Lag 1 ACF TOTMVAR x TOTMVAR Time B1 plus R n EDF Bias 7 TOTTVAR for a 1 2 for m gt 8 else EDF 5 Th ol Lag 1 ACF Th ol EDF x Th ol Bias B1 plus R n 17 17 or for a 1 2 Th oBR 18 Th oH Lag 1 ACF Th ol EDF x Th oBR 18 B1 plus R n 17 for a 1 2 TIE rms N A N A None N A MTIE N A N A None N A The Lag 1 ACF noise ID method is used when the of analysis points is gt 30 97 STABLE32 USER MANUAL References The following references apply to the Stable32 edf and bias functions 1L 2 10 11 12 13 14 15 16 17 18 98 IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology Random Instabilities JEEE Std 1139 1999 July 1999 C A Greenhall Estimating the Modified Allan Variance Proc IEEE 1995 Freq Contrl Symp pp 346 353 May 1995 D A Howe amp C A Greenhall Total Variance A Progress Report on a New Frequency Stability Characterization Proc 1997 PTTI Meeting pp 39 48 December 1997 C A Greenhall private communication May 1999 D A Howe private communication March 2000 D A Howe Total Variance Explained Proc 1999 Joint Meeting of the European Freq and Time Fo
40. Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text i Note text Null e Toolbuttons The Toolbuttons section of the STABLE32 INI file can contain the following flag parameters the order has no effect Keyword Description Default Open Show Open function toolbutton 0 Add Show Add function toolbutton 0 Read Show Read function toolbutton 0 Save Show Save function toolbutton 0 Conv Show Convert function toolbutton 0 Stats Show Statistics function toolbutton 0 Check Show Check function toolbutton 0 Run Show Run function toolbutton 0 Norm Show Normalize function toolbutton 0 Plot Show Plot function toolbutton 0 Drift Show Drift function toolbutton 0 Histo Show Histogram function toolbutton 0 Cal Show Calendar function toolbutton 0 Avg Show Average function toolbutton 0 Print Show Print function toolbutton 0 Noise Show Noise function toolbutton 0 Clear Show Clear function toolbutton 0 Power Show Power function toolbutton 0 Edit Show Edit function toolbutton 0 Sigma Show Sigma function toolbutton 0 Fill Show Fill function toolbutton 0 Scale Show Scale function toolbutton 0 Play Show Play program toolbutton 0 Tag Show Timetag function toolbutton 0 Reg Show Regularize function toolbutton 0 Dom Show Domain function toolbutton 0 323 STABLE32 USER MANUAL
41. Data File dialog box for averaging a data file as it is read The Non Numerics to Skip value sets the number of nonnumeric characters that are skipped at the beginning of each line of phase or frequency data as it is read This value normally 0 can be used to help read data files that contain non numeric markers at the start of each line Data files are parsed for numeric characters one line at a time and a non numeric character terminates the reading of the current line This is desirable to reject comments but can also prevent the reading of actual data Thus if the data lines start with non numeric characters this configuration variable can help when reading them The Use Comma checkbox allows commas to be substituted for decimal points in data files The Warn for Zero Frequency checkbox activates a warning message when two identical adjacent values occur in a phase data file that result in a zero fractional frequency value that is also used to indicate a gap in the data Note that the Adjust Zero Frequency option in the Convert function can be used to adjust those zero fractional frequency values to 1e 99 in order to avoid their treatment as gaps The Write Header option causes a header that includes the filename date amp time data type points and tau to be written at the top of a data file The Reset pushbutton restores the Max Data File Size and Non Numerics to Skip to their default values 54 GENERAL e Inputs The I
42. Edit Enter fractional frequency jump threshold Sigma Factor Edit Enter sigma factor jump threshold CUSUM Plot Checkbox Show CUMSUM plot inset Conf Factor Checkbox Calculate CUSUM jump confidence factor 223 STABLE32 USER MANUAL Control Type Description Alt Color Checkbox Use alternate color for frequency plot Reset Pushbutton Reset all parameters to defaults OK Pushbutton Accept parameters close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke this help topic Checking the CUSUM Plot box causes a cumulative sum plot inset to be drawn Checking the Conf Factor box enables a confidence factor calculation for a CUSUM jump based on the CUSUM ranges of 1000 randomly shuffled data sets Checking the Alt Color box causes the frequency data to be plotted in yellow to improve the visibility of the jump analysis lines The results of the freguency jump analysis are automatically written to the file Jump dat which contains the estimated frequency average of the analysis window at each data point with jumps denoted by a value of zero The results of the CUSUM analysis are automatically written to the file Cusum dat which contains the cumulative sum value at each data point e See Also Frequency Jump Detection 224 ANALYSIS FUNCTIONS Plot Lines Function e Purpose Use the Plot Lines function to add lines to a data plot The possible line types are as fo
43. File Combo Noise type for fit or select mask file Sigma 1 Text Noise line fit parameter Lines Text of lines entered Read Pushbutton Read line info from INI file Save Pushbutton Save line info to INI file Clear All Pushbutton Clear all lines Print Pushbutton Print all line parameters OK Pushbutton Perform the Run Line function amp close dialog box Cancel Pushbutton Abort the Run Line function close dialog box Help Pushbutton Invoke this help topic Operation All plot lines are cleared if the Run conditions are changed Noise Lines The following power law noise lines are supported The power law noise lines have the selected slope and a sigma 1 intercept determined by the stability points weighted by the reciprocal of the range of their error bars The weighting can be eliminated by setting Weight 0 in the Preferences section of Stable32 ini Use of the noise line type is not usually appropriate for TIE rms and MTIE 250 Noise Alpha Slope Remarks WPM 2 1 0 Slope 1 5 for mod sigma FPM 1 1 0 WFM 0 0 5 FFM kl 0 0 RW FM 2 0 5 Aging 1 0 FW FM 3 1 0 Hadamard sigma only RR FM 4 1 5 Hadamard sigma only ANALYSIS FUNCTIONS Masks Masks can be added to a stability plot to show specification limits and the like They are defined in user written msk files per the format shown below To add a mask first select Mask from the list of li
44. HP 1 Installation iii itv 3 Directories Program Model ssissicessscisesasssdcgesicasasansitsieedbontssissesdcnedssasnssasistaseotonbentesshaneetaseobebanssta cde 7 Menu Tree St tus Bar decet a 11 Function Keys TADS irradia 15 Dita 079111 ii 17 A A 21 Archive File Format arse 25 PIENAMEBS ii 27 ARTENE Te cd 29 Launching P 31 Command Line Options siii raciones 33 Automated Operation iet een i n guber ade EE E N ETERRA 35 Copy Command ise eter aE erica raise regn 37 lu NEIE 39 Goa rosino raar AREA EPEE E A AEREA AE ENAERE S 41 IIIS c n 45 Special c aken 47 Configure Function Configuration PIS i 57 TIME DOMAIN STABILITY Time Domain Stability sssrin ririri tinner aE rencor 59 Ala Ene M 61 Overlapping Allan Variance 63 Modified Allan Variant AA AAA 65 STABLE32 USER MANUAL Time Variances AIM AAA n eiecti deer EH seed 69 Total Modified Variance cde ERI I PR SERIES 71 Hadamard Variance ee uie RERUM A er 73 Overlapping Hadamard Variance 75 Total Hadamard Variance aaea EE E eene nnne TI Dynamic SAD TL OD PERDER EDD COE 87 Confidence Intervals iter RARO RARE Re AREA EUM
45. IER RENT REPRE ae A 179 Scale EUHGHON a a id ae do 181 VE see AT EE E 183 Filter FOO a AA E AAi 185 ANALYSIS FUNCTIONS Statistics Function Check T LE EDEN 189 Drift ButictiOn A e ete a aa AA 191 Sigma Function eon IO AS 195 Power PUNCHOME iee 201 Autocorrelation Eutictioh 44441012 ORO RR ERE ORE 207 Histogram Functions 211 Plot Function Ip Nude NP HN 215 Plot Options Function moria 217 STABLE32 USER MANUAL Jump Detection Parameters Plot Eines EUhctiob insit ene tire pier tette enn 225 Plot Notes FU 227 Timetags PUDO sta 229 Noise PONCHO bai S 231 SNS at FUNCOM a 235 Run FU ida 237 Run Plot Function Run Options F tictioli ia 245 IBN A A aa 249 Run NOtes Funct On ii 253 Dynamic Stability Function eese 255 Regularize FU co PERRO EPHRAIM 259 Domain Futiction o ERR RCM RR erra es 261 MISCELLANEOUS FUNCTIONS Autot Puid ose ees e extre edit apu i D RON RR RES eda 265 3 Cornered Hat Function Audio F tlction 1 t teet ener E 271 Vibra BUN CHOW m 273 Calendar Funct one eo Rm C t desd da ad 275 A teet eei Er e PT ene Nei EE teet 277 Pl y ds Ee RUNE DIRE RSEN AUR NN 279 OTHER INFORMATION Glossary References TT TD 285 OR OR 293 A AAA EAA OEA 295 Analysis Procedufe 5 sestertia Een tort per ene REEE 299 Validation REN 303 Acknowledgments id 305 APPENDICES I Stable 32 Functions 1e er HERE OE OR M
46. Inexpensive Frequency Calibration Service From NIST Proc 44th Annu Symp on Freq Contrl pp 107 116 June 1990 D W Allan M A Weiss and J L Jespersen A Frequency Domain View of Time Domain Characterization of Clocks and Time and Frequency Distribution Systems Proc 45th Freg Contrl Symp pp 667 678 May 1991 Hadamard Variance R A Baugh Frequency Modulation Analysis with the Hadamard Variance Proc 25th Freg Contrl Symp pp 222 225 April 1971 B Picinbono Processus a Accroissements Stationnaires Ann des telecom Tome 30 No 7 8 pp 211 212 July Aug 1975 K Wan E Visr and J Roberts Extended Variances and Autoregressive Moving Average Algorithm for the Measurement and Synthesis of Oscillator Phase Noise Proc 43rd Freg Contrl Symp pp 331 335 June 1989 S T Hutsell Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation Proc 27th PTTI Meeting pp 291 302 Dec 1995 S T Hutsell Operational Use of the Hadamard Variance in GPS Proc 28th PTTI Meeting pp 201 213 Dec 1996 D N Matsakis and F J Josties Pulsar Appropriate Clock Statistics Proc 28th PTTI Meeting pp 225 236 Dec 1996 W J Riley The Hadamard Variance Hamilton Technical Services Modified Hadamard Variance S Bregni and L Jmoda Improved Estimation of the Hurst Parameter of Long Range Dependent Traffic Using the Modified Hadamard Variance Proceedings of the IEEE ICC June 2006 T
47. Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 P Tavella and D Meo The Range Covered by a Clock Error in the Case of White FM Proc 30th PTTI Meeting Dec 1998 S Bregni and S Maccabruni Fast Computation of Maximum Time Interval Error by Binary Decomposition IEEE Trans I amp M Vol 49 No 6 pp 1240 1244 Dec 2000 Dynamic Stability L Galleani and P Tavella The Characterization of Clock Behavior with the Dynamic Allan Variance Proc 2003 Joint FCS EFTF Meeting pp 239 244 L Galleani and P Tavella Tracking Nonstationarities in Clock Noises Using the Dynamic Allan Variance Proc 2005 Joint FCS PTTI Meeting Confidence Intervals P Lesage and C Audoin Characterization of Frequency Stability Uncertainty due to the Finite Number of Measurements JEEE Trans Instrum Meas Vol 22 No 2 pp 157 161 June 1973 P Lesage and C Audoin Estimation of the Two Sample Variance with a Limited Number of Data Proc 31st Freq Contrl Symp pp 311 318 June 1977 K Yoshimura Degrees of Freedom of the Estimate of the Two Sample Variance in the Continuous Sampling Method IEEE Trans Instrum Meas Vol 38 No 6 pp 1044 1049 Dec 1989 C A Greenhall Recipes for Degrees of Freedom of Frequency Stability Estimators IEEE Trans Instrum Meas Vol 40 No 6 pp 994 999 Dec 1991 M A Weiss and C Hackman Confidence on the Three Point Estimator of Frequency Drift Proc 24th P
48. Mod Gota T and abbreviated as ADEV MDEV TDEV HDEV TOTADEV TOTMDEV and TOTTDEV respectively The TIE rms MTIE and Th ol statistics apply only to phase data e Operation The Sigma function begins with the selection of the Variance Type and the Avg Factor the of to measurement intervals averaged to form the averaging time t Entering an m or M will give the maximum allowable averaging factor The Cale button will then calculate the desired Sigma value The Show Details checkbox will change the dialog box to a more detailed format as described below The Help button invokes this Help screen while the Close button closes the dialog box A change in either the Variance Type or Avg Factor clears the results e Detailed Sigma Dialog Box The detailed Sigma dialog box provides additional options and results The Variance Parameters group box adds a BW Factor entry and a display of the Tau value The BW Factor is equal to 2nf to where f is the upper cutoff frequency of the measuring system in Hz and applies only to flicker PM noise The Sigma Results group box adds a display of the Std Dev standard deviation The Noise Type group box shows several parameters associated with the power law noise type based on the B1 or R n Ratio This ratio is used to estimate the Noise type and corresponding Alpha Mu and for normal AVAR Kn values as 197 STABLE32 USER MANUAL described below The a value is the exponent of the S f n
49. Most of the stability analysis functions use the FrequenC Library from Hamilton Technical Services NuMega BoundsChecker 5 03 Visual C Edition was used for debugging The help file was prepared with Help Writer s Assistant from Olson Software Limited and the installation program is InstallShield Express2 from InstallShield Software Corporation Extensive use was made of the mathematical algorithms in Numerical Recipes in C and the Quinn Curtis Science and Engineering Tools library Many of these products as well as Windows from Microsoft Corporation are covered by copyrights and trademarks The Database function uses PostgreSQL an open source client server relational database program Its software tools and documentation are of exceptional quality and are highly recommended Information about PostgreSQL can be found at www postgresql org e History Stable32 began as a set of programs for the HP 85 computer in 1980 When the IBM PC was introduced in 1981 a DOS version of Stable was written for it in 1982 The name besides its obvious implications for frequency stability came from the name of a bar in Nashua NH Its initial application was to support the development of rubidium clocks for the GPS navigation satellites Stable was ported to Microsoft Windows as Stable Win in 1992 and then to its current Stable32 form in 1997 when Windows evolved to 32 bits e Acknowledgments The author wishes to acknowledge the contributions of many collea
50. Notes The averaging factor AF is t to where t is the analysis averaging time and Tp is the basic measurement time The bandwidth factor is 2nf to where fh is the upper cutoff frequency of the measuring system in Hz It applies only to white and flicker PM noise e PSD and Sigma Plots Examples of PSD and sigma plots are shown below FREQUENCY DOMAIN STABIUTY TIME DOMAIN STABILITY Po 2 00e 22 h 2 O0 26 Ci tn 2 00e 22 an La ee a 10 6 t 10 95 N E bd jj 100 Ium i i id d 105 i il 100 Phase Noise L f dBc Hz Allan Deviation 110 B i i d 15 4 101 1290 i 10 3 10 z 103 o3 3 UCM a E E UU Sideband Frequency f Hz Averaging Time 1 moe PSD Plot Sigma Plot 263 STABLE32 USER MANUAL e Caution The domain conversions use simple closed form expressions for the 5 most common power law noise processes and their summation depends on the noise PSD slope decreasing toward higher sideband frequencies Better results may be obtained by numerical integration for real noise data and other expressions are required to handle particular cases such as a filter where the noise slope increases above a certain sideband frequency 264 e Purpose MISCELLANEOUS FUNCTIONS Auto Functions Use one of the Auto functions Autol Auto2 or Auto3 to automate a stability analysis The Auto functions execute automation scripts that describe the steps o
51. RATIS RE 89 OEC nein TO ICE 95 Dead Time uev RERO AURIUM 99 3 Cornered Hats RCRUM RERUM E E Ee Led 101 AutocotrelatiQn 2 reete tret terere er terere e rine tent terree ends 103 Frequency Jump Detecta cidcid 105 FREQUENCY DOMAIN STABILITY Frequency Domain Stability oooonnoninicicnininicnnninnnoncnnocnnnncnnonin coronan coro ron nnoincncanancno 109 RULCEuie Rt 111 Noise DRE 115 Domain Conversions eese tentent nennen 117 FILE FUNCTIONS EL e A a inte A ad 119 iv Filenames Function Open FUN 123 Read Archive Function eet ree ea vl 25 Read Archive Configure iet DG P AEREON SER 127 MiultiCOlunrin Data ecs ssscssvsssecasigssssissertesessesssscettesneseessaveiesedtoves A PSREN EELE RE 29 TABLE OF CONTENTS Add Function 143 Bi sust sE sass te Heri rh eee ie ns ase 145 Database Details eee PR SEN Ec REPRISE 149 Database Configure teet e Re er e OR HC tas 151 READ FUNCTIONS Read Function e E RBRUM AUSSEN CE AE 153 Read Plot Function e ee ERRORES KO ERREUR 8 155 Read Options Function ReadLities Puticti tc d RO E eda 159 Read Notes nc REUNIR 161 EDITING FUNCTIONS Print FUNCION s sci terit ett mie eU eerte dre teres 163 Edit F ticti D esas 165 Find Function ten IRR ROME A 169 Replace Functions NO 171 Convert FUNGON aee ap 173 Normalize Function Average Fun Von oTe a 225 4 erected eerte endete Rue tette e bet EU RE 177 Fill E fiCtlofi ee caneret ER
52. S Naval Observatory Contract No N70092 82 M 0579 1982 291 292 STABLE32 USER MANUAL Gernot M R Winkler Introduction to Robust Statistics and Data Filtering Tutorial at 1993 IEEE Freq Contrl Symp June 1993 Computation and Algorithms W H Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes in C Cambridge Univ Press Cambridge U K 1988 pp 216 217 W J Riley A Test Suite for the Calculation of Time Domain Frequency Stability Proc 1995 IEEE Freg Contrl Symp pp 360 366 June 1995 W J Riley Addendum to a Test Suite for the Calculation of Time Domain Frequency Stability Proc 1996 IEEE Freg Contrl Symp pp 880 881 June 1995 OTHER INFORMATION Example e Example 1 Double click on the Stable32 program group Start the Stable32 program by double clicking on its icon Go to the file open function by clicking on the Open toolbutton Select the frequency data type by clicking on the Frequency Radiobutton Open the SAMPLE DAT file by selecting it and pressing OK Observe the plot and statistics for this data file in the Data File Opened dialog box Close the Data File Opened dialog box by pressing OK BO A A Pi A UL Gg Notice the frequency data file information shown in the status bar at the bottom right of the screen 9 Display the frequency data by clicking on the Edit toolbutton 10 Use the scrollbars to examine the frequency data The Edit function can displa
53. SS ae E 1e12 H P H J B E z H a I 16 13 1 10 100 1000 10000 Tau The following wgnupl32 exe Gnuplot script was used for this stability plot set grid xtics ytics mxtics mytics 2 set nokey set logscale set title Frequency Stability set xlabel Tau set ylabel Sigma set zero le 20 plot sigma tau using 1 3 4 5 with yerrorbars e Detailed Stability Data File A detailed stability data file with a fixed name of STAB dat is also written to disk during each stability plot This file contains values related to the stability analysis with rows corresponding to each averaging factor and 9 columns Tau Analysis Points Minimum Sigma Maximum Sigma Nominal Sigma Standard Deviation Degrees of Freedom Alpha Averaging Factor as shown in the example below au Analy Pts Sigma Min Sigma Max Sigma Std Dev DE S a AF 000000e 000 9 980000e 002 2 921983e 001 2 851183e 001 2 998364e 001 2 885205e 001 7 812477e 002 0 1 000000e 000 4 980000e 002 1 968240e 001 1 898801e 001 2 045945e 001 2 004635e 001 3 556085e 002 0 2 000000e 000 2 480000e 002 1 503423e 001 1 428687e 001 1 591343e 001 1 460858e 001 1 707036e 002 0 4 000000e 000 1 230000e 002 1 052838e 001 9 799809e 002 1 144769e 001 1 004041e 001 8 342483e
54. Start MJD fe1026 00000000 I EndMJD 51078 51041867 e Controls The Read Archive dialog box contains the following controls Control Type Description File Text Archive filename Tau Text Text First MJD Text First MJD in archive file Last MJD Text Last MJD in archive file Channel Group Channel controls Measurement Edit Enter measurement channel Reference Edit Enter reference channel 0 LO reference Time Span Group Time span controls Record Radiobutton Select record time span 125 STABLE32 USER MANUAL Control Type Description Record Edit Enter record to read Last Checkbox Select last record Start MID Radiobutton Select MJD time span Start MJD Edit Enter start MJD End MJD Checkbox Select optional end MJD instead of all data End MJD Edit Enter optional end MJD OK Pushbutton Perform Read Archive amp close Cancel Pushbutton Abort Read Archive function amp close Display Pushbutton Display the archive file Index Pushbutton Show an index of the archive file Configure Pushbutton Configure the Read Archive function Help Pushbutton Invoke the Read Archive help topic e Operation Choose the desired TSC archive file with the Archive option of the Open function Then observe the resulting File Tau and Start MJD Use the Display button to display the contents of the archive file
55. and will be lost if the file is overwritten Unexpected results can occur if two adjacent phase data points are exactly the same This corresponds to zero frequency and can cause anomalies in the resulting stability analysis If converted to frequency data the resulting zero frequency data point will be treated as a gap unless the Adjust Zero Frequency option is activated 19 20 STABLE32 USER MANUAL GENERAL Gaps e Gaps Gaps and outliers can occur in clock data due to problems with the measuring system or the frequency source itself Stable32 includes provisions for handling gaps in phase or frequency data and for finding and removing outliers by replacing them with gaps see the Data Format and Check Function help topics for more details It can accept timetags along with the data and use them in the Regularize function to add gaps as placeholders for missing data The corrected and regularized data can then be analyzed e Gap Handling Stable32 supports four basic methods for handling gaps as described in the table below Stable32 Gap Handling Methods Method Description Use the Edit function or another text editor to omit gaps from the data Omit This eliminates the gaps but also changes the time sequence of the data It is best suited to removing a few isolated gaps Use the Part function to exclude gaps from the beginning or end of the Exclude data or use the analysis limits to exclude the gaps from t
56. based on the B2 and B3 definitions These bias functions depend critically on the power law noise type Requiring manual noise selection avoids the problem of noise identification for biased data having the wrong sigma tau slope Dead time correction is problematic for data having multiple noise types In addition to introducing bias measurement dead time reduces the confidence in the results lowers the maximum allowable averaging factor and prevents proper frequency to phase conversion Moreover no information is available about the behavior of the device under test during the dead time It is recommended that these issues be avoided by making measurements with zero dead time e References J A Barnes Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 January 1969 2 J A Barnes and D A Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 99 STABLE32 USER MANUAL 100 TIME DOMAIN STABILITY 3 Comered Hat e 3 Cornered Hat It is sometimes necessary to separate the noise contributions of the two sources that contribute to a variance measurement Methods exist for doing so by using the results of multiple measurements to estimate the variances of the individual sources Any freguency stability measurement includes noise contributions from both the device under test and the reference I
57. called phase to distinguish them from the independent time variable t Stable32 uses x t and y t arrays as its phase and frequency variables SSB Phase Noise f The SSB phase noise in units of dBc Hz is given by f 10 log S4 f These are the most common engineering units to specify phase noise 111 STABLE32 USER MANUAL e Variances Several types of variance are commonly used to describe the stability of a frequency source Standard Variance O 1 The N sample or standard variance is not recommended as a general purpose measure of frequency stability because it is not convergent for some types of noise commonly found in frequency sources It is used primarily in the calculation of the B1 ratio for noise recognition Allan Variance 0 T The Allan variance is given by o x A u t where t averaging time seconds It is the most common measure of the fluctuations of the fractional frequency y t v t vo vo Av vo x t It may be calculated by the non overlapping or overlapping method Modified Allan Variance Mod 6 1 The modified Allan variance employs phase averaging and is given by Mod 0 t B u t where p a 1 Total Allan Variance O q 1 The total Allan variance 1s similar to the Allan variance but uses a doubly reflected method that improves its statistical confidence at large averaging factors Total Modified Allan Variance Mod O ota t The total modified Allan variance is si
58. characters 4 Lines that have a non numeric character at the first character after nSkipChar characters are skipped where nSkipChar is set by the Non Numerics to Skip item on the Data tab of the Configuration property sheet e Notes Stable32 timetags are numeric only The preferred timetag format is the Modified Julian Date number MJD Other common timetag formats include the ordinal line number or another count of some sort Calendar dates cannot be used although several Stable32 functions have provisions for displaying MJD dates in various calendar date formats Stable32 divides each row of a data file into columns on the basis of multiple field delimiters generating a parsed row having only space delimiters The active delimiters are shown in the Delimiter section of the Multicolumn Details screen they always include spaces tabs and bars Commas are also field delimiters unless European comma decimal points are selected in the Data tab of the Configure property sheet Slashes and colons are changed to zeros in order to convert common date and time formats to crude numeric form Blank lines are skipped and only data file lines with numeric characters are read Leading whitespace is ignored and a selected number of non numeric leading characters may also be skipped as set by the Non Numerics to Skip value in the Data tab of the Configuration property sheet Then if the next character is numeric the rest of the row is parsed for column
59. confidence at long averaging times It uses the same phase averaging technique as MVAR to distinguish between white and flicker PM noise processes A TOTMVAR calculation as described in the reference below begins with an array of N phase data points time deviates x with sampling period t which are to be analyzed at averaging time t mty TOTMVAR is computed from a set of N 3m 1 subsequences of 3m points First a linear trend frequency offset is removed from the subsequence by averaging the first and last halves of the subsequence and dividing by half the interval Then the offset removed subsequence is extended at both ends by uninverted even reflection Next the modified Allan variance is computed for these 9m points Finally these steps are repeated for each of the N 3m 1 subsequences calculating TOTMVAR as their overall average These steps are shown in the diagram below Phase Data x i 1 to N lt 3m gt N 3m 1 Subsequences eee X eee i n to n 3m 1 Linear Trend Removed x X X C c freq offset 9m gt Extended Subseguence 0 _0 PE 0 0 3 Xu 7 Xa X Xwamda T Xaram 1 lt 1 lt 3m Uninverted Even Reflection ecc LN A 9 m Point Averages 6m 2nd Differences p Lr 3 mod o 1 1 2 z m where Calculate Mod 6 t for Subsequence E z m x m 2Xpsm M Xp 2m M Computationally the TO
60. data 1 The first is a least squares quadratic fit to the phase data x t a bt ct where y t x t b 2ct slope y t 2c This method is optimum for white PM noise It is the default and is also the method used for drift analysis when plotting phase data 2 The second method is the average of the 2nd differences of the phase data y t x t t x t t slope y t t y t 7 27 2x t 1 x t 1 This method is optimum for random walk FM noise 3 The third method uses the 3 points at the start middle and end of the phase data slope 4 x end 2x mid x start Mt where M data points It is the equivalent of the bisection method for frequency data Frequency offset may be calculated in phase data by either of three methods 1 The first optimum for white PM noise uses a least squares linear fit to the phase data x t a bt where slope y t b 2 The second method optimum for white FM noise uses the average of the first differences of the phase data y t slope x t t x t t 3 The third method simply uses the difference between the first and last points of the phase data slope y t x end x start M 1 where M phase data points This method is used mainly to match the two endpoints 193 STABLE32 USER MANUAL Frequency Data Four drift methods are also available for frequency data 1 The first the default is a leas
61. data file is read Set this parameter to a value appropriate to your computer s speed and RAM With the Average option there is essentially no limit to the size of the data file that can be read 136 FILE FUNCTIONS Data File Opened e Purpose The Data File Opened dialog box confirms the opening of a phase or frequency data file It displays the name and size of the file the of gaps and the maximum and minimum values of the data This dialog box also shows the first line of the selected file column s and a simple plot of the data Data File DataFileOpened 00900000 Filename PHASE DAT Data Type Phase Points 1001 Gaps Maximum 4 3565286198918e 00 Minimum 4 7078794262138e 00 Timetag Column Data Column From INI File Input Inputs Enter Tau 0 value for data Hel and press OK to continue 2 None pein Display Tau l 1 000008 01 In Scale Date e Controls Besides displaying information about the data file that has just been opened the Data File Opened dialog box contains the following controls Control Type Description Tau Edit Enter measurement interval for data OK Pushbutton Accept tau value and close dialog box Display Pushbutton Display data as text in Notepad Inputs Pushbutton Open Inputs dialog box Help Pushbutton Invoke the Data File Opened help topic e Operation Observe the properties of the data file that has bee
62. data point O last point 0 325 STABLE32 USER MANUAL e Audio The Audio section of the STABLE32 INI file can contain the following parameters Keyword Description Default Audio Player Path and filename of audio player program None SampleRate Playback sample rate samples sec 11025 e Run The Run section of the STABLE32 INI file can contain the following parameters Keyword Description Default NormalTime Run calc time estimate coefficient for Allan variance 2 5e 6 OverlappingTime Run calc time est coeff for overlapping Allan variance 2 5e 6 BothTime Run calc time est coeff for normal amp overlapAllan var 2 5e 6 ModifiedTime Run calc time est coeff for modified Allan variance 2 5e 6 TimeTime Run calc time estimate coeff for time variance 2 5e 6 TotalTime Run calc time estimate coeff for total variance 2 5e 6 HadamardTime Run calc time estimate coeff for Hadamard variance 2 5e 6 OverlapHadTime Run calc time est coeff for overlapping Hadamard var 2 5e 6 TIErmsTime Run calculation time estimated coefficient for TIE rms 2 5e 6 ModTotalTime Run calc time estmate coeff for modified total variance 1 5e 7 TimeTotalTime Run calc time estimate coeff for time total variance 1 5e 7 HadTotalTime Run calc time est coeff for Hadamard total variance 1 5e 7 Theol Time Run calculation time estimate coefficient for Th ol 2 0e 4 TheoHTime Run calculation time estimate c
63. e Pot SubTile 2 PHASE DAT e Close Message 3 TE ng Help Message Position Top Ler x ptions E Read Config Save Config Reset All Carrier Freg Hz 1 0000000e 07 Plot File C Program Files DevStudio MyProjects Sta Axis YAris Label Fourier Frequency f Hz PSD Type Jun dBc Hz y Phase Noise LIf dBc Hz FFT Points 1024 Window Type Hamming y Windowings 1 tt PSD Points 512 AvgFadod y PSD StdDev 1000 Fourier Interval Hz 9 7656e 04 psp Max Press Plot ESO Scale Max Max Fourier Freq Hz 5 0000e 01 pop Min ffoCale SCHEME PSD File C Program FilestDewSt T Smooth Max AF Ise r Options M Date M Box Cursor M Fit 5 itta ee v Points v Info Wide jpurs From Data 7 Enter settings S and press Plot www for PSD plot e Controls The Power dialog box contains the following controls Control Type Description Plot Pushbutton Plot power spectrum Title 1 Combo Edit or select plot title SubTitle 2 Combo Edit or select plot subtitle Message 3 Combo Edit or select plot message Position List Select message position Options 8 Pushbutton Open Options page of Configure property sheet Read Config Pushbutton Read configuration data from INI file Save Config Pushbutton Save configuration data to INI file Carrier Freq Edit Enter carrier frequency in MHz
64. is accomplished by highlighting a data point with the left mouse button or moving to it with the up or down arrow keys A new value such as 0 for a gap can then be inserted with a numeric key or the existing value can be edited by pressing the F2 key which will activate the EDIT MODE annunciator Timetag values are not editable e Controls The Edit dialog box contains the following controls Control Type Description Go To Group Go To controls Point Pushbutton Go to selected point Number Edit Enter point to go to Find Group Find controls Gap Pushbutton Find gap Prev Radiobutton Find previous occurrence Next Radiobutton Find next occurrence Outlier Pushbutton Find outlier 165 1 00000000 2 00000000 3 00000000 4 00000000 5 00000000 6 00000000 7 00000000 8 00000000 3 00000000 10 00000000 11 00000000 12 00000000 13 00000000 14 00000000 15 00000000 16 00000000 17 00000000 18 00000000 Timetag Format 8 5116010334397e 02 2 2047548258606e 0 1 4707417985148e 0 3 4175630294613e 0 2 1457633784021e 01 5 5127998572089e 01 3 7986709938518e 0 2 9386363828828e 0 6 8407016576504e 0 7 3555465081034e 0 8 8567199031108e 01 7 5817416248199e 01 7 5255902203245e 01 1 2292706697040e 00 1 1723102679510e 0 6 8921518932712e 01 1 1606059406016e 0 STABLE32 USER MANUAL m GoTo Point Number po Find Gap C Prev Next Outlier 2 r
65. jump in data The CUSUM plot for a data set having a single jump has a V or inverted V shape as seen in the plot insets above The value of the jump can be determined by the sum of the two slopes of the CUSUM curve For N data points having a cumulative sum frequency jump is equal to M M N P e References maximum or minimum value M at point P the CUSUM Slope M P 1 Slope M N P P Data Point WJ Riley Frequency Jump Detection in Stable32 Hamilton Technical Services 2 W A Taylor Change Point Analysis A Powerful New Tool for Detecting Changes Taylor Enterprises Inc 108 FREQUENCY DOMAIN STABILITY Frequency Domain Stability e Frequency Domain Stability Stable32 uses the following frequency domain measures of frequency stability Formula Units Description S f 1 Hz PSD of fractional frequency fluctuations SH sec Hz PSD of time fluctuations Sof rad Hz PSD of phase fluctuations f dBc Hz SSB phase noise to carrier power ratio where PSD Power Spectral Density SSB Single Sideband dBc Decibels with respect to carrier power The most common frequency domain stability measure is f dBc Hz the SSB phase noise to signal ratio in a 1 Hz BW as a function of sideband frequency f Other frequency domain stability measures are Sy f 1 Hz the power spectral density of the fractional frequency fluctuations S f sec Hz the power
66. label use the character sequence tE This will shift to the Greek math symbol set of the Newsgrm font changing the character t to a t and then return to the normal News font Lower case Greek letters are entered with the characters a through z in a fashion similar to the Windows Symbol set The News font is defined for codes between 33 and 199 while the Newsgrm font for 33 to 146 The News Swiss Newsgrm and Simplex fonts are shown in the tables on the following pages news fnt 3 ls Zier Cla Tim eln Viis C 152 y es 186 lo 3168 Dia U 102 fin w 15 Gc 70 187 i 35 2 46 Els Vo gv X 17 6 154 U 71 188 i s us 5 FlsWio hio Y 138 s Em A 189 7 5 6 n Gla Klis 1122 Zigo Y s 0 j 190 Us 72 His Y j 23 i 15 X m E 191 3 l 8173 Ew Zw Ki lw 1 Olr 192 5 9 Ja 108 l 25 42 A 159 f 76 ws U 58 75 Kio Mio mM in 43 10 m lis 2 59 gt 76 Lo o Mn 127 44 1 E 195 Y To I M Alin olw C 45 Q8 i mo i ws D 4 sie 57 No m pi us AB e 180 Ce 197 45 le gt 71 Ole nm q 130 lu lis Ali E 58 e ls Plo alum ru lus lis N 82 199 e 7 64 81 Q e Dim S 12 us w 183 amp Ole Ala Riso Cl tle s ls ss Blas Siwo d v uj s 18 85 N ews Font Numeric Code 0200 310 APPENDICES swiss fnt O co JO GI A CQ Iw o 9 wv Glis Vis
67. leave gaps unfilled 179 STABLE32 USER MANUAL 180 EDITING FUNCTIONS Scale Function e Purpose Use the Scale function to modify the selected phase or frequency data by an additive or multiplicative factor by adding a linear slope or by reversing the data OK Cancel Remove 1st Value Average Line Reverse Scaling Factors Addend Multiplier 1 0000000000000e 00 0 0000000000000e 00 0 0000000000000e 00 Slope Press OK to modify data by an additive or multiplicative factor or by adding a linear slope Or press Reverse to reverse order of data X e Controls The Scale dialog box contains the following controls Control Type Description Addend Edit Enter addend default 0 Multiplier Edit Enter multiplier default 1 Slope Edit Enter slope per t interval default 0 Remove Group Insert values to be removed from data 1st Value Pushbutton Insert 1st value into Addend Average Pushbutton Insert average value into Addend Line Pushbutton Insert linear slope value into Slope Reverse Pushbutton Reverse order of phase or frequency data OK Pushbutton Perform the Scale function amp close dialog box Cancel Pushbutton Abort the Scale function amp close dialog box Help Pushbutton Invoke the Scale help topic e Operation Enter the value of the Addend Multiplier and or Slope to be adde
68. linear fit by subtracting a line determined by the first differences or by calculating the drift from the difference between the two halves of the data The latter called the bisection drift is equivalent to the 3 point fit for phase data Other more specialized log and diffusion models may also be used The latter are particularly useful to describe the stabilization of a frequency source In general the objective is to remove as much of the deterministic behavior as possible obtaining random residuals for subsequent noise analysis 299 STABLE32 USER MANUAL A summary of commonly used preprocessing operations for frequency stability analysis is shown in the following table Preprocessing Operations for Frequency Stability Analysis What Why How Remarks Read Data Read data into Stable32 Use Read function Timetagged phase data for analysis recommended Add Data Concatenate two or more Use the Add function The new data is appended at data files into a longer the end of the existing data record Inspect Data Get an intuitive feel for Observe the data Make sure that the data type the character of the data visually as it is read in phase or frequency is Plan preprocessing and the status plots or with correct analysis the Stats function Inspect it with the Edit function Set Tau Tau must set to obtain The tau value can be It is a good idea to adopt the the correct data plot time preset automatically
69. people have contributed to the development of Stable32 reporting problems and offering ideas for new features Some of those persons are as follows Jim Barnes Dave Allan and Dave Howe for the statistical foundations Sam Stein for suggesting the GraphiC library Ed Powers for early evaluation and suggestions Ken Lyon for user interface suggestions Gernot Winkler for pratical robust statistics Todd Walter for power law noise generation Steve Kelley for GraphiC support Dave Howe for total statistics Trudi Peppler for programming collaboration Chuck Greenhall for many contributions related to edf Jack Kusters for the TDEV loci on MDEV plots Paul Koppang for suggesting the 1 of 2 option Paul Koppang and Chris Ekstrom for the 3 cornered hat edf Robert Lutwak for many many suggestions including the automation feature Ken Senior for careful checking of the Sigma and Run results Patrizia Tavella for unequally spaced data suggestions and dynamic stability analysis Tom Becker for user interface bug reports Tom Parker Doug Hogarth and John Hartnett for bug reports Richard Hambly and Tom Clark for suggesting Excel date compatibility Tom Van Baak for the many tau idea Dave Howe and Tiffany Tasset for Th ol Th BR and Th oH Nino De Falcis for suggesting the stability plot masks Robert Lutwak for suggesting the weighted stability plot noise fits Ryan Dupuis for supporting the Database function and many helpful s
70. points Multiplier Edit Factor to multiply data points by Tag Scale Edit Factor to multiply timetag values by Tag Offset Edit Value to add to timetags Options Page Controls The Options property sheet page contains the following controls Control Type Description Auto AF Params Groupbox Parameters for Auto AF PSD calculation Relative Max AF Edit Relative maximum averaging factor Absolute Max AF Edit Absolute maximum averaging factor LF Pts To Skip Edit of low Fourier freq PSD points to skip Smooth Params Groupbox Parameters for smoothing of PSD plot Weight Smoothed Checkbox Weight semilog power law smoothed PSD fit Smoothing PPO Edit points octave for smoothed PSD plot PSD Zero Padding Checkbox Use zero padding in PSD FFT calculations Spur Threshold Edit Enter PSD discrete component detection threshold dB Stability Plot Groupbox Parameters for stability plots Many Tau Checkbox Use many tau method for all tau plots Size Edit of many tau points Reset PSD Pushbutton Restore PSD default values Reset Many Tau Pushbutton Restore many tau default size e Audio Page Controls The Audio property sheet page contains the following controls Control Type Description WAV File Params Groupbox Parameters for playing WAV files Audio Player Edit Enter full path to audio player program Sampling Rate List Select samp
71. position of the note Notes Text Notes entered Border Checkbox Draw a border around the note Opaque Checkbox Hide grid in note area Read Pushbutton Read note info from INI file Save Pushbutton Save note info to INI file Clear All Pushbutton Clear all notes OK Pushbutton Accept the settings amp close dialog box Cancel Pushbutton Abort the changes amp close dialog box Help Pushbutton Invoke this help topic e Operation Enter the desired plot annotations and press OK to accept them or Cancel to abort Select the Border and Opaque options as desired Press Clear All to clear all annotations or use the Read and Save buttons to retrieve and store note information The X and Y positions are in user units that are the same as the plot scales 227 STABLE32 USER MANUAL 228 ANALYSIS FUNCTIONS Timetags Function e Purpose Use the Timetags function to generate regular timetags for evenly spaced data Such timetags can be useful for examining and editing data especially if the starting time is known Timetags are generated for the entire data array regardless of the analysis limits Data Type Start 1 00000000e 00 OK Phase Not Applicable increment C Frequency Units Help Seconds Tau C Days Tau 86400 Press OKto generate C Other Enter Increment timetag data e Controls The Timetags dialog box co
72. random frequency data points It is produced by the following prime modulus linear congruential random number generator n 16807 n Mod 2147483647 This expression produces a series of pseudo random integers ranging in value from 0 to 2147483646 the prime modulus 2 1 avoids a collapse to zero When started with the seed n0 1234567890 it produces the sequence n 395529916 n 1209410747 n3 633705974 etc These numbers may be divided by 2147483647 to obtain a set of normalized floating point test data ranging from 0 to 1 Thus the normalized value of ny is 0 5748904732 A spreadsheet program is a convenient and reasonably universal way to generate this data The frequency data set may be converted to phase data by assuming an averaging time of 1 yielding a set of 1001 phase data points Similarly frequency offset and or drift terms may be added to the data These conversions can also be done by a spreadsheet program The values of this data set will be uniformly distributed between 0 and 1 While a data set with a normal Gaussian distribution would be more realistic and could be produced by summing a number of independent uniformly distributed data sets or by the Box Muller method 24 this simpler data set is adequate for software validation 296 OTHER INFORMATION Table III 1000 Point Frequency Data Set Averaging Factor 1 10 100 Data Points 1000 100 10 Maximum 9 957453e 01 7 003371e 01 5
73. ratio of the SSB phase noise power in a 1 Hz BW to the total carrier power dBc Hz The Modified Julian Date is based on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 A modified version of the Allan or total variance that uses phase averaging to distinguish between white and flicker PM noise processes The maximum time interval error of a clock 281 Normalize Phase Data Phase Noise Sampling Time Sigma Slope SSB Sf S f Sy f Tau Total Th o1 Th oBR Th oH TIE 282 STABLE32 USER MANUAL To remove the average value from phase or frequency data A set of time deviates x i with units of seconds where 1 denotes equally spaced time samples Called phase data to distinguish them from the independent time variable The spectral density of the phase deviations See Tau The square root or deviation of a variance often the 2 sample or Allan deviation 6 t The change in frequency per tau interval Single sideband The one sided spectral density of the phase deviations rad Hz The one sided spectral density of the time deviations sec Hz The one sided spectral density of the fractional frequency deviations 1 Hz The interval between phase measurements or the averaging time used for a frequency measurement An analysis technique using an extended data set that provides better confidence at long
74. respectively where the index i refers to data points equally spaced in time These usually contain equivalent data and conversions between them are provided The x values have units of time in seconds and the y values are dimensionless fractional frequency Af f The x t time fluctuations are related to the phase fluctuations by t x t 2nvo where vo is the carrier frequency in Hz Both are commonly called phase to distinguish them from the independent time variable t The data sampling or measurement interval ty has units of seconds It is called tau in many of the dialog boxes The analysis or averaging time 1 may be a multiple of to t mto where m is the averaging factor If units other than seconds are used for tau some of the results such as the FFT Fourier frequency scale will not be correct In addition there are corresponding phase and frequency timetag arrays These optional arrays are useful for data editing but are not needed for analysis STABLE32 USER MANUAL e Results Display Results are displayed in static edge text controls e Parameter Entry Parameter entries are made in edit controls denoted by boxes Default values are offered for most entries and these often provide the desired result Entry error trapping is done either by correcting the value or displaying a dialog box showing the allowable range The program then restores the previous value and positions the caret in the field for editing
75. setting the Control Type Description Plot Pushbutton Plot the current phase or frequency data Options Pushbutton Select plot options Lines Pushbutton Add lines to the plot Notes Pushbutton Add notes to the plot Close Pushbutton Close the Plot dialog box Help Pushbutton Invoke this help topic AutoPlot item in the Configure function 213 STABLE32 USER MANUAL 214 ANALYSIS FUNCTIONS Data Plot Function e Purpose Use the Data Plot function to generate a plot of the current phase or frequency data E GraphiC Win phase tkf Eile Edit Draw Convert Help Dae 02 77 30 me 700 35 Dolo Palms 1 thru 1007 of 0 Toe 1 0001000e 00 Fhe ohosedal PHASE DATA 5 00 A 448 660 Data Point 215 STABLE32 USER MANUAL 216 ANALYSIS FUNCTIONS Plot Options Function e Purpose Use the Plot Options function to control the attributes of the data plot Phase Plot Options x Title PHASE DATA y OK SubTite PHASE DAT A Cancel Message Help Position Axis Top Left E Read 1 Save 2 Beset All p Y Axis Label Data Poit y F Keep8 Offset 0 00000e 00 X Divs Offset Multiplier 1 00000e 00 TEN st End4 1001 Label Phase Seconds gt o o0000e 00 Multiplier fi 00000e 00 Data Max 4 35653e 00 Scale Max 4 500002 00 Options Type None No Lines Iv Date V Box5 W Fte F Wide Cur Plot File c pro
76. stability run contains the following items Item Description AF Averaging factor t to Tau Averaging time t analysis points Alpha Estimated or selected noise exponent a Min Sigma Lower confidence limit as applicable Sigma Nominal sigma Max Sigma Upper confidence limit as applicable e Stability Results Plot Use the Plot button along with the Options Lines and Notes functions to plot the results of a stability run Many aspects of the plot can be customized as desired The individual stability points of a run are indicated by closed normal or open modified circles which are automatically made smaller when the number of points exceeds 100 e g an all tau run 239 STABLE32 USER MANUAL e Drift Removal The Run function allows linear frequency drift to be removed from phase or frequency data before performing the stability analysis Simply check the No Drift checkbox The drift day will be reported but the original phase or frequency data is not changed e 1of2 Scaling The Run function allows scaling the results for one of two identical units Simply check the 1 of 2 checkbox to scale the resulting sigma values by V2 e Dead Time Bias correction for measurement dead time Dead_Time is available for the normal and overlapping Allan variances when the noise type is manually selected Enter the T Tau dead time ratio where tau is the measurement time and T is the time between measur
77. that can be read is set by the Max Data File Size item in the Configure function The purpose of this setting is to automatically activate the data averaging dialog box when a large data file is read Set this parameter to a value appropriate to your computer s speed and RAM The Stats Edit and Check functions can be very slow when processing frequency data having many repeated values This is because of the gsort function used in finding the median value One way to work around this problem is to add a very small slope to the data with the Scale function in order to eliminate exactly identical data points Convenience Features Use the Inputs section of the STABLE32 INI configuration file to automatically set the tau and scale factor you use most often Use the stored text in the plot options drop down combo controls to avoid having to reenter labels between plots Use the Save and Read buttons to store and recall complete plot configurations Associate the dat filename extension with the Stable32 program to automatically launch it by clicking on a data file with the Open command on the Explorer File menu or by dragging the data to the Stable32 icon on the desktop Use the Copy command of the Drift Sigma Run and Domain functions to write their results to the clipboard The File Opened dialog box can be eliminated with the Show File Opened configuration item to speed data file entry APPENDICES Batch Files The WinBatch batch lan
78. the upper cutoff frequency in Hz It then calculates o t and Mod o t and uses their ratio to estimate the noise type This function then continues with the determination of single or double sided confidence intervals for the modified Allan deviation for the estimated noise type and desired confidence factor e Time Variance The time variance is a measure of time stability based on the modified Allan variance e Hadamard Variance The non overlapping Hadamard variance uses 3 rather than 2 fractional frequency samples which allows it to converge for a 3 Flicker Walk FM and a 4 Random Run FM noises and causes it to be unaffected by linear frequency drift e Overlapping Hadamard Variance The overlapping Hadamard variance uses fully overlapping samples to calculate the Hadamard variance e Total Allan Variance The total variance uses a double reflection method to form a o t estimate with better confidence at long averaging times e Total Modified Variance The total modified variance also uses a double reflection method to form a mod o t estimate with better confidence at long averaging times e Total Time Variance The total time variance is a measure of time stability based on the total modified variance 198 ANALYSIS FUNCTIONS e TIE rms The rms time interval error TIE rms is the rms value of the time deviations It can be calculated for phase data only e MTIE The maximum time interval error MTIE is ma
79. this help topic In addition the right amp left arrow keys will move the focus up and down through the pushbuttons and the spacebar can be used to press them e Operation Begin by selecting the Reference and Measurement clocks which will display their descriptions and load their measurement records into the tables under their names Then select the desired reference and measurement clock Records Measurement clock records shown in red are from a different MMS system than the reference record and cannot be read The time format for the start and end time in the clock records table can be chosen as a UTC timestamp or MJD Details about the clock database records can be displayed with the Details button Measurement record pairs without overlapping time spans cannot be read The Start and End times of measurement record pairs with overlapping time spans will be shown in the Read Times section along with their time Span and of data points Records that are continuing are denoted by Run Continuing and if both records are continuing the end time will be the current time Enter the desired AF averaging factor for the read data Then press Read to read the selected data from the MMS database and write it to a file The read operation can take a considerable time if the span is long and or the database connection is slow and can be aborted with the Abort button during a read The data read prior to the abort is valid and may be analyzed by any
80. to adjust an awkward x axis scale It is common to adjust the y axis Multiplier e g 1e 12 when the units e g pp10 are changed When this done for frequency data entering a pp10 label automatically adjusts the multiplier value The plot options when accepted with OK stick between dialog box openings User entered titles subtitles and messages are pushed onto their respective list boxes with a CR Tab or other focus change Up to six such options are automatically saved recalled and linked between the various plot option dialog boxes The plot options may be saved and recalled in the STABLE32 INI configuration file between program runs with the Save Config and Read 218 ANALYSIS FUNCTIONS Config buttons These configuration data contain additional parameters such as axis labels nd scale factors for each plot type The configuration file is read and saved automatically if the corresponding box is checked in the Configure dialog box The Keep box may be checked to retain the x axis settings for future plots When using the default directory new Stable32 GraphiC plot files PHASE TKF FREQ TKF SPECTRUM TKF and HISTO TKF will overwrite the previous ones If it is desired to keep one of these files it is important to rename it either from within the corresponding dialog box before plotting or manually from the command line after the plotting operation Plot files may also be sent to another directory by changing the Plot Filename o
81. track of changes and avoid overwriting previous data It is controlled by the Autoinc Filename Ext checkbox of the Configure function The filename of the current phase or frequency data file can be changed by editing it directly in the corresponding edit control of the status bar at the bottom of the screen e Plot Filenames A TKF plot file in Tektronix 4105 format is automatically written to the current disk directory after each plot The default names for these files are PHASE TKF FREQ TKF SIGMA TKF DAVAR TKF SPECTRUM TKF AUTO TKF and HISTO TKF for phase data frequency data stability dynamic stability power spectrum and histogram plots respectively These filenames may be changed as an option within their respective Plot Options functions A name of NOTEK will suppress the writing of the TKF file e Stability Filenames A stability file is optionally written to the current disk directory at the end of each stability run This file contains a table of averaging time of analysis points and minimum nominal and maximum sigma information that can be printed or re plotted with the Read function The default stability filename is SIGMA TAU which may be changed in the Run Options dialog box This file is particularly useful to combine with other such files to create a composite stability plot for multiple runs using data over a wide range of averaging times Writing of the stability file is controlled by the Write Sigma File checkbox of t
82. 0 07 2 10 2 Overlapping Allan Deviation 100 e gt 1 2 10 2 103 Averaging Time m Seconds 3 02187882 01 Slap Go to the Convert function and convert the frequency data into the corresponding phase data Notice that the status bar now shows a 513 point SAMPLE 004 phase data file Repeat some of the analysis and plotting functions with the phase data Try other Stable32 functions as desired Generate and analyze some simulated clock noise Try other plot options Try the domain conversions or generate and use timetags Use the context sensitive Help button as needed OTHER INFORMATION Test Suite e Test Suite The following tables summarize the values for several common frequency stability measures for both the classic NBS data set and a 1000 point portable test suite e NBS Data Set A classic suite of frequency stability test data is the set of nine 3 digit numbers from Annex 8 E of NBS Monograph 140 shown in Table I Those numbers were used as an early example of an Allan variance calculation This frequency data is also normalized to zero mean by subtracting the average value and then integrated to obtain phase values A listing of the properties of this data set is shown in Table II While nine data points are not sufficient to calculate large frequency averages they are nevertheless a very useful starting point to verify frequency stability calculations si
83. 07e 02 3 691e 02 9 710e 00 The stability file items for the Both sigma case are Tau Std Dev Sigma Mod Sigma and DF No DF information is available for Normal and Hadamard variances or for MTIE and TIErms and the DF value is set to zero The stability file contains no header or other text It is comprised of space delimited columns of ASCII characters in any numeric format Examine the files written by the Run function for more examples These stability files may be edited and combined as required to produce a composite stability plot The Tau values should be in numerical order The TIE rms and MTIE stability files do not contain Min amp Max Sigma or DF columns The Th oH stability file has a format comprising the columns Tau Sigma Th oBR Sigma Min and Sigma Max where Tau is the ADEV tau Sigma is the AVAR value Th oBR is the bias corrected Th ol value and Sigma Min amp Sigma Max are the error bars for either ADEV or Th oBR e Multiple Data Sets The Stable32 Read function includes provisions for reading and plotting multiple sets of stability data A new data set is started whenever the tau value is less than the previous one The points between multiple data sets are not connected Multiple data sets are plotted with up to five different symbols The first symbol is a circle e followed by a down triangle v diamond 4 up triangle and square M and they repeat thereafter The symbols are filled for normal variances
84. 1102 1110 Sept 2000 D A Howe and T K Peppler Definitions of Total Estimators of Common Time Domain Variances Proc 2001 Freq Cont Symp pp 127 132 June 2001 Modified Total Variance D A Howe and F Vernotte Generalization of the Total Variance Approach to the Modified Allan Variance Proc 31st PTTI Meeting pp 267 276 Dec 1999 Time Total Variance M A Weiss and D A Howe Total TDEV Proc 1998 IEEE Freq Cont Symp pp 192 198 June 1998 Total Hadamard Variance D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proc 32nd PTTI Meeting pp 255 268 Nov 2000 D A Howe R L Beard C A Greenhall F Vernotte W J Riley and T K Peppler Enhancements to GPS Operations and Clock Evaluations Using a Total Hadamard Deviation JEEE Trans UFFC Vol 52 No 8 Aug 2005 Th o1 Th oBR and Th oH D A Howe and T K Peppler Very Long Term Frequency Stability Estimation Using a Special Purpose Statistic Proc 2003 IEEE Freq Cont Symp pp 233 238 May 2003 T N Tasset and D A Howe A Practical Th ol Algorithm Unpublished private communication October 2003 D A Howe and T N Tasset Th ol Characterization of Very Long term Frequency Stability Proc 18th European Frequency and Time Forum April 2004 T N Tasset Th oH Unpublished private communication July 2004 T N Tassert D A Howe and D B Percival T
85. 2 Averaging Time v Seconds e References N J Kasdin and T Walter Discrete Simulation of Power Law Noise Proceedings of the 1992 IEEE Frequency Control Symposium pp 274 283 May 1992 2 C A Greenhall FFT Based Methods for Simulating Flicker FM Proceedings of the 34th Annual Precise Time and Time Interval PTTI Systems and Applications Meeting December 2002 pp 481 492 233 STABLE32 USER MANUAL 234 ANALYSIS FUNCTIONS Clear Function e Purpose Use the Clear function to clear phase or frequency data or the corresponding timetags Note It is not necessary to clear the data array before reading another data file Data To Clear Iv Phase Data Iv Phase Timetags Frequency Data MEregteneiimetede Y Press OK to clear selected data Controls The Clear dialog box contains the following controls Control Type Description Data To Clear Groupbox Choices for data to clear Phase Data Checkbox Clear phase data Phase Timetags Checkbox Clear phase timetags Freq Data Checkbox Clear frequency data Freq Timetags Checkbox Clear frequency timetags OK Pushbutton Perform the Clear function close dialog box Cancel Pushbutton Abort the Clear function close dialog box Help Pushbutton Invoke this help topic e Operation Select the Phase Data Phase Timetags Frequency Data or Frequency Timetags to be cleared Then press OK to clea
86. 9326320000000e 01 of multicolumn 12 2008 03 12 2008003012 2 00800301 2000000e 09 data optionally 13 08 35 08035 8 035000000000000e 03 set timetag 14 21 6963100 21 6963100 2 169631 000000000e 01 columns and 15 324 124 1 240000000000000e 02 then press Close 16 6093933 6093933 6 093933000000000e 06 to continue Parse Date and Time Help Date Column 3 y Date Format YYYY MM DD Y Date 2008 03 12 08 35 55 FREIE Opy Time Column ENN Time Format HH MM v MJD 54537 3576389 Close e Controls The Multicolumn Details dialog box contains the following controls Control Type Description Line Group Line selection section First Radiobutton Show information for first active line Last Radiobutton Show information for last active line File Group Filename of file being read Display Pushbutton Display data file in Notepad or other text editor None Text Number of file columns rows and rejected rows Table heading and brief operating instructions None Table File columns as raw parsed and numeric values Delimiters Group List of current field delimiters 131 STABLE32 USER MANUAL Control Type Description Decimal Point Group Current decimal point symbol Parse Date and Time Group Controls for date and time MJD conversion Date Column Combo Select date column Time Column Combo Select time column Date Format Combo Select d
87. A i e eder e Re A Support MEM A A A ed dei ederet e e pde a a Tal Setting AER 12 29 33 TUI 295 Time Domain Stability sere reiteeni ini enne eene trennen ener enne a E 59 Time Variance D EP 67 198 Timetag Types T 29 174 A SS 29 229 STABLE32 USER MANUAL Timetags Function ba ce eb tdt 229 Timing Solutions Corporation TSC sess 25 125 TKF Plot Files Xs Toolbars diet Total Visas tt ege egeta dep e ge e egeta 59 69 U Usada eae series ka M Maal p M M MU 7 V Validation s eate atte Ge teo ete Ue a e tede eatis 303 Variances ax 112 Vibra Function 0 273 WILE A iii A ii 256 W WebSite a tbe hie c bee rb de ode ee ta deba i de o rib eb ghee 2 Weigh ng cin ARE enm eee UP DE d eR ena ads teles 250 WinBatch aae iiiter eter st pen be de ea de ve C dete eo pt cred 35 328 Windows Metatiles wtf ii OR Ae a etie ege RI e rei eerte 327 X x Phase Data iino ocndae tee bam cnt A de b ttd 7 y Brequency Dit A E E atta aoe ean 7 Z LO AA ENON a aia 19 YA GRIPE 175 338 INDEX Salvador Dali 1931 The Persistence of Memory 339 STABLE32 USER MANUAL 340
88. ABLE32 USER MANUAL M A Weiss and C Hackman Confidence on the Three Point Estimator of Frequency Drift Proc 24th PTTI Meeting pp 451 460 Dec 1992 G Wei Estimations of Frequency and its Drift Rate EEE Trans Instrum Meas Vol 46 No 1 pp 79 82 Feb 1997 C A Greenhall A Frequency Drift Estimator and Its Removal from Modified Allan Variance Proc 1997 IEEE Freq Contrl Symp pp 428 432 June 1997 F Vernotte and M Vincent Estimation of the Measurement Uncertainty of Drift Coefficients Versus the Noise Levels Proc 12th European Freg and Time Forum pp 222 227 March 1998 Noise Identification J A Barnes The Generation and Recognition of Flicker Noise NBS Report 9284 U S Department of Commerce National Bureau of Standards June 1967 J A Barnes Effective Stationarity and Power Law Spectral Densities NBS Frequency Time Seminar Preprint Feb 1968 J A Barnes and D W Allan Recognition and Classification of LF Divergent Noise Processes NBS Division 253 Class Notes circa 1970 J A Barnes Models for the Interpretation of Frequency Stability Measurements NBS Technical Note 683 U S Department of Commerce National Bureau of Standards Aug 1976 C A Greenhall and J A Barnes Large Sample Simulation of Flicker Noise Proc 19th PTTI Meeting pp 203 217 Dec 1987 and Proc 24th Annu PTTI Meeting p 461 Dec 1992 D Howe R Beard C Greenhall F Vernotte and W R
89. C HVAR MMA TC E Window Size 100 L r Options Left Right Step Size fi 0 Y Date Gata Reverse 1 Down Enter Settings choose Variance amp Windows gi v Box Grid 1 D Options and set Views Then press Plotfor DAVAR plot e Controls The Dynamic Stability dialog box contains the following controls Control Type Description Plot Pushbutton Plot dynamic stability Title Combo Enter or select plot title SubTitle Combo Enter or select plot subtitle Message Combo Enter or select plot message Msg Position List Select message location on plot Read Config Pushbutton Read configuration data from INI file Save Config Pushbutton Save configuration data to INI file Plot Filename Edit Enter plot filename X Axis Label Groupbox X axis label Label Static Text X axis label Log AF Y Axis Label Groupbox Y axis label Label Static Text Y axis label Window Z Axis label Groupbox Z Axis label 255 STABLE32 USER MANUAL Control Type Description Label Static Text Z Axis label Log Sigma Settings Groupbox Window settings Window Size Edit Enter analysis window size Step Size Edit Enter analysis step size Windows Text Display analysis windows Variance Groupbox Variance choices AVAR Radio Button Allan variance HVA
90. Clock Name Combo Select name of desired measurement clock Description Text Show description of selected measurement clock Records Groupbox Clock measurement records Reference Data Table List of reference clock records Measurement Data Table List of measurement clock records Meas Info Text Information about measurement record 145 STABLE32 USER MANUAL Control Type Description Details Pushbutton Open Details box with database information Reset Pushbutton Reset clock and record lists UTC Radio button Show date time as timestamp MJD Radio button Show date time as MJD Read Times Groupbox Start amp stop times of data to be read Start UTC Edit Read start date time or message Start MJD Edit Read start MJD End UTC Edit Read end date time or message End MJD Edit Read end MJD Span Text Read span days hrs mins secs Text data points in read span Tau sec Groupbox Measurement and sampling interval Meas Tau Text MMS measurement interval AF Edit Averaging factor applied during read Read Tau Text Sampling interval of read data No Name Progress Bar Read progress indication No Name Text Program instructions and messages Read Pushbutton Read data from database Abort button during read Configure Pushbutton Open Configure dialog box Close Pushbutton Close Database function Help Pushbutton Invoke
91. Detailed Search 34 Eind Beplace Edit After Highlighted Point s Del 8 p T Coar outliers Iv Color Gaps Iv Show Timetags MJD 00000000 00000000 C Exp 0 00000000008 00 C DOY YYYY DDD HH MM SS C Date YY MM DD HH MM SS Press F2 to edit data in table Help OK Control Type Description Sigma Factor Edit Enter outlier criterion Detailed Search Group Detailed search amp replace controls Find Pushbutton Invoke Find function Replace Pushbutton Invoke Replace function Edit After Highlighted Point Group Insertion and deletion controls Ins Pushbutton Insert gap s Del Pushbutton Delete point s Edit points to insert delete Color Gaps Checkbox Highlight gaps in blue Color Outliers Checkbox Highlight outliers in red Show Timetags Checkbox Show timetags along with data Timetag Format Group Timetag format choices MJD Radiobutton Show timetags in MJD format DOY Radiobutton Show timetags in DOY format Exp Radiobutton Show timetags in exponential format Date Radiobutton Show timetags in date format OK Pushbutton Accept editing changes amp close dialog box Cancel Pushbutton Abort editing changes amp close dialog box Help Pushbutton Invoke the Edit help topic 166 EDITING FUNCTIONS e Operation The Edit function can be used for several purposes
92. E See Separate Flowchart 134 Flowchart for Parsing Data File Start All delimiters Scan Line for have been Next Space Delimiter converted to spaces No Selected Field Conv Field into Timetag Numeric Value phase or freq data arra Y y Store Value in Data Array TE Inc Scan Index No Yes Done End of line denoted by any control character e g LF CR EOS etc gt TN Move Thru Any More Spaces No Yes Done Flowchart for Parsing Data Line FILE FUNCTIONS Large Data File e Purpose The Large Data File function supports the reading of large data files Itis a sub function of the Open function Use the Large Data File function to select the desired option for handling a large data file This dialog box opens automatically during an Open operation whenever such a data file is detected The user then has the options of 1 averaging the data as it is read 2 using only the first portion of the data 3 using only the last portion of the data Large Data File Ed Data file size exceeds configuration limit Choose one of the following options or press Cancel to abort Y Average Data As It Is Read C Use First Portion Of Data Use Last Portion Of Data C Read All Data with AF 1 Help Points 2000000 Ava Factor E e Controls The Large Data File dialog box contains the following controls
93. ERO MES 307 TI Special Characters ettet e ER e RR EC DOR ok kka dee 309 vi INDEX TABLE OF CONTENTS TE al 315 IV Configuration Piles ereenn aanta ERR r 317 V Hints and Notes ii oed tere e te tee e RR 327 VI 5110Comm Communications Program eee 331 THO cette e re He o RT RS 333 ir EN RR 339 vii STABLE32 USER MANUAL viii GENERAL Stable32 e Introduction Stable32 is a 32 bit PC program for the analysis of frequency stability It allows the entry and editing of phase and frequency data the calculation of stability statistics and the plotting and printing of phase frequency and stability data Stable32 runs under Microsoft Windows 95 NT or higher and requires a 200 MHz Pentium class computer with a CD drive 32MB of RAM and a XGA color monitor A graphics printer is needed for text and graphics printouts General help information is available via the F1 key or by accessing the Help menu or toolbutton while context sensitive help is available by pressing the Help button within a particular function Complete information about the Stable32 program is available in the User Manual Stable32 uses the GraphiC scientific plotting package under the terms of a royalty license agreement with Scientific Endeavors Corporation Kingston TN 37763 It may include the PlayW program for replaying the TKF graphics files produced by GraphiC e Features Eile Edit Analysis Plot Generate Utility Options Help
94. Freg configuration variable can be displayed during phase data entry to warn of equal adjacent phase values which will result in zero frequency points that are treated as gaps e Zeros Besides their use to denote gaps zeros can occur as actual data values This happens most often at the beginning and end of phase data and those zeros are not considered to be gaps All other embedded zeros are considered as gaps in phase data as are all zeros in frequency data To preserve such zeros as actual values change them to a value close to zero e g le 99 The Find and Replace feature of the Edit function may be used to make that substitution A zero value in frequency data can also occur as the result of the conversion of two equal adjacent phase data points perhaps because of limited measurement resolution and an optional warning message is available to flag this possibility when phase data is read This situation can be handled in the Convert function by activating the option to adjust the value of the converted frequency point from zero to 1e 99 A certain number of zeros gaps can be inserted into or deleted from phase or frequency data with the Edit After Highlighted Point feature of the Edit function This can be used to insert gaps that correspond to an interruption in the data record That process can be accomplished automatically for time tagged data with the Regularize function e Caution Header rows in a data file are not read
95. Frequency Stability pp 160 165 R Burgoon and M C Fisher Conversion Between Time and Frequency Domain of Intersection Points of Slopes of Various Noise Processes 32th Freq Contrl Symp pp 514 519 June 1978 W F Egan An Efficient Algorithm to Compute Allan Variance from Spectral Density IEEE Trans Instrum Meas Vol 37 No 2 pp 240 244 June 1988 F Vernotte J Groslambert and J J Gagnepain Practical Calculation Methods of Spectral Density of Instantaneous Normalized Frequency Deviation from Instantaneous Time Error Samples Proc 5th European Freq and Time Forum pp 449 455 March 1991 F Thomson S Asmar and K Oudrhiri Limitations on the Use of the Power Law Form of Sy f to Compute Allan Variance IEEE Trans UFFC Vol 52 No 9 pp 1468 1472 Sept 2005 W J Riley Stable32 Frequency Domain Functions Hamilton Technical Services Simulation S K Park and K W Miller Random Number Generators Good Ones are Hard to Find Comm ACM Vol 31 No 10 pp 1192 1201 Oct 1988 Kasdin and T Walter Discrete Simulation of Power Law Noise Proc 1992 IEEE Freq Contrl Symp pp 274 283 May 1992 T Walter Characterizing Frequency Stability A Continuous Power Law Model with Discrete Sampling JEEE Trans Instrum Meas Vol 43 No 1 pp 69 79 Feb 1994 Robust Statistics D B Percival Use of Robust Statistical Techniques in Time Scale Formation Preliminary Report U
96. Function 3 ae al ie io eva 5 49 Convert PUNGEION iiss secsses coste e nore eie ee eoe p i m ali 173 A O MD Dala POTMAL SAS EE Data Plot Function ES Data Reversal MENSEM Data LaS RC re Database Function Day of Year DOY Dead Time Demo VOM A trn er reu oe E emt e NES ARR ERE CER enters A a DR RN ere EDS EUN d DialogBOoxesccsnik decocto a ALLIES Directories Domain Conversions esses eene SNE nnne nennen ES ANEA AEEA ESTESA 117 261 Domit PUM CLOT cei tei rer ei ete rover gus re er e eve s repu ee er ee tere Ton 261 Drift Putictlots ese A aii 191 Error Bars Iocund c AEEA Feedback File E nctions 25 osea od File Opened cr nde cater t otii eme pe eps e rep ep co eei rte da Filenames Fill Function Fill Gaps Filter Function Eitnid Eunctionmias do ide en bed rae o iss eius Find Interruptions de First Dittereneers ad ado eho S obo e sis RS AS FREQUEN vu rre Frequency Domain Stable BENE eeu Frequency Jump Detection nesnenin re tr po e e ERU i 105 220 223 EUHGUOH Flint ts A a io bee ie E 220 334 TA o EA A AM AL Ee 18 21 Generate Simulated Clock Noise c ccccsccssssesscecssecssscesecesseecsecesecececesseceseseeseecssecsseseeeeeenees 231 AA E ER 229 ALO isa 281 A em e aa aid aa ITER 276 GraphiC messes piira ssri npese 41 279 Graphics Interchange Fo
97. Function The B2 bias function is the ratio of the 2 sample Allan variance with dead time ratio r T t to the 2 sample Allan variance without dead time r 1 B2 r 4 o Q T T o 2 T 1 e B3 Bias Function The B3 bias function is the ratio of the N sample standard variance with dead time ratio r T t at multiples M t t of the basic averaging time to to the N sample variance with the same dead time ratio at averaging time t B3 N M r p 0 N M T 1 oN T 1 e RQ Function The R n function is the ratio of the modified Allan variance to the normal Allan variance for n phase data points Note R n is also a function of a the exponent of the power law noise type R n Mod o t e TOTVAR Bias Function The TOTVAR statistic is an unbiased estimator of the Allan variance for white and flicker PM noise and for white FM noise For flicker and random walk FM noise TOTVAR is biased low as t becomes significant compared with the record length The ratio of the expected value of TOTVAR to AVAR is given by the expression B TOTAL 1 a t T 0 lt t lt T 2 where a 1 3 In2 0 481 for flicker FM noise a 3 4 0 750 for random walk FM noise and T is the record length At the maximum allowable value of t T 2 TOTVAR is biased low by about 24 for RW FM noise 95 STABLE32 USER MANUAL The Stable32 program applies this bias function automatically to correct the reported TOTVAR result e TOT
98. GENERAL Menu Tree e Menu Tree The Stable32 program uses the following menu tree Open Edit Statistics l Phase Noise Calendar Show Tabs Save Convert Check Fi Timetags Domain Configure About requency Filenames Index Add Normalize Drift Inputs Status Bar Using Help Read Average Sigma Inserts r Auto File Tabs Stable on the Web Database Fill Run Play Auto Change Tabs Feedback Print Regularize DAVAR L TSC5110A Auto File Tabs Exit Scale Power r Stable32 ini Auto Noise Tabs Part Histogram r Log Save Current Data Filter Autocorrelation E Pad r Rename Selected Tab Clear 3 Cornered Hat r Audio H Write Selected Tab r Vibra Cf Close Selected Tab r Auto1 Close All Tabs r Auto2 Auto3 Item Function Description File Open Open phase or frequency data file Save Save current phase or frequency data Add Add data file to current phase or frequency data Read Read stability data file Database Read data from TSC MMS database Print Print phase or frequency data Exit Exit Stable32 program Edit Edit Edit phase or frequency data Convert Convert between phase and frequency data Normalize Normalize phase or frequency data for zero mean Average Combine data into a longer averaging time Fill Fill gaps in phase or frequency data Regularize Regularize data by using timetags to insert gaps Scale Scale phase or frequency data Part Remove all except part of phase or frequency data
99. Help Read Conta Seve Config Reset All Table Position Top Right y Stability File CAProgram FilestDevStudiot Append Message Position Top Left Axis Label Averaging Time EtE Secon TauMax 1 28000e 02 Scale Max fi 00000e 03 TauMin 1 00000e 00 Scale Min fi 00000e 00 Y Axis Label Overlapping Allan Deviatio y Sigma Max 2 92198e 01 Scale Max fi 00000e 00 Sigma Min 2 76603e 02 Scale Min fi 00000e 02 Options v Date Vv Box1 M Bars2 w Table3 v Ft4 Wide PlotFile C Program Files DevSt e Controls The Run Options dialog box contains the following controls Control Type Description Title Edit Enter plot title Sub Title Edit Enter plot subtitle Message Edit Enter plot message Msg Position List Choose message position Table Position List Choose stability table position Stability File Edit Enter name of stability file to be written Append Checkbox Append to stability data file X Axis Groupbox X Axis parameters Label Edit Enter x axis label Tau Max Text Display maximum tau value Scale Max Edit Enter y axis scale maximum Tau Min Text Display minimum tau value Scale Min Edit Enter y axis scale minimum Y Axis Groupbox Y Axis parameters Label Edit Enter y axis label Sigma Max Text Display maximum sigma value 245 STABLE32 USER MANUAL
100. Increment the filename extension when data changes 0 WriteSigmaFile Write a file containing sigma data after a Run 0 AutoCalc Automatically calculate when starting Run function 0 AutoPlot Automatically draw plot when starting Plot function 0 Notepad Use the specified text editor NOTEPAD EXE MaxSize Maximum size of data arrays 99999 Splash Show startup splash screen 1 SigmaType Variance type for Sigma function 0 RunType Variance type for Run fiction 0 PhaseDriftType Drift type for frequency data 0 FregDriftType Drift type for freguency data 0 NonNums non numeric characters to skip in lines of input data 0 Comma Use comma instead of decimal point in input data 0 WarnZeroFreg Warn about zero frequency points in input data 1 317 STABLE32 USER MANUAL Keyword Description Default SmartScale Use smart y axis data plot scales 1 ACFNoiseID Flag to use lag 1 ACF noise ID method foo Left Left main window screen position 0 Top Top main window screen position 0 Right Right main window screen position 0 foo 0 main window fills the desktop area foo Bottom Bottom main window screen position 0 LastOpened Type of data last opened 0 OpenScale Flag to scale input data 0 Header Flag to write header in data file 0 NoGreek Avoid Greek characters in stability plot labels 0 ShowWelcome Flag to show
101. Je 14 7 37e 06 1 48e 14 10 Allan Deviation pping Overla 2 a 104 z 10 10 10 10 107 Averaging Time t Seconds e Cursor Checking the cursor option activates crosshairs on the plot whose position is indicated at the right end of the GraphiC menu bar please ignore the strange characters This option also activates a line drawing feature The right mouse button starts a line and the right button ends it The line can be extended with another right button click or a new line started with the left button The lines can be deleted with the Del key Press the Esc key to deactivate the cursor function e Wide Lines Checking the Wide option causes the data to be plotted with wide lines with better visibility for presentations e References K Levenberg A Method for the Solution of Certain Non Linear Problems in Least Squares Quarterly of Applied Mathematics Vol 2 2 pp 164 168 July 1944 2 D W Marquardt An Algorithm for the Least Squares Estimation of Nonlinear Parameters SIAM Journal of Applied Mathematics Vol 11 2 pp 431 441 June 1963 3 K Madsen H B Nielsen and O Tingleff Methods for Non Linear Least Squares Problems Technical University of Denmark April 2004 221 STABLE32 USER MANUAL 222 ANALYSIS FUNCTIONS Jump Detection Parameters e Purpose Use the Frequency Jump Detection Parameters dialog box to set the parameters to detect and analyze jumps in frequency data
102. LcHadamardB1 LcHadamardDev LcInvChiSgr LcLinFregDrift LcLogFregDrift LcMTIE LcMean LcNormalProb LcPhaseHadamardDev lcPhaseModSigma LcPhaseOverlapHadamardDev LcPhaseOverlapSigma lcPhaseSigma lcPhaseStdDev lcQuadraticDrift lcRatio LcSecondDi ff LcStarBl Cal LcThreePointDrift 39 STABLE32 USER MANUAL CheckFrequenC CombinedEDF ConvDomain ConvFreqToPhase ConvPhaseToFreq ConvPhaseToFreqUsingTimetags CountEqualTimetags CountGaps DateConv DateToJulian DateToMJD DayOfWeek EDF FillFloatGaps FillGaps FindFreqOutliers FindMedian FindMinMax FindPlotScale GenNoise GetMJD HadTotvarBias HadTotvarCalc HadTotvarEDF HadamardEDF HistoCalc JulianToDate JDToDate JDtoDOY JDtoGPS akeDate edDev odTotvarBias odTotvarCalc odTotvarEDF ultiTaperSpectrumCalc NoiseID NormalizeData RemoveDiffusionFreqDrift RemoveFregOffset RemoveLinFregDrift RemoveLogFregDrift RemoveQuadraticDrift RoundAxes ScaleData SpectrumCalc TIErms Theol TheolBias TheolBiasToAlpha TheolEDF TotvarBias TotvarCalc TotvarEDF The FrequenC Library its functions and their documentation are available for purchase by special arrangement with Hamilton Technical Services 40 GENERAL GraphiC e GraphiC GraphiC is a library of scientific plotting functions used by the Stable32 program for its phase frequency stability power spectrum aut
103. MVAR Bias Function The TOTMVAR statistic is a biased estimator of the modified Allan variance The TOTMVAR bias factor the ratio of the expected value of TOTMVAR to MVAR depends on the noise type but is essentially independent of the averaging factor and of data points as shown in the following table Noise Bias Factor W PM 1 06 F PM 1 17 W FM 127 F FM 1 30 RW FM 1 31 Note The Stable32 program applies this bias factor automatically to correct the reported TOTMVAR result e Th ol Bias See the Th o section of this User Manual for a discussion of the Th ol bias e Summary of Stable32 EDF and Bias Functions The following table summarizes the use of the equivalent degrees of freedom confidence intervals and bias corrections in the variance calculations of the Stable32 Sigma and Run functions 96 TIME DOMAIN STABILITY Stable32 Noise ID EDF CI Bias Methods Variance Noise ID EDF Cale CI Error Bars Bias Calc Type Method Allan Lag 1 ACF N A o N and K NA AVAR B1 ratio Can t set CI Overlapping Lag 1 ACF CDF 1 x N A Allan AVAR BI ratio Modified Allan Lag 1 ACF HEDF 2 11 xi N A MVAR B1 plus R n w modified fora 1 2 arguments Time Lag 1 ACF HEDF 2 11 x NA TVAR B1 plus R n w modified for a 1 2 arguments Hadamard Lag 1 ACF N A Sigma None N A HVAR Run o VN and Ka Can t set CI Overlapping Lag 1 ACF HEDF 3 x N
104. Nos 12 P 129 U 146 63 U 180 C2 197 lt 5 52 gt a Olos n3 CG 13 E 14 A i T 98 45 da 28 Pla alm rim Alus les Nil Alis 7 4 Qia Qs bDins Si ls Ol 183 a Ole Ala Rio Con tius Oso Qi 184 c m A A c 49 1 66 D 83 1100 d 7 Us Q 151 U 18 C 185 2 Simplex Font Numeric Code 0203 313 STABLE32 USER MANUAL 314 APPENDICES Appendix III Editing Keys e Editing Keys The Stable32 program uses the standard Windows editing keys except that the Enter key can generally be used to terminate edit control entries This causes the entry to be reformatted and checked for validity The following special editing keys that apply to the Edit dialog box F2 The existing data may be edited by first pressing the F2 key It is necessary to delete a portion of the existing data to make room for the new entries Esc The original value may be restored with the Esc key Enter The changes are accepted with the Enter key 315 STABLE32 USER MANUAL 316 APPENDICES Appendix IV Configuration File e Files The Files section of the STABLE32 INI file can contain the following parameters Keyword Description Default LastFile Full filename of last file opened None PhaseFilel Full filename of last phase file opened None FregFilel Full filename of last freq file opened None PhaseFile2 Full filename of 2nd from last phase fi
105. Piti ode eee adio bd etu eet Power Function Power Law NOISE 4 satin er Sh ia S RE DR ERN SC 90 111 Power Spectral Density PSD e pte ttp cote eer p n E e REED RR FER Hen EHE 111 201 Precisa Preprocessing Prewhitening Print Function 336 Quadratie io AA AAA A tas RS 193 Read Funct 45452 Ao Aa kl sa haid lk eS Read Lines Function Read Notes Function Referer COS usado e p o e cam eO n a e caia e e con nc Regr SSIOD 5 S2 In eoe t Oi RE e a be Ree as Regularize Function Remov Prequency Ditto ia ados 191 Remove Gap swiss tbe covctaazs torenes pero ede o D e a pO be oc EE Remove Outliers Replace Function Run Function R n Eines 3 aps cite o c Oo e cam e Do p n rb cai epe pa i cO Run NOte335 Asen beet ds toe teda ble e ad al Ee este eats Run Options R n Plot Function d o OE RR bp Da qu IDE AME UNE 243 Save FUf ctione SAA Sala ECL haaa SA ELM 141 A deter er Rr e Itidem ed eerte es 181 Second Differences tee eee e eR 193 Separation of Variances cccccecssssscesecseeesceseceaecseesscsseceaecseeeecesecaaecseeeeeeaeceaecaeeeeeeeeeaeeneensees 101 SEOAY E ce deus su Cre obediunt e eed repu e oid fos Sigma Function Sigma T u DIASTAMS estet e ettet eder eri quee tee dee eee analisis denas saa 113 Special Clardetets ius aerei tree ree ue te ex Gk e sine eee a REEL ERAI Special Versions Stable32 Statistics Function E A EE PET Student Version s
106. R Radio Button Hadamard variance Options Groupbox Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Colors Checkbox Show multicolor surface plot Grid Listbox Select color surface plot grid Horiz View Groupbox Horizontal viewpoint trackbar None Slider Set horizontal viewpoint Reverse 1 Checkbox Reverse horizontal orientation Vert View Groupbox Vertical viewpoint trackbar None Slider Set vertical viewpoint None Progress Bar Show calculation progress Abort Pushbutton Abort calculation Close Pushbutton Close the Histogram dialog box Reset All Pushbutton Reset all parameters to defaults Help Pushbutton Invoke this help topic e Operation Enter desired plot Title SubTitle Message message Position Settings Options and Views Then press Plot to produce a dynamic stability plot or Close to close the dialog box The Window Size and Step Size set the width of the sliding analysis window and the of data points that it advances for each step Together these parameters determine the of analysis Windows and are constrained to be within acceptable limits A large of analysis windows will require a long calculation time which is shown in the Progress bar and can be stopped with the Abort button in which case the results obtained so far will be plotted The Horiz View trackbar slider sets the x and y axis left and right viewpoint of the plot the Vert View trackbar slider sets the y axis
107. S FNT SWISSBIT FNT SWISSBLD FNT SWISSITL FNT SWISSN FNT TRIPITAL FNT TRIPLEX FNT Help Files STABLE32 CHM GRAPHICW HLP 5110COMM CHM HONH CHM POSTGRESQL CHM Sample Data FREQ DAT PHASE DAT SAMPLE DAT TST_SUIT DAT NBS DAT NOISEPIX TKF STABLE32 USER MANUAL Stability Masks G 81IPRC MTIE MSK G 811PRC TDEV MSK TISTRATUM3 TDEV MSK G 824PRC MTIE MSK TEST MSK TISTRATUM2 3E TDEV MSK Miscellaneous MESSAGES TAB MESSAGES DAT HDR TIF HDRI POS HDR2 POS STABLE32 INI README TXT 5110COMM INI Icons STABLE32 ICO 5110COMM ICO PLAY ICO Documentation MANUAL154 PDF WELCOME PDF STABILITYCHART PDF FUNCTIONS PDF TECHNIOUES PDF STABILITY ANALYSIS SOFTWARE PDF Optional File Play and 5110Comm files not included with Student Version GENERAL Directories e Directories The Stable32 program support and data files are normally located in a single disk directory folder as described below e Installation All Stable32 files are by default stored in a single directory C Program Files Hamilton Technical Services Stable32 While any drive and directory can be used it is recommended that all these files be kept in that one place Stable32 will not start without access to its DLL files It is also important that the program be able to find the font and other GraphiC plotting support files While this condition is automatically satisfied by keeping all of the Stable32 files in a single directory the GPCWIN environment variable can a
108. SendKey PF Plot Frequency function Plot command P If WinExist Plot Then WinActivate Plot SendKey P Wait for plot to be drawn on screen Delay 5 GraphiC menu File Plot command ALT F P If WinExist Stable32 Main Then WinActivate Stable32 Main SendKey FP Wait for plot to be sent to printer Delay 15 Graphic menu File Exit command ALT F X SendKey FX Close Plot function with Escape ESC If WinExist Plot Then WinActivate Plot SendKey ESCAPE Keystrokes corresponding to the ALT keyboard access codes for the Stable32 functions are sent via SendKey statements The prefix denotes an ALT key WinActivate statements are used to direct these keystrokes to the appropriate window The Delay statements are needed to allow time for GraphiC plotting and printing The lines are simply comments e See Also See the WinBatch documentation for more information regarding these programs and commands See the Auto function for a limited means of stability analysis automation that is built into the Stable32 program 35 36 STABLE32 USER MANUAL GENERAL Copy Command e Copy Command Several of the Stable32 functions include a Copy button or menu item to copy information to the Windows clipboard where it can be viewed saved printed or pasted into another application The following table describes those functions and the information that can be copied
109. Stability Plot Close 9 fh Selectfunctions desired for automatic processing Script 1 Name AutoScript Cancel Help iP 265 e Controls STABLE32 USER MANUAL The Auto dialog box contains the following controls Control Type Description Open File Checkbox Open data file for analysis Otherwise existing data is used Browse Pushbutton Browse for data file Phase Radiobutton Choose phase data Freq Radiobutton Choose frequency data Filename Edit Name of data file From manual entry or browse Convert Checkbox Convert to other data type for analysis Remove Outliers Checkbox Remove bad frequency data Sigma Factor Edit Criterion for outlier removal Part 0 Checkbox Use part of data Start Edit Starting data point to use 1 first data point End Edit Ending data point to use 0 last data point Average 1 Checkbox Combine data into longer tau Avg Factor Edit Averaging factor Normalize Checkbox Remove mean value from analysis data Remove Drift 2 Checkbox Remove drift fit from analysis data Drift Type 3 Combobox Type of drift fit to use Data Plot Checkbox Plot data on screen Type 4 Listbox Type of data to plot Multiple selections allowed Print Data Plot 5 Checkbox Also print selected data type s Run 6 Checkbox Perform stability analysis Run Variance Type Com
110. TMVAR process requires 3 nested loops e An outer summation over the N 3m 1 subsequences The 3m point subsequence is formed its linear trend is removed and it is extended at both ends by uninverted even reflection to 9m points 71 STABLE32 USER MANUAL e An inner summation over the 6m unique groups of m point averages from which all possible fully overlapping 2 differences are used to calculate MVAR e A loop within the inner summation to sum the phase averages for 3 sets of m points The final step is to scale the result according to the sampling period to averaging factor m and number of points N Overall this can be expressed as le yl ety 20 Ta y N 3m 1 nel m 3 where the z m terms are the phase averages from the triply extended subsequence and the prefix denotes that the linear trend has been removed At the largest possible averaging factor m N 3 the outer summation consists of only one term but the inner summation has 6m terms thus providing a sizable number of estimates for the variance e References The following reference describes the TOTMVAR statistic D A Howe and F Vernotte Generalization of the Total Variance Approach to the Modified Allan Variance Proc 31 PTTI Meeting December 1999 pp 267 276 72 TIME DOMAIN STABILITY Hadamard Variance e Hadamard Variance The Hadamard variance is a 3 sample variance that is similar to the 2 sample Allan variance It ex
111. TTI Meeting pp 451 460 Dec 1992 M A Weiss and C A Greenhall A Simple Algorithm for Approximating Confidence on the Modified Allan Variance and the Time Variance Proc 28th PTTI Meeting pp 215 224 Dec 1996 F Vernotte and M Vincent Estimation of the Uncertainty of a Mean Frequency Measurement Proc 11th European Freq and Time Forum pp 553 556 March 1997 D A Howe Methods of Improving the Estimation of Long Term Frequency Variance Proc 11th European Freq and Time Forum pp 91 99 March 1997 W J Riley Confidence Intervals and Bias Corrections for the Stable32 Variance Functions Hamilton Technical Services C Greenhall and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 35th PTTI Meeting Dec 2003 T N Tasset D A Howe and D B Percival Th ol Confidence Intervals Proc 2004 Joint FCS UFFC Meeting pp 725 728 Aug 2004 Drift Estimation and Removal C A Greenhall Removal of Drift from Frequency Stability Measurements Telecommunications and Data Acquisition Progress Report 42 65 July Aug 1981 Jet Propulsion Laboratory Pasadena CA pp 127 132 1981 J A Barnes The Measurement of Linear Frequency Drift in Oscillators Proc 15th PITTI Meeting pp 551 582 Dec 1983 M A Weiss D W Allan and D A Howe Confidence on the Second Difference Estimation of Frequency Drift Proc 1992 Freq Contrl Symp pp 300 305 June 1992 289 ad 290 ST
112. The Basics of Frequency Stability Analysis Hamilton Technical Services C Audoin and B Guinot The Measurement of Time Cambridge University Press 2001 W J Riley The Calculation of Time Domain Frequency Stability Hamilton Technical Services W J Riley Techniques for Frequency Stability Analysis Tutorial at the 2003 Intl Freq Cont Symp May 2003 Standards and Specifications Report 580 Characterization of Frequency and Phase Noise International Radio Consultative Committee C C LR pp 142 150 1986 R L Sydnor Editor The Selection and Use of Precise Frequency Systems ITU R Handbook 1995 Guide to the Expression of Uncertainty in Measurement International Standards Organization 1995 ISBN 92 67 10188 9 IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology Random Instabilities JEEE Std 1139 1999 July 1999 MIL PRF 55310E Oscillators Crystal General Specification For March 2006 Classic Proc IEEE NASA Symp on the Definition and Measurement of Short Term Frequency Stability NASA SP 80 Nov 1964 Allan Variance D W Allan Statistics of Atomic Frequency Standards Proc IEEE Vol 54 pp 221 230 Feb 1966 Characterization of Frequency Stability NBS Technical Note 394 U S Department of Commerce National Bureau of Standards Oct 1970 J A Barnes et al Characterization of Frequency Stability JEEE Trans Instrum Meas Vol IM 20 N
113. USER MANUAL Stable32 Frequency Stability Analysis e CIS LEEKI ds rn 4 e a xw en edt i pu BIEN ee nuit iw U Hamilton Technical Services 650 Distant Island Drive N Beaufort SC 29907 USA 09 07 2008 Copyright Notice O 2007 8 Hamilton Technical Services All Rights Reserved The information in this document is subject to change without notice and is provided without any warranty of any type Please report any errors or corrections to the address below No part of this document may be reproduced or retransmitted in any form or by any means electronically or mechanically including photocopying or scanning for any purpose other than the purchaser s personal use without the express written permission of Hamilton Technical Services The software described in this document is licensed and may be used only in accordance with the terms of the Stable32 license agreement It may not be copied on any medium except as specifically allowed therein Stable32 User Manual Version 1 54 09 07 2008 Printed manual available from www lulu com as ID 4 212944 Hamilton Technical Services Phone 843 525 6495 650 Distant Island Drive Fax 843 525 0251 Beaufort SC 29907 1580 E Mail stable32 wriley com USA Web www wriley com ii TABLE OF CONTENTS Table of Contents FRONT MATTER IS sting cite ii T ble Of Cotten tS is ene eerie RE HERR AEK TASU SIGA E relate E iii GENERAL A
114. V log sigma versus averaging time log tau or log averaging factor AF as a function of time window Sigma is calculated using fully overlapping samples at all possible averaging factors up to one quarter of the window size In the axes orientation used the tau scale is opposite to that usually used AF and tau increase toward the left which is the convention for a dynamic stability plot and has the advantage of best showing the sigma tau surface that usually has lower sigma at longer tau The y axis and z axis are labeled as log sigma and log AF respectively and a log log grid is shown in the back x plane while the linear x axis is labeled as window The dynamic stability plot includes annotations that show the sigma range tau range window parameters and time span A plot title can be included at the top a sub title at the bottom and a message can be shown in any of 9 positions Date time data analysis limits and data filename can be included at the top and an optional plot label e g organization name can be included at the bottom The dynamic stability 3D surface plot can be shown as a full red mesh or as a sigma dependent multicolor display with or without an adjustable density mesh The mesh density also depends on the window and step sizes For a large of analysis windows it is desirable to use the grid control to reduce the number of mesh points shown this does not affect the underlying surface plot The dynamic ov
115. a certain tau value to be set and an automation script to be executed when the program starts e Operation The command line options may be entered directly from the command line from the Windows Start Run prompt or from a batch file They are entered immediately after the STABLE32 command that starts the program The command line options begin with a minus and may be entered in upper or lower case Stable32 Command Line Options Command Description P FILENAME Automatically load the phase data file FILENAME F FILENAME Automatically load the frequency data file FILENAME A FILENAME Automatically open the archive file FILENAME T TAU Automatically load the tau value TAU O SKIP Skip display of multicolumn amp file opened dialogs O AUTO Execute automation script script number 1 3 e Example To start the Stable32 program by loading a t 900 sec phase data file named CLOCK DAT enter and execute the following statement from the Windows command line STABLE32 P CLOCK DAT T 900 e Notes The tau value set with the T command line option applies to whichever type of data is loaded It takes precedence over any tau value set with the PhaseTau or FreqTau keyword items in the Inputs section of the STABLE32 INI configuration file Phase frequency and archive documents can be automatically opened by Stable32 by associating an extension with a corresponding action that includes the respective command li
116. a potential jump is detected the following points are examined in an averaging window to accept or reject the jump The SEQAVG plot shows the actual frequency averages in each jump regime and is able to locate the jump more closely but does not show trends in the data The SEQAVG jump detection algorithm is shown in the following flowchart 106 FREQUENCY DOMAIN STABILITY lim can be set manually on basis of either absolute fractional freg or sigma factor Start Set Igth Calc lim pe Default gth npts 10 m Default lim 3 0 c at AF npts Igth y Calc avg of 1st group Calc jump limits r Jump Limits avg lim gt All Y Data Loop thru all data Tested pn pina HL Bone m starting at i gth 1 129 between jumps No Limit Yes occu eu Exceeded E j fr Y Average over from 1 to gth points Calc local avg starting at suspected jump Calc new avg which becomes Then For i j Ves Limit No I lt newbase toi j lgth 1 Exceeded Juri Go back to Get next val Di P ij isproved Jump Y Confirmed Keep testing at izj 1 An example of a SEQAVG plot is shown below 107 STABLE32 USER MANUAL Date 02 27 08 Time 15 38 19 Data Paints 1 thru 100 of 100 Tou 1 0000000e 00 FREQUENCY DATA NEW FRD File NEW FRD
117. afianee ua no bee A uento See rea 71 M TIE meteraene lalia bodes Silelihased Palate boo ca ba hae re e lapata koe 83 Multicolumn Data 129 Multicolumn Details vc 32 2 09 eio roi ere ease in bre re e ro Ope e 131 Multiple Stability Plots ices si p t e e bee ai dede 154 N NE AAA REEE ESAR MM aM MN 231 Noise Ide tifiCallofi jue eee Si E x VO Rt 90 Noise Lines 250 Noise Spectra 115 Non Numeric Characters ETSA E A EEE E E E E et teen ena 17 Normalize Function ccccccccssscesscescecssecssececcecseecssecseceseeeeseecsseceuseeeeecssecsseceseeeeseecsseenseeeaes 175 iNotepadians doe ic 277 O Ote of Two Scaling vesccscccccsccudecencecessacstcetenicasacsbien de bedena a seven inde ev un ova a ad riri a dicas 240 Open Function 121 123 Outliers Overlapping Allan Variance eene eeter 63 Overlapping Hadamard Variance essessssseseeeee eene eene etre nre en 75 P Pad Functions ueste etenim t er Pa ee o i de gebe 277 Part Function 183 Phase Noise Diagram 2 tct t orb om ep eto ep ei ect o eene 116 Picinbono Variance 3 3 44455 eb e e S e o ook e e OR i eee to b e oo po E 73 Play Function T Play Wan 2 AD m S dh PEE ees Plot Annotatiofis rms diri att Gensel ig br 227 Plot Function Plot Inserts Plot Lines s Plot Optiofis tre egt cabe ele tee st aed ve t ER E dt Cete t bep e Polynomial
118. again unless the Reset button is pushed or the program is restarted When the user selects a clock from one of these boxes all of the records for that clock are put into the corresponding table Again this represents a snapshot of the database if a continuing run is subsequently ended the table contents will not dynamically reflect that change Records for MMS systems different from the one selected as the reference are flagged in red and cannot be read Finally after the user has selected the records and the start amp end times to be read the corresponding data is read from the database For a continuing run for both clocks the current date time is used for the end of the record which will change each time the Read button is pushed If data collection on one or both of the clocks has stopped without a end time having been entered the read operation will end when the last pair of measurement amp reference points is read In that case the actual number of points read will be less than indicated for the time span e Reference Timing Solutions Measurement Database Hardware and Software User Manual Timing Solutions Corp 4775 Walnut St Boulder CO 80303 148 FILE FUNCTIONS Database Details e Database Details Additional information about the selected reference and measurement clock records can be obtained from the Database Details dialog box While this information is not necessary to use the database function it can be helpful
119. age Position Top Left Read Config Save Config Reset All Table Position Top Right y Stability File SIGMA TAU Axis Y Axis Label Averaging Time tE Secon y Label Allan Deviation sEJy tE v TauMax 6 40000e 01 Sigma Max 4 81700e 00 Scale Max 1 000008 02 Scale Max 1 000008 01 Tau Min 1 00000e 00 Sigma Min 7 30400e 01 Scale Min fi 00000e 00 Scale Min fi 00000e 01 Options Iv Date M Box MBars1 M Table2 v Ft3 PlotFile DADEVSTUDIO MyProjectsi e Controls The Read Options dialog box contains the following controls Control Type Description Title Edit Enter plot title Sub Title Edit Enter plot subtitle Message Edit Enter plot message Message Position Combo Choose message position Table Position Combo Choose table position Read Config Pushbutton Read options from INI file Save Config Pushbutton Save options in INI file Stability File Text Display name of stability file X Axis Groupbox X Axis parameters Label Edit Enter x axis label Tau Max Text Maximum tau value Scale Max Edit Enter x axis tau scale maximum Tau Min Text Minimum tau value Scale Min Edit Enter x axis tau scale minimum 157 STABLE32 USER MANUAL Control Type Description Y Axis Groupbox Y Axis parameters Label Edit Enter y axis label Sigma Max Text Maximum si
120. al purpose mathematical and spreadsheet programs such as MathCAD and Excel amp were compared with the program output 5 Consistency Checks The program was verified for internal consistency such as producing the same stability results for phase and frequency data The standard and normal Allan variances should be approximately equal for white FM noise and the Allan variance should be approximately equal to 1 5 times the standard variance for white PM noise The normal and Modified Allan variances should be identical for an averaging factor of 1 For other averaging factors the Modified Allan variance should be approximately one half the normal Allan variance for white FM noise The normal and overlapping Allan variances should be approximately equal The various methods of drift removal should yield similar results 6 Simulated Data Simulated clock data also served as a useful cross check Known values of frequency offset and drift were inserted analyzed and removed Known values of power law noise were generated analyzed plotted and modeled 303 STABLE32 USER MANUAL 304 OTHER INFORMATION Acknowledgments e Credits Stable32 was written by W J Riley in C using the Win32 API and the Microsoft VisualC 5 0 compiler Two major 3rd party software components were used GraphiC Win 7 1 from Scientific Endeavors Corporation for the plotting functions and DataTable 3 0 from ProtoView Development Corporation for the data tables
121. alog box amp restore original data Stop during run or Pushbutton Stop run Clear when stopped Abort run Help Pushbutton Invoke this help topic e Operation Select the desired Variance Type Alpha and if applicable Conf Factor Optionally check Remove Drift and 1 of 2 choose Decade 1 2 4 10 Octave 1 2 4 8 or All Tau tau increments no error bars are displayed for the All Tau option or enter a Start AF Enter the Dead Time ratio if it is not unity Then Press Cale to perform a stability run and Plot Copy or Print the results as desired To quit press Close The default Alpha selection is Auto which will automatically estimate the noise type If the noise type is known a priori then choose one of the specific alpha values In either case the alpha value for each averaging factor AF is used to determine each confidence interval A progress bar is displayed during a TOTMDEV TOTTDEV or All Tau analysis Those runs may be Stopped and then Resumed While stopped the current results may be printed plotted or copied To abort a stopped run press the Clear button e Variance Types The 2 sample or Allan variance is the principal method for describing the stability of a frequency source in the time domain Several types of Allan Hadamard Total or Th ol variances may be calculated as shown in the table below In addition both the overlapping and modified Allan deviations can be calculated and p
122. amard Variance Total Hadamard Variance The total Hadamard variance TOTHVAR is total version of the Hadamard variance that rejects linear freguency drift and offers improved confidence at long averaging times The algorithm for calculating the total Hadamard variance from a set of N fractional freguency values y at an averaging time t mr is very similar to that used to calculate TOTMVAR from phase data 1 Select a 3m point subsequence y of the frequency data y i n n 3m n 3m 1 2 Remove the linear trend c frequency drift from the subsequence obtaining y y c i where c is found by averaging the Ist and last halves of the sequence divided by the interval Extend the subsequence at both ends by uninverted even reflection to form the 9m point subsequence y having the tripled range from i n 3m to n 6m 1 The extended subsequence can be constructed by the expressions y y 4 1 and Ynt3m k 1 Y Fn 3m x for k 1 to 3m Calculate the Hadamard 3 sample variance for this extended subsequence by forming the 6 m point frequency averages and finding the square of their 2nd differences Find TOTHVAR as the simple average of the N 3m HVAR subestimates References The following references apply to the total Hadamard statistic 1 2 D A Howe et al A Total Estimator of the Hadamard Function Used For GPS Operations Proc 32 PTTI Meeting Nov 29 2000 pp 255 268 D A Howe R L Beard C A Greenhal
123. amines the 2nd difference of the fractional frequencies the 3rd difference of the phase variations Because of this the Hadamard variance HVAR or Ho t converges for the Flicker Walk FM a 3 and Random Run FM a 4 power law noise types It is also unaffected by linear frequency drift For frequency data the non overlapping Hadamard variance is defined as M 2 2 Ho t ET 2 XI 42 2 i X i l where y i is the ith of M fractional frequency values at averaging time t For phase data the non overlapping Hadamard variance is defined as 1 Ho 1 NDA 3 xs S ra 33 x where x 1 is the ith of N M 1 phase values at averaging time T Like the Allan variance the Hadamard variance is usually expressed as its square root the Hadamard deviation HDEV or Ho t Note The Picinbono variance is a similar 3 sample statistic It is identical to the Hadamard variance except for a factor of 2 3 73 74 STABLE32 USER MANUAL TIME DOMAIN STABILITY Overlapping Hadamard Variance e Overlapping Hadamard Variance In the same way that the overlapping Allan variance makes maximum use of a data set by forming all possible fully overlapping 2 sample pairs at each averaging time t the overlapping Hadamard variance uses all 3 sample combinations It can be estimated from a set of M frequency measurements for averaging time t mto where m is the averaging factor and to is the basic measuremen
124. an Avoid use with large gaps Fill gaps for faster calculation PO Total Avoid use with large gaps Modified Total Avoid use with large gaps Avoid use with large gaps Avoid use with large gaps Time Total Hadamard Total e Spectral Analysis The Stable32 spectral analysis functions fill gaps in the data before performing their calculations This can affect the low frequency portion of the spectrum 23 e 24 STABLE32 USER MANUAL References J A Barnes Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 January 1969 J A Barnes and D A Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 P Tavella and M Leonardi Noise Characterization of Irregularly Spaced Data Proceedings of the 12th European Frequency and Time Forum pp 209 214 March 1998 C Hackman and T E Parker Noise Analysis of Unevenly Spaced Time Series Data Metrologia Vol 33 pp 457 466 1996 W J Riley Gaps Outliers Dead Time and Uneven Spacing in Frequency Stability Data Hamilton Technical Services GENERAL Archive File Format e TSC Archive File Format Timing Solutions Corporation TSC now Symmetricom archive files have lines that start with either a or symbol The lines have 1 additional field the MJD for the data on the fo
125. an be restarted and the connection should succeed The same procedure can be followed any time a change is required in the access parameters 151 STABLE32 USER MANUAL e Configuration File A typical Stable32 configuration file contains the following database items Database Host 192 168 1 100 Database tsc User Bill Password A1B2C3D4 The password is encrypted in the Stable32 configuration file each password ASCII character becomes two hex characters The Database section of the STABLE32 INI file contains four parameters associated with database access Name Description Default Value Remarks Host IP address 1 Blank for localhost Database Database name tsc postgres Required User User name tsc Required Password Password tsc Not always required Encrypted These items of the Stable32 configuration file may be manually edited with a text editor but the preferred method is to use the Database Configue dialog within the Stable32 program If no STABLE32 INI file or Database item exists in the Stable32 exe program folder the program will almost certainly follow the failed connection process and a Database configuration file item will be created The STABLE32 INI configuration file is rewritten each time the program closes 152 READ FUNCTIONS Read Function e Purpose Use the Read function to read print and plot stability data from disk This stability data may be a table of possibl
126. and habit of checking the tau scale stability plot tau set manually in several value in the Data File scale and PSD plot ways see below Opened dialog box whenever Fourier frequency scale a data file is read Select Portion Analyze only a certain Use the Part function Only part of the data may be of Data portion of the data of interest for the analysis Edit Data Change or correct data Use the Edit function Manual editing is another way to find and remove outliers Convert Data Obtain the desired phase or frequency data Use the Convert function It is generally better to acquire phase data but it may be better to analyze it as frequency data Reverse Data Reorder data for certain analysis purposes Use the Reverse button in the Scale function Data reversal can provide better frequency jump location correct tau units settings Scale Data May need to scale data Scale data as it is read Phase data should have units to obtain correct phase per Inputs settings or of seconds Frequency data or frequency units with the Scale function should have units of dimensionless fractional frequency Scale May need to scale Scale timetags as they Timetags should have units Timetags timetags to obtain are read per Inputs of seconds MJD timetags should therefore be scaled by 86400 Average Data Average data to longer tau Average data with Average function Phase data is decima
127. and open for modified ones One application for multiple data sets is to show both stability data and its corresponding specification limit e Other Options By default all data points are shown with symbols and are included in the data table If however the of analysis points is made zero for the first row of a set that data will be plotted without symbols This may be desirable for showing spec limits In addition all data rows having 0 are excluded from the data table Thus spec limits can be excluded from the table by setting the analysis points to zero and placing them at the end of the data file 154 READ FUNCTIONS Read Plot Function e Purpose Use the Read Plot function to generate a stability plot GraphiC Win cAstable324sigma tkf Eile Edit Draw Convert Help Dole 09 24 98 Time 15 07 41 File SIGMA TAL FREQUENCY STABILITY SIGMATAU e y9 2 o o 1010 Allan Deviat 2 Tou Sigma d 9 00e 02 2 25e 10 1 80e 03 2 23e 10 3 608 03 1 61e 10 7 20e 03 1 17e 10 1 44e 04 6 88e 11 2 88e 04 5 34e 11 5 76e 04 4 03e 11 1 15e 05 3 07e 11 101 gt 10 10 Averaging Time t Seconds 155 STABLE32 USER MANUAL 156 READ FUNCTIONS Read Options Function e Purpose Use the Read Options function to control the attributes of the stability plot Title JFREQUENCYSTABILITY gg OK SubTitle iGMATAU e Cancel Message po mw Help Mess
128. ase fluctuations by t x t 2nvo where vo is the carrier frequency in Hz Both and x t and O t are commonly called phase to distinguish them from the independent time variable t These data are taken at a uniform measurement time ty The phase data may be sampled at a multiple t n ty by using every nth point decimation During subsequent analysis the x t may be converted to y t values of dimensionless fractional frequency Af f The Stable32 Database function reads and stores timetags and phase x values in the phase timetags and data arrays The measurements are equally spaced at an averaging time tau that can be chosen within the database function as any integer multiple of the basic MMS measurement interval The timetags are formatted as Modified Julian Date MJD The MJD is based on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 it starts at zero at midnight on November 17 1858 Stable32 handles MJDs over the span of the 21st century and it has provisions for displaying them in several formats The MMS system usually takes data on each clock at a rate of once per second and each resulting row in the measurements table has a source id INT a pps count INT a utc TIMESTAMP and a meas NUMERIC 30 10 as shown in character format below 3 1129343209 2005 10 15 02 26 16 9814320 4886926900 These rows require 42 bytes The database for a 12 channel syst
129. ate format Time Format Combo Select time format Date Text Composite date and time value MJD Text Converted MJD value Help Pushbutton Invoke this help topic Copy MJD Pushbutton Copy MJD value to Windows clipboard Close Pushbutton Close Multicolumn Details dialog box e Operation Select the desired data file Line First or Last for display Rows in the table correspond to columns of the data file The columns of the table show the column numbers the raw data values as they appear in the file the parsed data values and their numeric values The number of columns appears at the left above the table The number of data lines in the file and the number of rejected lines is shown at the right above the table The currently active field delimiters and decimal point symbol are also shown Optionally it is possible to parse certain date and time formats and convert them to MJD First select the desired Date Column and then the Date Format Next as appropriate select the desired Time Column and Time Format The composite Date and time and the MJD including the fractional day if applicable is then shown The MJD may be copied to the Windows clipboard with the Copy MJD button When finished press Close to close the Multicolumn Details dialog box e Date and Time Formats The following date and time formats are supported Note that no separate time value is used with the UNIX and Excel date time formats Format Description
130. aution Be certain to enter the correct tau value for the phase and frequency data Many of the conversion and analysis functions depend on this value to obtain the correct results so enter the tau value immediately after the data is opened 12 GENERAL Function Keys e Purpose The Stable32 program uses the following function keys to provide rapid access to some of its functions Besides the standard F1 Help command the F2 F12 function keys provide another way to execute common commands and the Shift F1 key provides immediate access to the Stable32 User Manual The F2 F4 keys reopen previous phase or frequency data The F5 key performs a phase frequency conversion from the current data type which can be selected with the F12 key The F6 and F8 keys open the Edit or Statistics dialogs The F7 F9 F10 and F11 keys execute the Plot Run Power and Autocorrelation functions producing their respective plots with a single keystroke 13 14 STABLE32 USER MANUAL GENERAL Tabs e Data Tabs Stable32 has a data tab feature that supports the saving of phase or frequency data and their optional timetags in a row of up to 12 tabs buttons above the status and message bars at the bottom of the main screen These data tabs operate independently for phase and frequency data and can be created to save the current data manually or automatically whenever it changes Clicking on a tab then restores the data that it holds This is a conven
131. ave been reported on some systems if this is done See the Plot Options section for information about the cursor feature Launch PlayW and use it to make an unlimited number of copies of GraphiC plots as metafiles to the Windows clipboard 327 328 STABLE32 USER MANUAL Stability Analysis Repetitive Stable32 stability analysis procedures can be automated with WinBatch scripts This can save time assure consistency and allow the analysis to be done by less experienced personnel see batch Files below Time can be saved and errors avoided during a complex analysis by first setting up the data and plot filenames with the Files function Enter the tau value in the Data File Opened dialog box as a PhaseTau or FreqTau Inputs item in the configuration file or automatically using timetag data without the Inputs values In the latter case the tau value can be scaled to seconds with the TagScale Inputs item The resulting tau value may have some small rounding error Observe the blue symbol at the top center of the status bar that indicates if the two data types are synchronized Large Data Sets The most important factor for analyzing large data sets with Stable32 like most Windows applications is RAM memory size not processor speed If possible average large data sets before beginning an analysis run Use the Stop button on All Tau runs if the full results are not needed at longer averaging factors The maximum size data file
132. averaging times A statistic for analyzing stability at large averaging factors extending out to 75 of the record length A bias removed version of Th ol A hybrid version of Th ol combining Th oBR with the Allan variance The time interval error of a clock Can be expressed as the rms time interval error TIE rms or the maximum time interval error MTIE OTHER INFORMATION Total Variance A 2 sample variance similar to the Allan variance with improved confidence at large averaging factors x t The instantaneous time deviation from a nominal time x t Q t 2nvo seconds where vo is the nominal frequency Hz This dependent time variable is often called phase to distinguish it from the independent time variable t y t The instantaneous fractional frequency deviation from a nominal frequency y t v t vo vo x t where vo is the nominal frequency 283 STABLE32 USER MANUAL 284 OTHER INFORMATION References References The following references are recommended to support the use of the Stable32 program for the analysis of frequency stability 10 11 12 13 14 15 16 17 18 19 20 21 22 General Special Issue on Frequency Stability Proc IEEE Vol 54 Feb 1966 J A Barnes Atomic Timekeeping and the Statistics of Precision Signal Generators IEEE Proceedings vol 54 pp 207 219 Feb 1966 Proc IEEE Vol 55 June 1967 G E P Box and G M J
133. ay to the mask label because it is the means for the user to select it The mask file must reside in the same directory as the Stable32 exe executable file that launched the program Any number of such files can exist and are available for selection in the Run Plot Lines dialog Example of mask file test msk Test mask to use with PHASE DAT test data TDEV plot 3 10 5 5 Test Mask 1 5 105 100 5 251 STABLE32 USER MANUAL Eile Edit Draw Convert Help Dale 11 04 05 Time 09 47 40 Dala TIME STABILITY Filer PHASE DAT gt PHASE DAT Uu ti e o o nA al o gt sg I i i idioma E Sigma E 1 69e 01 o 1 83e 01 A 2 49e 01 o 3 43e 01 3 82e 01 E kad 6 32e 01 1 03e 00 1 38e 00 10 2 10 2 10 2 103 Averaging Time T Seconds 252 ANALYSIS FUNCTIONS Run Notes Function e Purpose Use the Run Notes function to add annotations to a stability plot Run Plot Notes rx Note Up Point Size E OK Iv Border M Opaque s Text Cance Note amp H E Clear All A Position Notes 1 E Read Save e Controls The Run Notes dialog box contains the following controls Control Type Description Note Edit Enter the of the note to edit Up Pushbutton Increment the note Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of th
134. because white and flicker phase noise have the same Allan variance t dependence When performing any of these conversions it is necessary to choose a reasonable range for o and t in the domain being converted to The main lobe of the o t and Mod o t responses occur at the Fourier frequency f 1 21 e Domains Conversions Domain conversions may be made for power law noise models by using the following conversion formulae Noise Type o x S f RW FM A f S f t Alt o af F FM B f SO B 12 os f WFM C f S H 17 C t o 1 f F PM D f S f t D t cQ f W PM E f S 8 1 E 1 401 where A 47 6 B 2 1n2 C 12 D 1 038 3 In 2nf t 4n E 3f 472 and f is the upper cutoff frequency of the measuring system in Hz and ty is the basic measurement time The fj factor applies only to white and flicker PM noise 117 STABLE32 USER MANUAL 118 FILE FUNCTIONS File Functions e Purpose Stable32 offers several functions for setting opening adding saving and reading data files The Open function applies to phase frequency and archive data files the Add and Save functions apply to phase and frequency data files and the Read function is used to read a stability file e Controls The Stable32 Open Add and Save file functions use the standard Windows file open and save dialog boxes except that the Open and Add dialog boxes contain the following additional contro
135. bobox Type of variance to use Stability Plot Checkbox Plot stability on screen Print Stability Plot 7 Checkbox Print sigma tau plot Print Table 8 Checkbox Print sigma tau table Close X Checkbox Close last screen at end of script Add Delay 9 Checkbox Add delay between steps to see results msec Edit Amount of delay to add in msec Script Name Edit Name of automation script Go Pushbutton Close dialog box amp execute script OK Pushbutton Save script amp close dialog box Cancel Pushbutton Abort the Auto function Help Pushbutton _ Invoke this help topic 266 MISCELLANEOUS FUNCTIONS e Manual Use The Auto functions may be used manually by setting the desired analysis steps and either saving them by pressing OK or executing them by pressing Go Pressing Cancel aborts any changes made The analysis functions are the same as provided for a non automated Stable32 analysis The automation script options are interlocked so as to simplify their selection All reasonable combinations are allowed but their order may not be changed Default timetag and data columns are used for multicolumn data The Close checkbox determines whether the last result remains on the screen Extra delay may be added with the Add Delay and msec controls to allow viewing of the intermediate results e Command Line Use The Auto functions may be invoked from the command line with the o autol o auto2 or o auto3 options When in
136. btain the final PSD result The averaging factor can be selected in integer power of 2 increments which improves the PSD standard deviation by the square root of the averaging factor The tradeoff in this averaging process is that each section of the data is shorter yielding a result with coarser frequency resolution that does not extend to as low a Fourier frequency The Auto AF periodogram PSD plot option uses a variable power of 2 series of averaging factors that increase from 1 to a default maximum of N 64 or 256 whichever is less where N is the of data points raised to the next higher power of 2 as the Fourier frequency increases The sequence of PSD points have averaging factors of 1 2 4 8 up to that maximum unless the first points are skipped see below This allows the analysis to extend down to the lowest possible Fourier frequency while reducing the PSD variability at higher frequencies The maximum AF used for the PSD plot is shown in the message box unless another message has been entered The PSD standard deviation at the upper Fourier frequencies is equal to 100 VMax AF 203 STABLE32 USER MANUAL e Multitaper PSD Analysis The Stable32 Power function also includes a multitaper PSD analysis method that offers a better compromise between bias variance and spectral resolution Averaging is accomplished by applying a set of orthogonal windowing tapering functions called discrete prolate spheroidal sequences DPSS or S
137. ce at Long Term Proc 1995 IEEE Int Freq Cont Symp June 1995 pp 321 329 2 D A Howe and K J Lainson Simulation Study Using a New Type of Sample Variance Proc 1995 PTTI Meeting Dec 1995 pp 279 290 3 D A Howe and K J Lainson Effect of Drift on TOTALDEV Proc 1996 Intl Freq Cont Symp June 1996 pp 883 889 4 D A Howe Methods of Improving the Estinmation of Long term Frequency Variance Proc 1997 European Frequency and Time Forum March 1997 pp 91 99 5 D A Howe and C A Greenhall Total Variance a Progress Report on a New Frequency Stability Characterization Proc 1997 PTTI Meeting Dec 1997 pp 39 48 6 D B Percival and D A Howe Total Variance as an Exact Analysis of the Sample Variance Proc 1997 PTTI Meeting Dec 1997 pp 97 105 7 C A Greenhall D A Howe and D B Percival Total Variance an Estimator of Long Term Frequency Stability JEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 46 No 5 pp 1183 1191 Sept 1999 8 D Howe and T Peppler Definitions of Total Estimators of Common Time Domain Variances Proc 2001 Intl Freq Cont Symp June 2001 pp 127 132 70 TIME DOMAIN STABILITY Total Modified Variance e Total Modified Variance The total modified variance TOTMVAR is another new statistic for the analysis of frequency stability It is similar to the modified Allan variance MVAR and has the same expected value but offers improved
138. ce the proper size Zoom Out box is chosen clicking the right mouse button will start the drawing of the entire plot in the zoom box selected The zoomed out plot can then be printed or converted Redraw or a space key will redisplay the original plot before it was zoomed GENERAL The Convert menu s Bitmap command is used to generate a Windows Bitmap BMP file from the current plot The user may select the client Bitmap area plot only entire Play window or entire screen to include in the bitmap The Bitmap file may then be used by other applications such as desktop publishing packages The Convert menu s Metafile command is used to generate a Windows Metafile WMF file from the current plot A dialog box is displayed that prompts the user for the file name and page orientation The page Metafile orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The metafile file once generated may then be used by other applications such as desktop publishing packages Convert The Convert menu s PostScript command is used to display a PostScript conversion dialog box to select the filename and type of PostScript file to be produced The user is asked to select either Encapsulated PostScript PostScript with or without a TIFF image embedded PostScript level 1 or 2 page orientation color separations and font The page orientation refers to which side left right or top of
139. cel Help m HA Print Clear All Read Save Bead Save Lines 1 Sigma ly 11 00157e 02 e Controls The Read Lines dialog box contains the following controls Some parameters do not apply to all line types Control Type Description Line Edit Enter of line to edit Up Pushbutton Increment line Down Pushbutton Decrement line Type Combo Select line type Tau Group X Axis line parameters Start Edit Combo Enter x axis start of line End Edit Combo Enter x axis end of line Sigma Group Y axis line parameters Start Edit Enter y axis start of line End Edit Enter y axis end of line 159 STABLE32 USER MANUAL Control Type Description Slope Combo Noise type for fit Sigma 1 Text Noise line fit parameter Lines Text of lines entered OK Pushbutton Perform Read Lines function amp close dialog box Cancel Pushbutton Abort Read Lines function close dialog box Help Pushbutton Invoke the Read Lines help topic Print Pushbutton Print line parameters Clear All Pushbutton Clear all lines Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file e Operation Select the desired Line and Type Enter the applicable Tau Start Tau End Sigma Start and Sigma End parameters Choose the applicable Slope for a Noise Line and press OK to accept th
140. choice of proceeding or canceling Eod nd ma e Caution Data added should have the same tau as the current data 143 STABLE32 USER MANUAL 144 FILE FUNCTIONS Database Function e Purpose Use the Database function to select read and save clock data from a Symmetricom previously Timing Solutions Corporation Multichannel Measuring System MMS database TSC MMS Database x Mms chi Stat Time EndTime 2005 10 14 22 41 42 2005 10 14 21 54 19 Run Continuing 02 2005 10 17 15 46 20 Reference Measurement Glock Neme Cesium Clock Name Decription Cs Clock Decription Rb Clock m Records Reference Measurement IMMS Ch StetTime EndTime 2005 10 14 22 41 58 Run Continuing Meas Info measurement Details Reset UTC C MJD m Read Times Tau sec _ Read UTC MJD Meas M Start 2005 10 14 22 41 58 53657 94581 0 Tau as Saisie End Both Runs Continuing AE ep cisci ca Read to extract data _ Cancel Span 83d 9h 59m 42s amp 72071 82 Bead a from MMS database ei e He e Controls The Database function main dialog box contains the following controls Control Type Description Reference Groupbox Reference clock information Clock Name Combo Select name of desired reference clock Description Text Shows description of selected reference clock Measurement Groupbox Measurement clock information
141. combination The Save Current Data command Rename Selected Tab creates a new tab for the current data The Rename Selected Tab command renames the data file of the Write Selected Tab selected tab The Write Selected Tab command writes the data of the selected tab to disk The last group of Close Selected Tab two items contains the Close Selected Tab and Close Close All Tabs All Tabs commands to remove either the selected or all of the data tabs and free their memory Clicking on a tab selects it and reloads its data for analysis This can also be done by moving between the tabs with the left or right arrow keys or using the Home and End keys move between the first and last tabs respectively and pressing the spacebar To select a tab without loading its data press the CTRL key while clicking the tab The only significant disadvantage of the data tabs is that they require allocated memory to hold their data and this can take a significant amount of RAM for many tabs with large data sets 15 STABLE32 USER MANUAL e Tab Toolbutton The Tab toolbutton can be used to activate the data tabs and store the current data to a new tab 16 GENERAL Data Format e Data Format Stable32 data files are comprised of essentially any number 513 in Student Version of lines of numeric data in ASCII format with each line terminated by a carriage return line feed Such a file can be read and edited with Windows Notepad The data may be
142. crete FM is modified to use the peak Af g T f where g is the peak applied g level T is the acceleration sensitivity of the device expressed as a fractional frequency per g and f is the nominal carrier frequency For random vibration the vibration PSD in g Hz is used instead of the g and the resulting phase noise is expressed as dBc Hz Note that both the applied vibration and the vibration sensitivity of most devices is directional e References J R Vig Introduction to Quartz Frequency Standards R L Filler The Acceleration Sensitivity of Quartz Crystal Oscillators A Review IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control Vol 35 No 3 pp 297 305 May 1988 3 IEEE Guide for Measurement of Environmental Sensitivities of Standard Frequency Generators IEEE Standard 1193 2003 Ne e See Also Power Function 274 MISCELLANEOUS FUNCTIONS Calendar Function e Purpose Use the Calendar function to display a monthly calendar showing the Day of Year DOY and Modified Julian Date MJD The MJD can be used as a timetag for phase or frequency data It is common to append the decimal fraction of a day to the MJD integer to indicate the exact date date and time When this is done the time is usually UTC Calendar x GPS Weeks 171 176 December 2002 EE Year Up Thu i Year Down 336 337 438 5 339 6 Bao 52610 as 52612 52613 52614 Monk UR 3 p43s fiofsaa 1 345 fejas 3 347 Month Down
143. ct the next time the Stable32 program is started e Caution Stable32 may be run without a STABLE INI file but no toolbuttons will be displayed Use the Configure function to select the desired toolbuttons A STABLE INI file will be generated automatically when the program is closed 57 58 STABLE32 USER MANUAL TIME DOMAIN STABILITY Time Domain Stability e Time Domain Stability Stable32 implements the following measures of time domain frequency stability Statistic Name Symbol Description Allan Variance 7 Based on square of 1st differences of fractional frequency deviation values Modified Allan Variance Mod 0 t Based on square of 2nd differences of averaged phase deviation values Total Allan Variance O total T Based on square of 1st differences of fractional frequency deviations of an extended data set Total Modified Variance Mod o u x Based on square of 2nd differences of averaged phase deviations of an extended data set Time Variance o 1 Equal to 1 3 Mod Allan variance Total Time Variance O total T Total version of time variance Hadamard Variance Ho t Based on square of 2nd differences of fractional frequency values Total Hadamard Variance Ho t Total version of Hadamard variance Theoretical Variance 1 Th ol Allan estimator for large avg factor Bias Removed Th ol Th oBR Same expected value as Allan variance Allan amp Th ol H
144. ction to calculate Allan or Hadamard variance statistics for the selected portion of the current phase or frequency data at a single averaging time The Run function is available for performing these calculations over a range of averaging times Variance Type Overlap Allan Calc Avg Factor Close E Help Sigma 2 921983e 01 E gy Das calculate selected Show Details dd e Controls The basic Sigma dialog box contains the following controls Control Type Description Variance Type Combo Choose desired variance type Avg Factor Edit Enter averaging factor Sigma Text Display Sigma result Show Details Checkbox Select detailed Sigma dialog box format Calc Pushbutton Calculate sigma Close Pushbutton Close Sigma dialog box amp restore previous data Help Pushbutton Invoke this help topic Activating the Show Details option adds the following controls to the Sigma dialog box Control Type Description Variance Parameters Groupbox Variance information BW Factor Edit Enter bandwidth factor Tau Text Display tau Sigma Results Groupbox Sigma information Std Dev Text Display standard deviation Noise Type Groupbox Power law noise information Bias Ratio Text Display B1 R n or Bias ratio Noise Text Display estimated noise type Alpha Text Display estimated a value 195 STABLE32 USER MANUAL
145. ctrum White Header inl Reset Autocorrelation NX r Plot Label These parameters control the reading and writing of phase or freq data files The Max Data File Size is not an IV Label Plots Label Stable32 NX absolute program limit but determines when the averaging box opens automatically See Help file for more information Cancel Help Page 3 Plots Page 4 Data e Plots Page Controls The Plots property sheet page contains the following controls Control Type Description Read Plot Info Groupbox Select plots for which to read configuration info Phase Checkbox Check to read config information for phase data plot Frequency Checkbox Check to read config information for freq data plot Sigma Checkbox Check to read config information for stability plot Dynamic Stab Checkbox Check to read config info for dynamic stability plot Histogram Checkbox Check to read config information for histogram plot Spectrum Checkbox Check to read config information for spectrum plot Autocorrelation Checkbox Check to read config info for autocorrelation plot 50 GENERAL Control Type Description Plot Settings Groupbox Select settings for plots Use Smart Scales Checkbox Use smart y axis scales for data plots Weight Sigma Plot Fits Checkbox Weight power law noise fits on stability plot Plot Label Groupbox Select and enter settings for plot labels Label Plot
146. d save the resulting phase data Then read this RW FM phase data as frequency data and convert it to a new set of RR FM phase data e Sine Generation The Sine peak and Sine Period controls allow entry of the fractional frequency amplitude and period seconds of a sinusoidal component to be added to the simulated noise A finite amount of noise must still be included to avoid zero sigma These parameters are useful for simulating the effect of a periodic disturbance such as temperature or vibration The phasing is that of a positive sinusoid on the fractional frequency data No sinusoidal component is added unless both the peak value and period are non zero e Memory Usage Noise generation is a memory intensive process that requires about 48 bytes of peak memory usage per data point Large data sets can therefore involve relatively slow virtual hard drive swap memory e Caution The results from the Noise function overwrite the current data in the phase and frequency arrays e Example An example of the frequency stability of simulated data with a combination of white PM noise and a sinusoidal term is shown below 232 ANALYSIS FUNCTIONS FREQUENCY STABILITY A Allan Deviation Degradation 10 0 7 1079 ti sii pos Allan Deviation a pest CIVIL a LE an ER E f m 3 gt R 1 n H r 1 o gt pais S Os g 2 x 9 3 x amp 1x 2 Si iili i ill 103 2 1072 2 107
147. d to the data Or automatically insert the negative of the Ist Value or Average into the Addend or the negative of the Linear slope into the Slope Then Press OK to scale the data Reverse to reverse the data or Cancel or OK with defaults to abort 181 STABLE32 USER MANUAL e Scaling Equation The data is scaled according to the following equation Scaled Value Original Value Multiplier Addend Slope Data Point e Data Reversal Data reversal is particularly useful in conjunction with the frequency jump detection and analysis function where it can provide a better average location estimate for a frequency jump Repeating the reversal will restore the original data e Caution It is possible to scale only a portion of a data array but this is unlikely to produce a satisfactory overall result 182 EDITING FUNCTIONS Part Function e Purpose Use the Part function to clear all except a portion of the current phase or frequency data The Part function changes the data in memory Use the analysis limits on the status bar to temporarily change the range of the data to be analyzed Part Data Range Point Timetag Start hi m Date 2001 05 07 Time 14 35 10 Close End 96761 Date 2001 05 18 Time 19 21 50 Help ddi Timetag Type KS Press OK to remove all except selected Date part of data e Controls The Part dialog box contains the following controls
148. deally the reference noise would be low enough that its contribution to the measurement is negligible Or if the noise of the reference is known it can be removed by subtracting its variance A special case is that of two identical units where half of the measured variance comes from each and the measured deviation can be corrected for one unit by dividing it by 2 Otherwise it may be useful to use the so called 3 cornered hat method for separating the individual variances Given a set of three pairs of measurements for three independent freguency sources a b and c whose variances add ap Oa 0 Oac Ga 0 Ooc 0 0 The individual variances may be separated by the expressions 02 Y Sab ka ac Orc 0 Y Sab SS be z ac 0 Y ac y 0 be i ap Although useful for determining the individual stabilities of units having similar performance the method may fail by producing negative variances for units that have widely differing stabilities if the units are correlated or for which there is insufficient data The three sets of stability data should be measured simultaneously The 3 cornered hat method should be used with discretion and it is not a substitute for a low noise reference It is best used for units having similar stability e g to determine which unit is best Negative variances are a sign that the method is failing because it was based on insufficient measurement data or because the units under test have d
149. dom for the processed data The former requires maximum and minimum sigma data while the latter requires that the number of measured degrees of freedom be available The availability of these data are indicated by their respective MM and DF indicators e Reference Noise Removal The 3 Cornered Hat function can also be used to remove the contribution of a reference whose noise is known apriori either from its specification or by a separate determination Denote the device under test as unit A and the known reference as units B and C Enter the measured data as both A B and A C multiply the stability data for the reference by 2 and enter it as B C After the 3 cornered hat calculation the corrected stability data for the unit under test will be in column A e Results Data Files Three data files containing the results of a 3 cornered hat calculation are written to disk in the same folder as the original data These files named UnitA sig UnitB sig and UnitC sig have the same stability file format as the input file see Read Function e Caution Do not use results that contain negative variances The 3 cornered hat method is not a substitute for a low noise reference It is best used for units having similar stability e g to determine which unit is best Negative variances are a sign that the method is failing because it was based on insufficient measurement data or because the units under test have disparate stability Plots containi
150. e 00 Multiplier 1 0000000000000e 00 1 0000000000000e 00 Tag Scale 8 6400000000000e 04 1 0000000000000e 00 Tag Offset 0 0000000000000e 00 0 0000000000000e 00 Enter data input scaling values Tau sets data sampling interval sec Addend and multiplier modify data values For example use 16 9 multiplier to convert data to nsec Tag scale and offset modify tau value Use 86400 as tag scale to convert MJD timetags into seconds Cancel Help Page 5 Inputs r PSD Auto AF Parameters PSD Smoothing Parameters BelativeMaxAF 64 TO Weight Smoothed PSD Fit absolute MaxaF 255 Baniv aeve 194 ae PonsTo fT psp Zero Padding Stability Plot Spur Threshold 40 a Restore PSD Defaults Reset Restore Many Tau Size Reset Enter PSD Auto AF and Smoothing values All except LF Points must be a power of 2 Use Reset button to restore defaults Select other PSD parameters as desired IV Many Tau Size 500 Select enter stability plot Many Tau option size as desired Use Reset to restore default size Cancel Help Page 6 Options 51 STABLE32 USER MANUAL e Inputs Page Controls The Inputs property sheet page contains the following controls Control Type Description Scaling Values Groupbox Data input and timetag scaling values for phase and frequency data Tau Edit Tau value in seconds Addend Edit Value to add to data
151. e 01 ACF Noise ID Std Dev 2 885205e 01 Min ADEV Not Applicable m 0987 Noise Type Alpha 0 05 81 Ratio 0 975 Noise WFM Alpha 0 Mu H Apply m Dead Time T Tau fi 00 B2 B3 gw Press Calc to calculate sigma 196 ANALYSIS FUNCTIONS e Variance Types The Allan and Hadamard variances are the principal method for describing the stability of a frequency source in the time domain Those variances and other statistics may be calculated as shown in the table below Variance Abbreviation Symbol Normal AVAR s t Overlapping AVAR s t Modified MVAR Mod s t Time TVAR s t Total TOTVAR Sot Modified Total MTOTVAR Mod S ota1 t Time Total TTOTVAR S oat Hadamard HVAR s y t Overlapping Hadamard HVAR s y t Hadamard Total HTOT Htotai t RMS Time Interval Error TIE rms Maximum Time Interval Error MTIE Theoretical Variance 1 and its variants Th ol Th oBR and Th oH The Type column shows the variance types of the Sigma function list These short original Stable32 names are retained to avoid breaking batch files The currently accepted names and abbreviations for these variance types are shown in the Variance and Abbreviation columns These are all functions of the averaging time t and are usually expressed as their square roots the deviation or sigma oy t Mod 6 t 6 t Hoy t Stora t
152. e 02 T No Drift Freq Drit Day 5 608146e 01 Dead Time roo Press Calcto calculate C 1of2 T Tau 0n Xe selected variance type C All Teu Controls The Run dialog box contains the following controls Control Type Description Variance Type Combo Choose variance type Alpha Combo Choose automatic or specific alpha value Conf Factor Edit Enter desired confidence factor Results Table Display results of stability run Drift Day Text Display linear frequency drift Plot Pushbutton Plot stability results Print Pushbutton Print stability results Not available for All Tau Options Pushbutton Open Run Options dialog box Lines Pushbutton Open Run Lines dialog box Notes Pushbutton Open Run Notes dialog box No Drift Checkbox Remove frequency drift from data lof2 Checkbox Scale results for 1 of 2 identical units Start AF Edit pre run Enter starting averaging factor for run Dead Time Edit Enter T Tau dead time ratio 237 STABLE32 USER MANUAL Control Type Description Decade Radio Button Select decade tau increments Octave Radio Button Select octave tau increments All Tau Radio Button Select all tau increments or Fast u Select fast MTIE method Calc or Resume when Pushbutton Calculate table of stability statistics stopped Resume stopped run Copy Pushbutton Copy results to clipboard Close or Close di
153. e Frequency Stability of an Individual Oscillator Proc 28 Freq Contrl Symp pp 243 246 May 1974 J Groslambert D Fest M Oliver and J J Gagnepain Characterization of Frequency Fluctuations by Crosscorrelations and by Using Three or More Oscillators Proc 35th Freg Contrl Symp pp 458 462 May 1981 S R Stein Frequency and Time Their Measurement and Characterization Chapter 12 Section 12 1 9 Separating the Variances of the Oscillator and the Reference pp 216 217 Precision Frequency Control Vol 2 Edited by E A Gerber and A Ballato Academic Press New York 1985 ISBN 0 12 280602 6 P Tavella and A Premoli Characterization of Frequency Standard Instability by Estimation of their Covariance Matrix Proc 23rd PTTI Meeting pp 265 276 Dec 1991 P Tavella and A Premoli A Revisited Tree Cornered Hat Method for Estimating Frequency Standard Instability ZEEE Trans Instrum Meas IM 42 pp 7 13 Feb 1993 C R Ekstrom and P A Koppang Error Bars for Three Cornered Hats JEEE Trans UFFC Vol 53 No 5 pp 876 879 May 2006 W J Riley Application of the 3 Cornered Hat Method to the Analysis of Frequency Stability Hamilton Technical Services Domain Conversion A R Chi The Mechanics of Translation of Frequency Stability Measures Between Frequency and Time Domain Measurements Proc 9th Annu PTTI Meeting pp 523 548 Dec 1977 J Rutman Relations Between Spectral Purity and
154. e Play W program to redisplay a previous GraphiC TKF plot 32 C stable32 noisepix tkf e Operation Consult the Play W help topics for information regarding that program e Note The Play W program is not included with all versions of the Stable32 software package 279 STABLE32 USER MANUAL 280 Glossary e Glossary OTHER INFORMATION The following terms are used in the field of frequency stability analysis and the Stable32 program Aging Allan Variance Averaging Averaging Time BW Confidence Limit Drift Dynamic Stability Frequency Data Hadamard Variance f MJD Modified Sigma MTIE The change in frequency with time due to internal effects within the device The 2 sample variance 02 t commonly used to measure frequency stability The process of combining phase or frequency data into samples at a longer averaging time See Tau Bandwidth Hz The uncertainty associated with a measurement Often a 6896 confidence level or error bar The change in frequency with time due to all effects including aging and environmental sensitivity A form of the Allan variance showing the stability versus time A set of fractional frequency values y i where i denotes equally spaced time samples A 3 sample variance HVAR that is similar to the 2 sample Allan variance It uses the 2nd differences of the fractional frequencies and is unaffected by linear frequency drift The
155. e cycling 302 OTHER INFORMATION Validation e Validation Considerable effort has been taken to insure that the results obtained from Stable32 are correct In particular each of the six validation methods listed below have been employed Stable32 uses the same basic analysis functions of Stable DOS and the FrequenC Library both of which have been used extensively by a number of individuals and organizations for over ten years In addition feedback and peer review has been and still is encouraged Please report any suspected discrepancies A convenient way to do this is via the Feedback item under the Help menu One important validation method is comparison of the program results against the test suite described above Copies of the NBS and 1000 point test data are included with the Stable32 distribution e Validation Methods Several methods were used to validate the Stable32 frequency stability analysis software 1 Manual Analysis The results obtained by manual analysis of small data sets such as NBS Monograph 140 Annex 8 E were compared with the program output 2 Published Results The results of published analyses were compared with the program output 3 Other Programs The results obtained from other specialized stability analysis programs such as that from a previous generation computer or operating system were compared with the program output 4 General Programs The results obtained from industry standard gener
156. e data sets Stable32 always initializes the Append flag to the off position thus assuring that the first stability file will be a new one After each run the Run Plot Options dialog box may be opened to change the Append flag thus allowing the results multiple runs to be combined New phase or frequency data may be opened the current data may be manipulated or the run parameters may be changed between the runs that are combined e g to compare different data sets preprocessing steps or variances e Run Messages Messages describing all noise fits are available by exposing the run message drop down list 247 STABLE32 USER MANUAL 248 ANALYSIS FUNCTIONS Run Lines Function e Purpose Use the Run Lines function to add lines to a stability plot The possible line types are as follows ene Description Parameter None No line None Endpoints Line between certain endpoint values None Horizontal Horizontal line at certain sigma value None Vertical Vertical line at certain tau value None Noise Fit to certain power law noise model Sigma 1 Run Plot Lines EI Line fi Up Noise Down Tau Start 9 000008 02 start Print b K End End fi 15200e 05 nd Cleer All Noise Line Slope Pos WFM y Sigma l 9 53214e 09 Cancel Help Ep E E Read Save Lines 1 e Controls The Run Line dialog box contains the following controls Some parameters do
157. e info to INI file Clear All Pushbutton Clear all lines Print Pushbutton Print all line parameters Copy Pushbutton Copy line info to clipboard OK Pushbutton Accept changes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke this help topic e Operation Select the desired Line and Type The Enter the X Axis Start X Axis End Y Axis Start and Y Axis End values as applicable and press OK to accept them or Cancel to abort Press Clear All to clear all lines Copy to copy the line parameters to the clipboard or Print to print the line parameters 226 ANALYSIS FUNCTIONS Plot Notes Function e Purpose Use the Plot Annotations function to add annotations to a data plot Phase Plot Notes x Note 1 E Up Point Size fe OK Down Iv Border M Opaque T Help Clear All JA Position Notes 0 x 0 00000e 00 Y 0 00000e 00 Bead Save Tex e Controls The Plot Annotations dialog box contains the following controls Control Type Description Note List Select the of the note to edit Up Pushbutton Increment the note Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of the note Position Groupbox Note position values X Edit Enter the x position of the note Y Edit Enter the y
158. e intervals For the Th ol and Th oH variance types the Auto BR option invokes the Th oBR Bias Removed algorithm for automatic bias correction and noise identification that provides the best average match to the ADEV results The Auto BR algorithm is computationally intensive and can be stopped to shorten the analysis time If those runs are interrupted and resumed their bias corrections will be based on only the first portion which begins at the longest averaging factor e Dead Time Bias correction for measurement dead time is available for the normal and overlapping Allan variances when the noise type is manually selected Enter the T Tau dead time ratio where tau is the measurement time and T is the time between measurements Dead time corrections are made using the B2 and B3 bias ratios which handle cases of single and multiple distributed measurement dead time respectively e Auto Calc A run can be done automatically when the Run function is invoked by setting the AutoCalc item in the Configure function 240 FPOWPOANEH ANALYSIS FUNCTIONS e Stability File A stability file with a default name of sigma tau is written to disk after each run This file contains sigma tau and errorbar data as described in the Read Function help topic and may be used to document or replot the stability results It may even be used to create a stability plot with another program such as Gnuplot as shown below Frequency Stability ES
159. e lines or Cancel to abort Press Clear All to remove all lines 160 READ FUNCTIONS Read Notes Function e Purpose Use the Read Notes function to add annotations to a stability plot Read Plot Notes x Note Up Point Size E OK Down Y Border 5 Iex Cance Note 1 m zl Clear All Position Notes 1 id v p 00000e 00 Read Save e Controls The Read Notes dialog box contains the following controls Control Type Description Note Edit Enter the of the note to edit Up Pushbutton Increment the note Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of the note Position Group Note position values X Edit Enter the x position of the note Y Edit Enter the y position of the note Notes Text notes entered Border Checkbox Draw a border around the note Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file OK Pushbutton Accept the settings close dialog box Cancel Pushbutton Abort the changes close dialog box Help Pushbutton Invoke the Read Notes help topic Clear All Pushbutton Clear all notes 161 STABLE32 USER MANUAL e Operation Enter the desired plot annotations and press OK to accept them or Cancel to abort Press Clear All to clear all annotations 162 EDITING FUNCTIONS P
160. e method for identifying power law noises based on the properties of discrete time fractionally integrated noises having spectral densities of the form 2 sinnf 1 For 8 Y the process is stationary and has a lag 1 autocorrelation equal to p 9 1 6 and the noise type can therefore be estimated from 6 r 1 r For frequency data white PM noise has p 1 2 flicker PM noise has p 1 3 and white FM noise has p 0 For the more divergent noises first differences of the data are taken until a stationary process is obtained as determined by the criterion 8 lt 0 25 The noise identification method therefore uses p round 28 2d where round 28 is 28 rounded to the nearest integer and d is the number of times that the data is differenced to bring 8 down to lt 0 25 Ifz is a t average of frequency data y t then a p if z is a t sample of phase data x t then a p 2 where a is the usual power law exponent f thereby determining the noise type at that averaging time When there are a sufficient number of data points this method has excellent discrimination for all common power law noises for both phase and frequency data including difficult cases with mixed noises The dominant power law noise type can also be estimated by comparing the ratio of the N sample standard variance to the 2 sample Allan variance of the data the B1 bias factor see below to the value expected of this ratio for the pure noise ty
161. e note Position Groupbox Note position values x Edit Enter the x position of the note Y Edit Enter the y position of the note 7 Notes Text Notes entered Border Checkbox Draw a border around the note Opaque Checkbox Hide grid in note area Read Pushbutton Read note info from INI file Save Pushbutton Save note info to INI file Clear All Pushbutton Clear all notes OK Pushbutton Accept the settings amp close dialog box Cancel Pushbutton Abort the changes amp close dialog box Help Pushbutton Invoke this help topic 253 STABLE32 USER MANUAL e Operation Enter the desired plot annotations and press OK to accept them or Cancel to abort Press Clear All to clear all annotations 254 ANALYSIS FUNCTIONS Dynamic Stability Function e Purpose Use the Dynamic Stability DVAR function to perform a dynamic Allan or Hadamard variance DAVAR or DHVAR stability analysis A dynamic stability analysis is useful to show stability changes nonstationarity noise bursts and other aspects of clock behavior Dynamic Stability Plot x Title DYNAMIC STABILITY y Help Plot SubTitle PHASE DAT v Reset All Close Message y Plot Calc Message Position Top Right Read Config Save Config Plot Filename CADAVAR TKF AGA XAxis Label p Y Axis Label Z Axis Label Vert View Log AF Window Log Sigma E Up Settings Variance Horiz View E 5 AVAR
162. e phase number by the nominal frequency in MHz Corrected clock time is obtained from that value by subtracting the corresponding value for the reference channel This subtraction removes the contribution of the common offset local oscillator Fractional frequency is of course the difference between two adjacent time values divided by the time interval between them e Archive File Processing Clock data for a certain time span can be extracted directly from TSC archive files by choosing the desired measurement and reference channels and then reading an archive file that has data for those sources during that period TSC archive file data can be processed either by using data from two measurement channels one serving as the reference or by using the common offset local oscillator LO as the reference In the former case the contribution of the offset LO cancels out Using the LO as the reference usually requires that it be synthesized from a standard source rather that being a free running crystal oscillator but measurements against a low noise crystal source can be an advantage for short averaging times An important feature of the TSC clock measuring system is that the reference for a particular measurement channel can be chosen after the fact and a single archive file can provide data versus several references Stable32 can process TSC archive data either between two measurement channels or between a single channel and the offset LO The
163. e plot line flag 0 Y Tic y axis tics 5 Date Date annotation flag 0 Box Draw box around plot flag 0 Fit Draw fit line flag 0 Points Show PSD points on plot flag 1 PSD PSD type 0 WinType FFT windowing type 1 Win FFT windows 1 Mouse Mouse flag 0 Info Show PSD info on plot flag 0 Y Min Y axis scale minimum value Null Y Max Y axis scale maximum value Null Freg Carrier frequency Hz 0 320 APPENDICES e HistoPlot The HistoPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null Position Message position 0 e AutoPlot The AutoPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null Position Message position 0 Wide Use wide plot line flag 0 Date Date annotation flag 1 Box Draw box around plot flag 1 Zero Draw horizontal line at 0 flag 1 Lagl Show lag k scatter plot flag 1 Lag Scatter plot lag 1 Lags lags on plot 1 Mouse Mouse flag 0 AutoFile ACF data filename Null PlotFile ACF TKF plot filename Null AF Averaging factor 1 AXDefault Flag to set x axis scale to default 1 e DAVARPIot The DAVARPlot section of the STABLE32 INI file can contain t
164. eeks Weeks Tau 604800 DOY Days Same as days if no timetags DOY with year if timetags MJD Days Same as days if no timetags MJD coarse MJD if timetags Timetag Point Regularized data point Selecting the x axis label automatically sets the x axis offset and multiplier If there are timetags they are automatically used to annotate the year and MJD The units for the x axis offset are those of the data points The x axis start and end controls may be used to select a portion of the data for plotting The Timetag Point option is available only for data with associated timetags It offers a preview of how the data will look if regularized to show gaps indicated by the timetags The Timetag Point x axis scale automatically changes to the x1000 mode as necessary The plot lines are not available for this option but the fit lines may be used Use the Regularize function to prepare the data for further analysis 219 STABLE32 USER MANUAL e Curve Fits The Options Type control offers several choices for curve fits as shown in the following table Fit Type riim Description None Both No curve fit Linear Frequency y a bt Quadratic Phase x a bt ct Log Frequency y a In bt 1 c Diffusion Frequency y a b t c Average Both x X y y Polynomial Both x ory Zad ti Function Both General x t or y t Jumps Frequency Detect freq jumps The Fit checkbox controls the display of the fit param
165. efault name AUTO DAT and must be manually renamed before the next plot to save it An example of the first 5 lines of an AUTO dat file is shown below 9 99654114e 01 1 59891486e 01 5 67231514e 02 4 17460054e 02 4 83987387e 03 SO NDIPO e Notes The autocorrelation sequence is calculated using the Fast Fourier Transform FFT which produces autocorrelation points at lags up to one half of the data length The phase or frequency data is averaged by the entered averaging factor to the corresponding tau before the autocorrelation is calculated Gaps in the data are filled with interpolated values before the analysis which can result in linear features on the lag scatter plot for a group of gaps The autocorrelation plot can be restricted to fewer points to better show values at smaller lags The autocorrelation sequence is most useful for determining the non whiteness of data or residuals for detecting periodic components and for identifying the dominant power law noise type The autocorrelation results are available in a data file for further analysis Deselect the inserted lag scatter plot to print or convert an autocorrelation plot or use the Play program to replay and plot or convert an autocorrelation plot with the inserted lag scatter plot 209 STABLE32 USER MANUAL 210 ANALYSIS FUNCTIONS Histogram Function e Purpose Use the Histogram function to plot a histogram of the current phase or frequency data Histogram Plot
166. em taking data a once per second grows in size by about 1 million points day or 42 MB day This is a large amount of data to store read and analyze The meas value which represents phase in cycles has a resolution of 1e 8 cycle When divided by a nominal frequency of 5e6 this provides a resolution of 2e 15 sec The actual system resolution is limited by white phase noise to about 0 5 psec 5e 13 sec rms for a 1 second measurement interval 147 STABLE32 USER MANUAL The Database function automatically generates a phase data filename based on the measurement clock name with a phd extension e MMS Database Connection The computer on which the Stable32 program is run must be connected to the MMS database server via a network before the Database function can be used Follow the directions for the MMS database system to establish this connection which should be verified before running the Stable32 Database function When it is run for the first time a Database Configure dialog box will appear to enter the necessary access parameters host IP address database name user name and password Those settings will be saved for subsequent use by the program the password is encrypted e Database Queries The MMS database is queried when the program is opened to gather a list of all the clocks it contains which is put into both the reference and measurement combo boxes This represents a snapshot of the clocks in the database which is not updated
167. ements Dead time corrections are made using the B2 and B3 bias ratios which handle cases of single and multiple distributed measurement dead time respectively e Overlap amp Th ol Hybrid Th oH the Overlap amp Th ol hybrid provides stability data over the entire range of averaging times from the measurement interval to 75 of the record length Manually enter the type of power law noise that applies to the data to invoke the appropriate bias correction or use the Auto BR Bias Removed feature to automatically determine and remove the bias correction e All Tau The All Tau option is useful as a means of spectral analysis to identify periodic components in time domain stability data Without the Many Tau option it will calculate the stability at every possible tau value which can take a very long time With the Many Tau option which may be selected in the Configure Function a selectable subset of the possible tau values will be used to provide a quasi uniform distribution of points on the stability plot which can provide much faster calculating plotting and printing The default setting for the approximate number of points is 500 which may be set with the ManySize parameter in the Preferences section of the STABLE32 INI configuration file e Automatic Noise Determination and Matching Selection of the automatic noise type Alpha will automatically estimate the noise type to be used to determine the bias corrections and confidenc
168. enkins Time Series Analysis Forecasting and Control San Francisco Holden Day 1970 J A Barnes et al Characterization of Frequency Stability ZEEE Trans Instrum Meas Vol IM 20 No 2 pp 105 120 May 1971 B E Blair Editor Time and Frequency Theory and Fundamentals NBS Monograph 140 Annex 8 E p 181 May 1974 G Winkler A Brief Review of Frequency Stability Measures Proc 8th PTTI Meeting pp 489 527 Dec 1976 J Rutman Oscillator Specifications A Review of Classical and New Ideas Proc 31th Annu Symp on Freq Contrl pp 291 310 June 1977 J Vanier and M Tetu Time Domain Measurement of Frequency Stability Proc 10th PITI Meeting pp 247 291 Nov 1978 P Lesage and C Audoin Characterization and Measurement of Time and Frequency Stability Radio Science Vol 14 No 4 pp 521 539 1979 D A Howe D W Allan and J A Barnes Properties of Signal Sources and Measurement Methods Proc 35th Annu Freq Control Symp pp A1 A47 June 1981 V F Kroupa Editor Frequency Stability Fundamentals and Measurement IEEE Press Institute of Electrical and Electronic Engineers New York 1983 ISBN 0 87942 171 1 S R Stein Frequency and Time Their Measurement and Characterization Chap 12 Precision Frequency Control E A Gerber and A Ballato Eds Academic Press Inc Orlando 1985 ISBN 0 12 280602 6 Vol 2 Proc IEEE Vol 74 Jan 1986 C A Greenhall Frequency Stability R
169. equency domain power law exponents are also related to the slopes of the following time domain stability measures Allan variance o T u a l a lt 2 Modified Allan variance Mod o 1 y a l a lt 3 Time variance 02 T n a 1 a lt 3 115 STABLE32 USER MANUAL e Phase Noise Diagram The following diagram shows the slope of the SSB phase noise f dBc Hz versus log f Fourier frequency Hz for various power law noise processes 100 f 120 dBc Hz 140 160 116 SSB Phase Noise Diagram FT S D f a 1 u S f f B a 2 f 10 ana m 1 10 1 2 Op Slopes in Eun DAN od dB decade 0 1 4 5 FREQUENCY DOMAIN STABILITY Domain Conversions e Time and Frequency Domains The stability of a frequency source can be specified and measured in either the time or frequency domain Examples of these stability measures are the Allan variance o 1 in the time domain and the spectral density of the fractional frequency fluctuations S f in the frequency domain Conversions between these domains may be made by an analytical method based on a power law spectral model for the noise processes involved This method the one used by the Stable32 Domain function can be applied only when the dominant noise process decreases toward higher sideband frequencies Otherwise a more fundamental method based on numerical integration must be used The general time to frequency domain conversion is not unique
170. equency noise toward the red end has a low rumbling sound And random walk FM phase noise in the infrared region cannot be heard at these sampling rates Some media players have oscilloscope spectrum analyzer and other visualizations that can add another dimension to noise observations 271 STABLE32 USER MANUAL 272 Vibra Function e Purpose MISCELLANEOUS FUNCTIONS Use the Vibra function to calculate the level of spectral components caused by sinusoidal or random vibration or sinusoidal frequency modulation Source Carrier Freg MHz Gamma 1 9 fi 0 000 Calc te t De Copy Close r Vibration a peak Vib Freg Hz i 0000e 00 i 00 000 Sine Vib C Random Vib Sine FM Spurious Level L f dBc e Operation The Vibra dialog box contains the following controls Control Type Description Source Group Controls related to the frequency source Carrier Freq MHz Edit Enter RF carrier frequency in MHz Not used for FM modulation Enter vibration sensitivity as fractional frequency per g Gamma 18 Poit Does not apply to FM modulation Vibration OPEM Group Controls related to the vibration or modulation level Modulation g peak g Hz or Dev Edit Enter sine vibration in g peak random vibration PSD in Hz peak g Hz or peak FM deviation in Hz Vib Freq Hz or Mod Enter vibration frequency in Hz o
171. equency spacing in Hz which is a negative number for typical sub Hz bandwidths 205 STABLE32 USER MANUAL The PSD plot will fail and an error message will be shown if there are too few data points to produce a plot An AF 1 periodogram or multitaper spectrum requires at least 6 data points and an Auto AF periodogram at least 10 data points The cursor can be used to help identify the frequency and amplitude of discrete components on the PSD plot Press the ESC key to deactivate it before closing the plot A spectral analysis involves many non parsimonious choices which depend on the analyst s objective judgment and taste Stable32 offers several PSD types and calculation methods The choice of PSD type e g L f depends mainly on the data type and noise specification The choice of calculation method e g periodogram and its options depend mainly on how to best satisfy the analysis objectives e g determining the noise type or detecting a discrete component Because most frequency stability spectral analyses are concerned with noise it is usually desirable to use a fairly large averaging factor to better determine the average noise level But a smaller averaging factor is better able to detect discrete components The auto AF periodogram method is generally a good compromise between frequency resolution andsmoothing The less familiar multitaper method is often the best of all especially for determining the noise type power law slope
172. erlapping Allan and Hadamard deviation calculations are performed from phase data after frequency to phase conversion if necessary All zero values including the first and last data points of an analysis window are treated as gaps If all the data points within an analysis window are gaps then there will be a corresponding gap in the stability data which is shown as having a sigma value at the bottom of the plot Thus a group of missing data points will appear as a trough in the dynamic stability plot and will have z values equal to the minimum sigma value 257 STABLE32 USER MANUAL The dynamic stability plot requires an All Tau overlapping Allan or Hadamard deviation calculation for each of its analysis windows which can take a considerable time for a large data set However the plot can be redrawn with different options without repeating the calculation e XYZ Data File A data file comprising 3 columns of x Averaging Factor y Window and z Sigma data named XYZ dat is written to the Stable32 working directory each time a dynamic stability plot is generated This file must be manually renamed before the next plot to save it The XYZ dat data is the actual stability analysis results before log scaling and interpolation An example of the first 5 lines of an XYZ dat file is shown below 1 000000e 000 1 000000e 000 2 952219e 001 2 000000e 000 1 000000e 000 1 895182e 001 3 000000e 000 1 000000e 000 1 582051e 001 4 000000e 000 1
173. es dialog box Copy Pushbutton Copy stability results to Windows Clipboard 269 STABLE32 USER MANUAL Control Type Description Print Pushbutton Print stability results Plot Group Plot type and unit controls Sigma Type List Choose sigma type Unit List Choose unit to plot A B C or All MM Indicator Indicates if min amp max sigma data read DF Indicator Indicates if degrees of freedom data read e Operation Enter stability data filenames using A B A C and B C edit boxes or Browse These stability files must contain 3 sets of data with the same sigma type and tau range in the standard Stable32 stability data file format as described for the Read function Only a placeholder value e g 1 is needed for the of analysis points and no entries are needed for the minimum and maximum sigma columns Then press Read to read the 3 sets of stability data which will be shown in the table and can be examined with Plot Options Lines and Notes buttons Then press Calc to separate the variances which can also be examined with Plot Options Lines and Notes features copied to the clipboard with the Copy button or printed with the Print button When done end the 3 Cornered Hat function with the Close button Error bars can be shown on the stability plots for a single unit They are determined by the maximum and minimum sigmas of the measured stability and the reduced number of degrees of free
174. esults Frequency outliers are found by comparing each data point with the median value of the data set plus or minus some multiple of the absolute median deviation These median statistics are more robust because they are insensitive to the size of the outliers The outliers can be replaced by gaps or filled with interpolated values Frequency jumps can also be a problem for stability analysis They are an indication that the statistics are not stationary and it may be necessary to divide the data into portions and analyze them separately 301 STABLE32 USER MANUAL e Data Plotting Data plotting is often the most important step in the analysis of frequency stability Visual inspection can provide vital insight into the results and is an important preprocessor before numerical analysis A plot also shows much about the validity of a curve fit Phase data is plotted as line segments connecting the data points This presentation properly conveys the integral nature of the phase data Frequency data is plotted as a horizontal line between the frequency data points This shows the averaging time associated with the frequency measurement and mimics the analog record from a frequency counter As the density of the data points increases there is essentially no difference between the two plotting methods Missing data points are shown as gaps without lines connecting the adjacent points e Variance Selection It is the user s responsibility to
175. eters at the bottom of the plot The results of these curve fits are also placed in the Windows clipboard e Polynomial Fitting A polynomial fit to phase or frequency data can be selected up to 9th order Gaps zeros in the data should be filled before performing a polynomial fit e Function Fitting An arbitrary function can be fitted to phase or frequency data by entering its expression and optional initial parameter values The function expression which does not include the x t or y t left hand portion comprises the basic arithmetic operators and a maximum of 10 parameters starting with a and proceeding continuously up to j and mathematical functions such as log and exp Parentheses should be used in pairs as necessary to denote functions and order of execution All parameters must be followed by an operator 1 e ab is not allowed to denote a b The following mathematical functions are supported sin cos tan asin acos atan sinh cosh tanh exp log log10 sqrt floor ceil abs and hypot The expression format and function names generally follows C language conventions e g use log not In for the natural logarithm Gaps zeros in the data should be filled before performing a function fit Function fitting uses the Levenberg Marquardt algorithm for nonlinear least squares curve fitting 1 3 It may be necessary to enter appropriate initial guesses for the function parameters in order to obtain a useful fit
176. eview Telecommunications and Data Acquisition Progress Report 42 88 Oct Dec 1986 Jet Propulsion Laboratory Pasadena CA pp 200 212 Feb 1987 D W Allan Time and Frequency Time Domain Characterization Estimation and Prediction of Precision Clocks and Oscillators JEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 34 No 6 pp 647 654 Nov 1987 D W Allan et al Standard Terminology for Fundamental Frequency and Time Metrology Proc 42nd Annu Freq Control Symp pp 419 425 June 1988 Characterization of Clocks and Oscillators NIST Technical Note 1337 D B Sullivan D W Allan D A Howe and F L Walls Eds U S Dept of Commerce National Institute of Standards and Technology March 1990 Special Issue on Time and Frequency Proc IEEE Vol 79 July 1991 D W Allan Time and Frequency Metrology Current Status and Future Considerations Proc 5th European Freq and Time Forum pp 1 9 March 1991 J Rutman and F L Walls Characterization of Frequency Stability in Precision Frequency Sources Proc IEEE Vol 79 July 1991 J A Barnes The Analysis of Frequency and Time Data Austron Inc Dec 1991 285 23 24 25 26 27 286 STABLE32 USER MANUAL C A Greenhall The Generalized Autocovariance A Tool for Clock Statistics Telecommunications and Mission Operations Progress Report Vol 42 137 Jet Propulsion Laboratory Pasadena CA May 1999 W J Riley
177. f 0 for the timetag column e See Also Multicolumn Details Function 130 FILE FUNCTIONS Multicolumn Details e Purpose The Multicolumn Details function displays the raw parsed and numeric values of the first and last lines of the data file as it is read It also shows the number of data columns the number of data lines and the number of rejected data lines This function also supports the conversion of certain data and time formats into MJD format which can be copied and pasted into the Timetags function to generate a complete set of timetags for uniformly spaced data having no missing points Multicolumn Data Details x Line File gui C Documents and Settings William Riley4Desktop4080312 0 NTP 080312 0 NTP csv Display C Last tt Cols 16 Selected active line of raw and numerically parsed multicolumn data Rows 75530 Note that 4 row in this table corresponds to a column in the data file 3 Rejected zo 1 1 000000000000000e 00 sad 2 i 92 168 1 201 i 92 168 1 201 1 921680000000000e 02 Ta 3 2008 03 12 2008003012 2 00800301 2000000e 09 Bars 4 08 35 55 08035055 8 035055000000000e 06 5 21 6902052 21 6902052 2 163020520000000e 01 PISCIS Feini 6 2008 03 12 2008003012 2 00800301 2000000e 09 7 08 35 08035 8 035000000000000e 03 US 8 21 6932524 21 6932524 2 169325240000000e 01 3 2008 03 12 2008003012 2 00800301 2000000e 09 10 08 35 08035 8 035000000000000e 03 Review details 11 21 6932632 21 6932632 2 16
178. f a frequency stability analysis These steps are arranged in a standard order and can be individually selected or skipped Plots and tables can be drawn and printed to show the results The available options are as follows Step Description Options Plot Print Open File Open data file Phase or freq data Original data Browse for file Convert Convert data To other analysis type Converted data Remove Outliers Remove bad data Frequency only Corrected data Set sigma factor Part Use part of data Set start end points Selected data End 0 last point Average Combine data for longer t Set averaging factor Averaged data Normalize Remove median from data Remove Drift Remove fit Choose fit type Residual data Run Stability analysis Choose variance type Stability plot Stability table Close Close last screen Leave open for manual Add delay to observe steps analysis Script M OpenFile Browse Data Type Phase C Freg Filename C Data FM202phd Iv Convert Analysis of Freq Data M Remove Outliers Sigma Factor 5 000 Part 0 Start EES End Dp Average 1 Avg Factor EEE Normalize M Regularize Remove Drift 2 Drift Type 3 Unes I DataPlot Type 4 Original Print Data Plot 5 Run Variance Type Overlapping Print Stability Plot 7 T Print Table 8 AddDelay 8 msec 300 Iv
179. f this function is to examine phase or frequency data for gaps outliers and other anomalous values relating them to their point number or timetag For example this function can be used to quickly find the date and time of an outlier in a set of frequency data outlier identification is not available for phase data The Edit function is not intended for manual data entry or heavy editing tasks Use Windows Notepad or another ASCII text editor for that purpose Notepad or the substitute defined in the STABLE32 INI configuration file can be invoked from within Stable32 from the Utility Notepad menu or the Pad toolbutton If timetag information is available check the Show Timetags box to display it It is also helpful to check the Color Gaps and Color Outliers boxes to emphasize those points Several Timetag Formats are available including Modified Julian Date MJD Day of Year DOY Date and Exponential Exp The MJD format also serves to display any decimal numeric format The Go To group allows easy access to the data by point number while the Find group allows easy access to any gaps and outliers The Detailed Search group provides more detailed Find and Replace functions as described in the next sections of this User Manual The Edit After Highlighted Point group allows inserting or deleting a certain number of points The inserted points are 0 s gaps and this can be a convenient way to correct the data for missing points Data editing
180. factors at the expense of a significantly longer computational time 59 STABLE32 USER MANUAL e Hadamard Variances The Hadamard variance is a 3 sample variance that is similar to the 2 sample Allan variance It examines the 2nd difference of the fractional frequencies the 3rd difference of the phase variations Because of this the Hadamard variance HVAR or Ho t converges for the Flicker Walk FM a 3 and Random Run FM a 4 power law noise types It is also unaffected by linear frequency drift The Hadamard variance can also be calculated by either the non overlapping or overlapping method the latter provides better statistical confidence at the expense of somewhat longer computational time The total Hadamard variance TOTHVAR is a total version of the Hadamard variance e Modified and Total Variances The modified and total variances are not distinct variances but are considered to be techniques applied to the Allan and Hadamard variances e Th ol Variances Th ol is a special purpose statistic that provides information equivalent to the Allan variance out to averaging factors equal to 75 of the record length Th oBR is a biased removed version of Th ol while Th oH is a hybrid statistic combining Th oBR with the Allan variance e Other Statistics Other statistics used for time domain frequency stability analysis include MTIE and TIE rms which are most commonly used in the telecom industry e Summary A summa
181. fer Timetags M Use Timetags for Tau 4 Press OK to convert between phase and frequency data e Controls The Convert dialog box contains the following controls Control Type Description Conversion Group Choose conversion type Phase to Frequency Radiobutton Select f conversion Frequency to Phase Radiobutton Select f 4 conversion Normalize Frequency Checkbox Remove average frequency before f conversion Adj Zero Frequency Checkbox Adjust zero freq to 1e 99 in gt f conversion Transfer Timetags Checkbox Transfer timetags along with data Use Timetags for Tau Checkbox Use timetags as tau for conversion OK Pushbutton Perform conversion amp close box Cancel Pushbutton Abort conversion amp close dialog box Help Pushbutton Invoke the Convert help topic Transfer Timetags Checkbox Transfer timetags along with data e Operation Select desired Conversion type and desired Normalize Frequency or Adjust Zero Frequency Transfer Timetags and Use Timetags for Tau options then press OK To abort press Cancel 173 STABLE32 USER MANUAL e Conversions Phase to frequency conversion is done by dividing the first differences of the phase points by the averaging time y Xi Xi t The inverse frequency to phase conversion is done by piecewise integration using the averaging time as the integration interval Xi Xi y i t Any gaps in the freque
182. for SQL queries to directly access the database The database entries associated with these items are shown in the table below Database Details x Item Reference Measurement Clock Name Cesium Rubidium Clock ID 1 2 System 1D 1 1 Sys Name Test Test Frequency 5000000 0000000000 5000000 0000000000 Channel 3 4 Source lD 3 4 Meas ID 2 3 Begun By Ended By Details of selected reference and measurement clock records Details Item Database Table Database Item Remarks Clock ID clock names clock id Unique key measurement list clock id Foreign key System ID measurement systems system id Unique key meas system data system id Primary key measurement sources system id Foreign key timer groups system id Primary key Frequency measurement list frequency 149 STABLE32 USER MANUAL Details Item Database Table Database Item Remarks Channel measurement sources channel Source ID measurement sources source id Primary key measurement list source id Foreign key measurements source id Meas ID measurement list meas id Primary key Begun By measurement list begun by Ended By measurement list ended by 150 FILE FUNCTIONS Database Configure e Database Configure Configuration information for the database function is stored in the STABLE32 INI initialization file in standard Windows format co
183. gaps to maintain a regular time sequence The Regularize function can be used to insert gaps into timetagged data that has missing points The Edit function highlights the first timetag value after a gap in blue The Insert feature of the Edit function can be used to manually insert a group of gaps 22 GENERAL e Variance Analysis The Stable32 variance analysis functions include provisions for handling gaps Some of these functions yield satisfactory results in all cases while others have speed limitations or provide unsatisfactory results for frequency data having large gaps The latter is most apparent at longer averaging times where the averaging factor is comparable to the size of the gap The speed limitations are caused by more complex gap checking and frequency data algorithms while the poor results are associated with the total variances for which conversion to phase data is required Filling can often help for the total variances Two general rules apply for the variance analysis of data having large gaps 1 use unconverted phase data and 2 check the results against the normal Allan deviation which has the simplest fastest gap handling ability The following table summarizes the gap handling limitations of the Stable32 variance functions See Reference 1 for more information Stable32 Gap Handling Limitations in Variance Functions Avoid freq to phase conversion Overlapping Allan Generally OK Modified All
184. ge frequency offset The raw phase data will be essentially a straight line representing the frequency offset and the instability information is contained in the small deviations from the line A large number of digits must be used unless the frequency offset is removed by subtracting a linear term from the raw phase data Similar considerations apply to the quadratic phase term linear frequency drift Many frequency stability measures involve averages of first or second differences Thus while their numerical precision obviously depends upon the variable digits of the data set there is little error propagation in forming the summary statistics e Data Preprocessing Preprocessing of the measurement data is often necessary before performing the actual analysis which may require data averaging or removal of outliers frequency offset and drift Phase data may be converted to frequency data and vice versa Phase and frequency data can be combined for a longer averaging time Frequency offset may be removed from phase data by subtracting a line determined by the average of the first differences or by a least squares linear fit An offset may be removed from frequency data by normalizing it to have an average value of zero Frequency drift may be removed from phase data by a least squares or 3 point quadratic fit or by subtracting the average of the second differences Frequency drift may be removed from frequency data by subtracting a least squares
185. gma value Scale Max Edit Enter y axis sigma scale maximum Sigma Min Text Minimum sigma value Scale Min Edit Enter y axis sigma scale minimum Options Groupbox Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Bars 1 Checkbox Show error bars on plot Table 2 Checkbox Draw stability table on plot Fit 3 Checkbox Show fit parameters on plot Plot File Edit Enter plot filename Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke the Read Options help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort Press Clear All to reset all attributes to their default values 158 READ FUNCTIONS Read Lines Function e Purpose Use the Read Lines function to add lines to a stability plot The possible line types are as follows Line Type Description Parameter None No line None Endpoints Line between certain endpoint values None Horizontal Horizontal line at certain sigma value None Vertical Vertical line at certain tau value None Noise Fit to certain power law noise model Sigma 1 Read Plot Lines x A Up Line fi Down Tau Sigma Start 9 000008 02 Bt End 1 152008 05 Endi m Noise Line Slope Pos WFM Noise bd Type Can
186. gram files stable32 phase Hi Data Min 4 70788e 00 Scale Min f5 s0000e 00 Y Div fro Ticks E e Controls The Plot Options dialog box contains the following controls Control Type Description Title Combo Enter plot title Sub Title Combo Enter plot subtitle Message Combo Enter plot message Position Combo Choose message position X Axis Groupbox X Axis parameters Label Combo Enter x axis label Keep 8 Checkbox Keep x axis scale for future plots Offset Edit Enter x axis scale offset Multiplier Edit Enter x axis scale multiplier X Divs Edit Enter x axis major scale divisions Start 3 Edit Enter of starting data point End 4 Edit Enter of ending data point Y Axis Groupbox Y Axis parameters Label Combo Enter y axis label Offset Edit Enter y axis scale offset Multiplier Edit Enter y axis scale multiplier 217 STABLE32 USER MANUAL Control Type Description Data Max Text Display maximum data value Scale Max Edit Enter y axis scale maximum Data Min Text Display minimum data value Scale Min Edit Enter y axis scale minimum Y Divs Edit Enter y axis major scale divisions Ticks Edit Enter y axis minor scale tics Options Groupbox _ Plot options curve fits Poly Order 7 Listbox Polynomial fit order 1 9 y t Edit Enter function to be fi
187. grams applet in Control Panel under Start Settings or simply execute D SETUP from Start Run where D is the drive letter of your CD drive By default this will create a C Program Files Hamilton Technical Services Stable32 directory on your hard disk and will copy and decompress all the Stable32 files to it The installation program will also create a Stable32 program group containing an icon for Stable32 and will associate the dat frd and phd filename extensions with Stable32 Only about 22 MB of disk space is required Use the included uninstall program to remove the Stable32 program files any user generated files must be removed manually e Files The Stable32 installation comprises the following files which are all located in the STABLE32 directory Please examine the README TXT file for any supplementary information It may be read with Notepad Executables STABLE32 EXE PLAYW EXE 5110COMM EXE Dynamic Link Libraries DTBL32 DLL FREQUENC DLL GPCWDLL DLL GPCWDRVN DLL LICENS32 DLL CGM DLL HPGL DLL POSTSCR DLL TIFF DLL SCODL DLL PIC DLL GEM DLL LIBPQ DLL LIBEAY32 DLL LIBINTL3 DLL LIBICONV2 DLL SSLEAY32 DLL COMERR32 DLL KSSPRT32 DLL LIBXML2 DLL PGAEVENT DLL GSSAPI32 DLL KRB5 32 DLL MSVCR71 DLL ZLIBI DLL LIBXML2 DLL LIBXSLT DLL GraphicC Fonts BLOCK FNT COMPGRMA FNT COMPITAL FNT COMPLEX FNT COMSCR FNT DUPLEX FNT ENGOTH FNT MATRIX FNT MICROB FNT MICROG FNT NEWS FNT NEWSGRM FNT RUSSIAN FNT SIMGRMA FNT SIMPLEX FNT SIMSCR FNT SWIS
188. grees of freedom for an overlapping Allan variance estimation and using that to establish single or double sided confidence intervals for the estimate with a certain confidence factor based on Chi sguared statistics Sample variances are distributed according to the expression df s x gt o where x is the Chi square s is the sample variance o is the true variance and df is the of degrees of freedom not necessarily an integer The df is determined by the of data points and the noise type The Stable32 program includes those procedures for the overlapping Allan variance function 63 64 STABLE32 USER MANUAL TIME DOMAIN STABILITY Modified Allan Variance e Modified Allan Variance The modified Allan variance Mod 0 7 MVAR is another common time domain measure of freguency stability It is estimated from a set of M freguency measurements for averaging time c m1 where m is the averaging factor and ty is the basic measurement interval by the expression 2 1 M 3m 2 j m lf i m 1 M d gt mE 0d At y FU 32 2 2 Ebo 2 In terms of phase data the modified Allan variance is estimated from a set of N M 1 time measurements as 2 1 N 3m4 j m 1 2 gt 5s mu 2X em x gt i j Modo T ated al a SN Daa The result is usually expressed as the square root MDEV or Mod o t the modified Allan deviation The modified Allan variance is the sa
189. guage program for Windows from Wilson WindowWare Inc is highly recommended to automate repetitive analysis procedures with Stable32 Information is available at http www windowware com Screen Setup Use 1024 x 768 XGA screen resolution or higher if possible in order to support the mini data plots on the Stable32 status bar This resolution also supports the use of all toolbar buttons With lower than XGA resolution use the Configure function to select the toolbar buttons that you want The phase and frequency mini data plots can be eliminated by deselecting the Status Plots box in the Configure function This can save screen space and reduce update time on older systems Data Output The results of an analysis can be documented or captured in several ways for use in another analysis or application The results of a Check or Run can be printed The results of a Sigma or Drift calculation a stability Run or a Domain conversion can be copied to the clipboard with the Copy button Software such as the Microsoft ClipBook Viewer can be used to capture multiple outputs The results of a Run are written to a stability file that can be read by the Read function or another application All of the GraphiC plots can be printed copied to the clipboard or converted and saved in a number of file formats And finally a synopsis of a Stable32 analysis session is recorded in a log file Run Function Don t press Stop during an octave or decade run un
190. guency drift per t interval Sine peak Edit Enter peak amplitude of sinusoidal term 231 STABLE32 USER MANUAL Control Type Description Sine Period Edit Enter period of sinusoidal term OK Pushbutton Perform the Noise function close dialog box Cancel Pushbutton Abort the Noise function amp close dialog box Copy Pushbutton Copy the noise parameters to the clipboard Help Pushbutton Invoke this help topic e Operation Enter the Number of data points wanted and their Tau interval Then enter the o 1 Noise Parameters for the desired power law clock noise At least one noise parameter must be non zero Next enter any fractional frequency Offset and Drift and or the peak value and Period of any Sine term that may be wanted Then press OK to generate the simulated clock noise or Cancel to abort e F FM Noise Generation The long term phase excursions of the generated flicker FM noise are too small on average see Reference 2 below This does not affect the Allan deviation results and can be avoided by generating twice as many points as needed and using only the second half of the output e FW FM and RR FM Noise Generation The more divergent flicker walk FM a 3 and random run FM a 4 power law noise types may be generated by using the 1 f spectral property of a frequency to phase conversion For example to generate RR FM noise first generate a set of RW FM noise an
191. gues in the Time and Frequency community who have contributed the analytical tools that are so vital to this field Some of those persons are listed in the References help topic David W Allan has had a major impact on this field and has been a source of much inspiration and encouragement for the Stable programs The work of the late J A Barnes influenced the drift analysis and noise recognition techniques while that of C A Greenhall C Ekstrom and P Koppang has helped with the numerical methods and confidence limits T Walter has contributed particularly toward the noise simulation as has G Winkler toward outlier detection Credit also goes to M A Weiss for work regarding modified and time sigma and D A Howe for the new total variances and for contributing many beneficial suggestions toward this program More recently important work was done by D A Howe C A Greenhall F Vernotte and T K Peppler on implementing the modified and Hadamard total variances while D B Percival amp A T Walden s book and J M Lees amp J Park s code supported multitaper spectral analysis D A Howe and T N Tasset have contributed significantly with the Th ol statistic Perkin Elmer Inc supported the development of the Database function and Matthew Phillips of Timing Solutions Corporation assisted in its writing Cosmo Little and Wolfgang Klische have contributed suggestions regarding the Power function 305 STABLE32 USER MANUAL Contributors Many
192. h ol Confidence Intervals Proc 2004 IEEE Freq Cont Symp pp 725 728 August 2004 D A Howe Th oH A Hybrid High confidence Statistic that Improves on the Allan Deviation Metrologia No 43 pp 322 331 August 2006 D A Howe D B Percival J A McGee and T N Tasset Th oH Bias Removal Method Proc 2006 IEEE Freq Cont Symp pp 788 792 June 2006 J A McGee and D A Howe Th oH and Allan Deviation as Power Law Noise Estimators JEEE Trans on UFFC Vol 54 No 2 pp 448 452 February 2007 J A Taylor Unpublished private communication August 2007 J A Taylor and D A Howe Fast Th oBR A Method for Long Data Set Stability Analysis to be published MTIE G Zampetti Synopsis of Timing Measurement Techniques Used in Telecommunications Proc 24th PTTI Meeting pp 313 326 Dec 1992 Bregni Measurement of Maximum Time Interval Error for Telecommunications Clock Stability Characterization JEEE Trans Instrum Meas Vol IM 45 No 5 pp 900 906 Oct 1996 P Tavella A Godone amp S Leschiutta The Range Covered by a Random Process and the New Definition of MTIE Proc 28th PTTI Meeting Dec 1996 pp 119 124 10 11 OTHER INFORMATION M J Ivens Simulating the Wander Accumulation in a SDH Synchronisation Network Master s Thesis University College London UK November 1997 S Bregni Clock Stability Characterization and Measurement in Telecommunications IEEE Trans
193. h noise discrete spectral PSD function analysis component Detect Frequency Look for frequency Use jumps option of Frequency jump removal Jump jump frequency data Plot must be done manually function View Histogram Look for unusual amplitude distribution Use Histo function Not ordinarily part of stability analysis effect editor Filter Data Remove selected Use Filter Function Low pass high pass band spectral region pass and band stop filtration supported Multivariate Detect correlations Use spreadsheet or Used to investigate Plotting between variables scientific plotting environmental sensitivity program Compensation Remove deterministic Spreadsheet or data Used to remove environmental sensitivity Reference W J Riley Preprocessing for Frequency Stability Analysis Hamilton Technical Services e Gaps Jumps and Outliers It is not uncommon to have gaps and outliers in a set of raw frequency stability data Missing or erroneous data may occur due to power outages equipment malfunctions and interference For long term tests it may not be possible or practical to repeat the run or otherwise avoid such bad data points Usually the reason for the gap or outlier is known and it is particularly important to explain all phase discontinuities Plotting the data will often show the bad points which may have to be removed before doing an analysis to obtain meaningful r
194. hase Data UE Total 1001 Freq Data Total 1000 ui a File PHASE DAT 1000 File PHASE 001 1000 Tau 9 00000e 02 Stat 1 End 1000 W Tau 9 00000e 02 Stat f 1 End 1000 Controls The Status Bar contains the following controls Control Type Description Phase Data Radiobutton Select the phase array as the active data array Freq Data Radiobutton Select frequency array as the active data array Total Text Display the total of points in the data array File Text Display the current phase or freq data file title Text Display the of analysis points Tau Edit Enter the averaging time t for the current data Start Edit Enter the analysis start data point End Edit Enter the analysis end data point Plot Graphic Show data plot between analysis limits Unmarked Button Pushbutton Restore full analysis range 11 STABLE32 USER MANUAL e Bitmaps Several bitmaps appear on the status bar beside the Phase and Freq Data buttons to indicate when the changed data is unsaved when there are timetags and whether the analysis limits are either restricted or too small The latter bitmap changes when the of analysis points is below the minimum A button to the right of the analysis limit bitmap restores the full analysis range A bitmap at the top center of the status bar indicates when the phase and frequency arrays contain equivalent data e Operation Click o
195. he Add function to append phase or frequency data from disk to the end of the current data in memory FILE FUNCTIONS Append Data File x File Name C stable32 phase dat 3_col dat archive dat arcindex dat clkpit dat freg dat freg x dat messages DAT nbs dat E List Files of Type Data Files dat Directories c stable32 a CA y stable32 amp c drive c Drives OK Network Help JA Data Type Phase C Frequency C Archive Controls The Add dialog box contains the standard Windows file open controls plus the following custom controls Control Type Description Data Type Group Box Controls to choose the data type Phase Radiobutton Read additional data into the phase array Frequency Radiobutton Read additional data into the frequency array e Operation Select Phase or Frequency data type and perform the usual Windows file dialog box operations Attempting to add excessive data will be trapped with an error message The results of an Add operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function Notes The Add function does not apply to archive data Averaging is not supported while adding data The maximum data file size applies to the total after the added data Adding more than that number of points opens a dialog offering a
196. he Configure function e Plot Data Filenames The Autocorrelation and Dynamic Stability functions write plot data files each time a plot is drawn The autocorrelation plot data file default name AUTO DAT comprises rows of lag and ACF value The dynamic stability plot data file fixed name XYZ DAT comprises rows of averaging factor window and sigma value 27 28 STABLE32 USER MANUAL GENERAL Timetags e Timetags The Stable32 program supports the limited use of timetags to help manipulate phase and frequency data Timetag arrays are associated with each of the phase and frequency arrays e Timetag Usage Timetags may be read from a file or they may be generated automatically with the Timetags function Actual timetags may be used to identify interruptions in the data with the Regularize function which can also insert gaps into the data at these points Generated timetags are suitable only for data inspection and editing The presence of timetags is indicated by a small yellow tag next to the filename in the status bar Timetags are not required for any of the analysis functions They may be stored to disk along with their corresponding data If there is timetag data and no tau input from the STABLE32 INI file then the spacing of the first two timetags scaled by the TagScale configuration file value is used as the default tau when a data file is opened For example MJD timetags scaled by 86400 can be used to automaticall
197. he Variances of the Oscillator and the Reference pp 216 217 Precision Frequency Control Vol 2 Edited by E A Gerber and A Ballato Academic Press New York 1985 ISBN 0 12 280602 6 P Tavella and A Premoli Characterization of Frequency Standard Instability by Estimation of their Covariance Matrix Proceedings of the 23rd Annual Precise Time and Time Interval PTTI Applications and Planning Meeting December 1991 pp 265 276 J A Barnes The Analysis of Frequency and Time Data Austron Inc May 1992 P Tavella and A Premoli A Revisited Tree Cornered Hat Method for Estimating Frequency Standard Instability EEE Transactions on Instrumentation and Measurement IM 42 February 1993 pp 7 13 P Tavella and A Premoli Estimation of Instabilities of N Clocks by Measuring Differences of their Readings Metrologia Vol 30 No 5 1993 pp 479 486 F Torcaso C R Ekstrom E A Burt and D N Matsakis Estimating Frequency Stability and Cross Correlations Proceedings of the 30th Annual Precise Time and Time Interval PTTI Systems and Applications Meeting December 1998 pp 69 82 C Audoin and B Guinot The Measurement of Time Cambridge University Press ISBN 0 521 00397 0 2001 Section 5 2 8 C Ekstrom and P Koppang Three Cornered Hats and Degrees of Freedom Proceedings of the 33rd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting November 2001 pp 425 430 C R Ekstrom and P A Ko
198. he analysis This eliminates the gaps but also shortens the record It is best suited to removing gaps near the start or end of the record Ski Gaps are automatically skipped by some variance functions P see table below This is the preferred method where applicable Use the Fill function to fill gaps with interpolated values Fill Gaps are automatically filled by some variance functions see table below This method is satisfactory as long as there are fewer than about 5 gaps in the record see Reference 1 The Stable32 variance functions automatically handle gaps by either skipping or filling them as shown in the table below Stable32 Variance Function Gap Handling Variance Type Gaps Skipped Gaps Filled Allan Overlapping Allan Modified Allan Hadamard Overlapping Hadamard 21 STABLE32 USER MANUAL Variance Type Gaps Skipped Gaps Filled Total Allan Total Modified Total Time Total Hadamard e Analysis of Data with Gaps The Stable32 analysis functions include provisions for handling gaps in the data These provisions have limitations however and it is important to understand those limitations to avoid errors see Reference 1 The general process is to use the Open function to read timetagged phase data use the Regularize function to insert gaps for missing points use the Convert function to convert the data to frequency data use the Check function to replace any outl
199. he currently displayed TKF plot When the users Windows is enlarged the current plot will automatically be redrawn A space entered from the keyboard will generate a Redraw command and is a useful way to return to the original plot size after zooming in or out The Draw menu s Go To Plot command opens the Go To Plot dialog box to allow the user to input the number of the plot to draw in the currently open TKF file The user enters an integer number for the index of the plot and that plot in the TKF file is drawn in the Play window Only TKF files with an accompanying OFF file TKF offset file are enabled for specifying a particular plot to draw Note This does not apply to Stable32 plots The Draw menu s Zoom In command is used to zoom in on a portion of the currently displayed TKF plot Once the user selects Zoom In a cross hair cursor is presented By clicking the left mouse button and moving the mouse a Zoom In box will appear Once the proper size Zoom In box is chosen clicking the right mouse button will start the drawing of the selected portion of the plot The zoomed portion of the plot can then be printed or converted Redraw or a space key will redisplay the original plot before it was zoomed The Draw menu s Zoom Out command is used to zoom out the currently displayed TKF plot Once the user selects Zoom Out a cross hair cursor is presented By clicking the left mouse button and moving the mouse a Zoom Out box will appear On
200. he following parameters Keyword Description Default Position Message position 0 Date Date annotation flag 0 Box Draw box around plot flag 0 SigmaType Allan or Hadamard sigma type 0 WindowSize Analysis window size 100 StepSize Analysis step size 10 Colors Use colors flag 0 Title Plot title text Null Subtitle Plot subtitle text Null Message Plot message text Null Grid Show plot grid flag 1 321 e FreqLines STABLE32 USER MANUAL The FregLines section of the STABLE32 INI file can contain the following parameters the items are repeated for each line as indicated by the index i i 1 to 12 Keyword Description Default Typeli Line type 0 5 0 None 0 X Start i X axis start point 0 0 X End i X axis end point 0 0 Y Start i Y axis start point 0 0 Y End i Y axis end point 0 0 Slopeli Line slope 0 5 0 e PhaseLines The PhaseLines section of the STABLE32 INI file can contain the following parameters the items are repeated for each line as indicated by the index i 1 to 12 Keyword Description Default Typeli Line type 0 5 0 None 0 X Start i X axis start point 0 0 X End i X axis end point 0 0 Y Start i Y axis start point 0 0 Y End i Y axis end point 0 0 Slope i Line slope 0 5 0 e SigmaLines The SigmaLines section of the STABLE32 INI file can contain the following
201. he plot is to appear The default is the top The Convert menu s HPGL and HPGL2 commands are used to display a HPGL conversion dialog box to select the filename and page Convert orientation of the HPGL file to be produced The user is asked to select cont the page orientation and margin lengths to be used The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The Convert menu s SCODL command is used to display a SCODL conversion dialog box to select the filename and page orientation of the AGFA SCODL file to be produced The user is asked to select the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top e Operations Copying to Clipboard GraphiC and Play use the clipboard to copy a bitmap of the client area of the window for use by other applications Use the Edit Copy Bitmap command to copy the bitmap to the clipboard Use the Edit Copy Metafile command to copy the metafile to the clipboard The clipboard utility may be used to view the clipboard Any application that will import a bitmap or metafile from the clipboard such as Word for Windows can paste the Play generated bitmap or metafile to its client area Converting TKF File GraphiC and Play can convert a TKF file to one of several different types of file by using the Convert pull down menu Simply p
202. hould be set to scale the data for analysis generally to seconds and fractional frequency The Addend value is then added to the scaled values e Tag Scale Use the tag scale multiplier to convert the timetag units to seconds For example if the timetags are MJD in whole and fractional days the Tag Scale value should be set to 86400 The tag scale does not affect the timetag itself but only its interpretation as a tau value e Tag Offset Use the tag offset to make time zone corrections or to convert general timetag dates to MJD For example if the timetags are the default dates used by Microsoft Excel that start at zero at midnight on December 31 1899 the Tag Offset value should be set to 15018 to convert them to MJD Note Excel incorrectly treats 1900 as a leap year The tag offset is applied as the timetags are read 140 FILE FUNCTIONS Save Function e Purpose Use the Save function to save phase or frequency data to disk Save Data File CAstable32 phase dat 3_col dat Sci archive dat y stable32 arcindex dat clkplt dat freg dat freq x dat messages DAT nbs dat Data Files de e Controls The Save dialog box contains the standard Windows file save controls plus a Save Timetags checkbox to choose whether or not to also save the timetags e Operation Perform the usual Windows file save dialog box operations 141 STABLE32 USER MANUAL 142 Add Function e Purpose Use t
203. ics df df and O S Xp df X 0 p df where y is the Chi square value for probability p and degrees of freedom df s is the sample variance o is the true variance and df is the of degrees of freedom not necessarily an integer The df is determined by the number of data points and the noise type The much smoother results it produces compared with the normal Hadamard statistic as shown in the plots below make it a more useful analytical tool 2 2 O min S 75 STABLE32 USER MANUAL Dele 03 13 99 Time 11 44 00 Dala Points 1 inru 1001 of 1001 Teu 1 0000006e4 00 FREQUENCY STABILITY File PHASE DAT 10 tion Ho 9 1a 7 10 Hadamard Dev e 2 i lb i i A i LIILLILIIJ 10 2 10 2 10 2 103 Averaging Time t Seconds Dele 03 13 99 Time 11 55 30 Data Polnis 1 inry 1001 of 1001 Teu 1 0000000e4 00 FREQUENCY STABILITY PHASEDAT File PHASE DAT Hadamard Deviation Ho t 101 Yio 107 pping Overla 103 o 10 2 10 2 10 Averaging Time t Seconds e References The following references apply to the overlapping Hadamard statistic 1 T Walter A Multi Variance Analysis in the Time Domain Proc 24 PTTI Meeting pp 413 424 December 1992 2 S Hutsell Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation Proc 27 PTTI Meeting pp 291 302 December 1995 76 TIME DOMAIN STABILITY Total Had
204. ient way to analyze and compare multiple data sets and it also serves as an undo feature to restore data after it has been changed The data tabs are labeled with the filename of the corresponding data An example of Stable32 data tabs is shown below Noise01 frd Noiset2 rd Noise03frd Noisen4trd Noise05 frd Noise06 fed Date 11 18 06 MJD 54057 C PhaseData N Total amp 513 Aa Freq Data E Total 512 File Noise06 phd 53 i File Noise06 frd 512 Tau 000000806 Start 1 End 513 Tau 0 00000e 00 Start 1 End 512 Data tab operation is controlled by the Tabs main menu item that has several sub items as shown below Imm MELLE LUI Us aut AL udi Initially after the Stable32 program is launched no Tabs Options Help data tab row is displayed Clicking on the top Show e Show Tabs Tabs item in the Tabs menu activates a blank tab row for both phase and freguency data switched in the v Auto File Tabs usual way That also activates all of the other Tab menu items The second group of four items Auto a IT ee File Tabs Auto Change Tabs Auto Edit Tabs and v Auto Edit Tabs Auto Noise Tabs select whether new data tabs are v Auto Noise Tabs automatically created when a new data file is read the current data file is changed or edited or a new noise Save Current Data file is generated These options can be selected in any
205. iers with gaps and then analyze the regularized and corrected frequency data The same process can be followed by reading timetagged frequency data and using the Regularize function on it Some of the analysis functions have speed or other limitations associated with data having gaps and the Fill function can sometimes be useful to replace gaps with interpolated values For phase data having gaps but no outliers it is better to perform a stability analysis directly on the phase data In all these cases judgment is needed to assure a correct result It may be more prudent to simply analyze a gap free portion of the data e Phase Frequency Conversions Conversion from phase to frequency data is straightforward for data having gaps Because two phase points are needed to determine each frequency point as the difference between the phase values divided by their tau a single phase gap will cause two frequency gaps and a gap of N phase points causes N 1 frequency gaps Conversion from frequency to phase is more problematic because of the need to integrate the frequency data The average frequency value is used to calculate the phase during the gap which can cause a discontinuity in the phase record Analysis of phase data resulting from the conversion of frequency data having a large gap is not recommended e Drift Analysis The Stable32 drift analysis functions perform well for data having gaps It is important that missing data is represented by
206. if equivalent data exists Press the Close button to close the Statistics dialog box e Zooming The plot and statistics can be zoomed in and out by clicking the R and L mouse buttons while the cursor is in the plot The zooming is centered on the mouse position The width of the scroll box thumb indicates the relative span of the plot and the zoom factor is shown in its text box The status bar plots are not affected by Statistics plot zooming and if set to the full range can serve as a guide to the overall data e Scrolling The usual horizontal scrolling operations apply Dragging the scroll box scrolls the plot Clicking on the L and R arrows or pressing the left up or right down arrow keys moves the plot one point in the corresponding direction Clicking on the L and R scrollbar shaft regions or pressing the page up or page down keys moves the plot one plot width in the corresponding direction Pressing the home or end keys moves the plot to the first or last point The scrollbar must have the input focus be blinking for the keyboard inputs to work During scrolling the point range is shown in the text box below the scrollbar e Plot Scale The plot is scaled to a standardized value at the top of the plot During scrolling the plot scale and or of divisions may change e Average A green horizontal line is drawn to show the average value of a frequency plot e Data and Timetag Readout Data point s and their corresponding
207. igure dialog box When using the default directory the new Stable32 GraphiC sigma plot SIGMA TKF and stability file SIGMA TAU will overwrite the previous ones If it is desired to keep the previous file rename it either from within the Run Options dialog box before plotting or manually from the command line after the plotting operation The SIGMA TAU stability data file is written immediately after the stability calculation before the Run Options box is available so the calculation may have to be repeated if the stability file name is changed Stability data and plots may also be sent to another directory by changing the Stability File and Plot Filename fields in the Run Options dialog box Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The default table position is at the top right or bottom right of the stability plot depending on slope of the sigma tau results See the Special Characters help topic for information about adding subscripts superscripts Greek letters etc to stability plot titles subtitles and labels 246 ANALYSIS FUNCTIONS e Append Checking Append in the Run Plot Options dialog box causes the stability data from the next run to be appended to an existing stability file with the specified filename default SIGMA TAU This can be used with the Read function to easily produce a stability plot with multipl
208. ile Open Stable32 log file Invoke Windows Notepad or another text editor program Listen to phase or frequency data as WAV file Calculate vibrational or FM spectral component Execute automatic analysis script 1 Execute automatic analysis script 2 Execute automatic analysis script 3 Activate the Tabs feature Activate automatic file opening tab creation Activate automatic file change tab creation Activate automatic file editing tab creation Activate automatic noise generation tab creation Save current file data in new tab Rename selected tab data file Write selected tab data to disk Close remove selected tab Close remove all tabs Set Stable32 program configuration options Set filenames Opens submenu to access status bar controls Display information about the Stable32 program Display the general Help index Display information about using Help Access the Hamilton Technical Services web site Send feedback re Stable32 via e mail GENERAL Status Bar e Purpose The Status Bar is a permanent area at the bottom of the screen that displays status information about the current phase and frequency data arrays Some of this information is editable The top row of the status bar displays either a prompt message about the current operation or shows the full filename of the active data plus the current date and MJD The active data type is selected with the Phase Data or Freq Data radio buttons or by clicking the L mouse button on
209. iley A Total Estimator of the Hadamard Function Used for GPS Operations Proc 32nd PTTI Meeting pp 255 268 Nov 2000 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Freg and Time Forum April 2004 Bias Functions J A Barnes Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 Jan 1969 W J Riley Confidence Intervals and Bias Corrections for the Stable32 Variance Functions Hamilton Technical Services Dead Time J A Barnes and D W Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 U S Department of Commerce National Institute of Standards and Technology 1990 D B Sullivan D W Allan D A Howe and F L Walls Editors Characterization of Clocks and Oscillators NIST Technical Note 1337 U S Department of Commerce National Institute of Standards and Technology TN 296 335 March 1990 J A Barnes The Analysis of Frequency and Time Data Austron Inc Dec 1991 D A Howe and E E Hagn Limited Live Time Measurements of Frequency Stability Proc Joint FCS EFTF pp 1113 1116 April 1999 W J Riley Gaps Outliers Dead Time and Uneven Spacing in Frequency Stability Data Hamilton Technical Services OTHER INFORMATION 3 Cornered Hat J E Gray and D W Allan A Method for Estimating th
210. immediately after their respective calculations so to use a different name it must be changed before performing the calculation STABLE32 USER MANUAL GENERAL Program Model e Overview The Stable32 program is based on a simple main window with a number of modal dialog boxes to implement the functions These functions manipulate phase or frequency data arrays e Main Window The main window is empty except for menu and toolbar rows at the top and status bar rows at the bottom The menu and toolbar provide the command interface while the status bar displays information about the current phase and frequency data e Dialog Boxes Modal dialog boxes support all of the Stable32 functions These child windows use a consistent button naming convention The OK and Cancel buttons either accept or reject any changes that have been made while the Calc and Close buttons control functions that can be either repeated or ended All of the Stable32 dialog boxes may be closed with the Escape key Other standard Windows buttons and controls are used as appropriate for the particular function The use of default buttons is avoided so that the Enter key can be used to terminate edit control entries This causes the entry to be reformatted and checked for validity The only modeless dialog boxes are those for the Find and Replace functions e Data Arrays The basic Stable32 idiom is a pair of phase really time and frequency data arrays x i and y i
211. in integer floating point or exponential format Each line can have 1 or more space or comma delimited columns and up to 8 columns can be processed A value of zero is treated as a gap in the data Stable32 reads processes and stores data in double precision 15 digit floating point format The Stable32 file reading routine is quite robust It will read an input file with any number of columns and will allow selection from up to 8 columns of data Additional columns are simply ignored One or more spaces or commas must separate the columns and each line may contain up to 1024 characters A single column is assumed to the phase or frequency data which is automatically loaded into the selected array Multicolumn data opens a special dialog box where the desired columns for the data and optional timetags can be selected The last line of the file that contains a numeric 0 9 character determines the number of columns and first 80 characters are displayed for easy reference Non numeric header and trailer lines at the top and bottom of the file are ignored including lines beginning with the UNIX style comment symbol Fields of numeric data in header rows may be read incorrectly and require subsequent editing but they will not interfere with the reading of later rows of actual data Slashes and colons as used in dates 04 23 97 and times 18 50 are converted to zeros 0 so that numeric data on the same row can be read Provision
212. ines for spectrum plot Spurs Checkbox Detect and analyze discrete spectral lines Remove From Plot 6 Checkbox Remove discrete components from PSD plot Checkbox Remove discrete components from PSD data Plot File Edit Enter PSD plot filename Reset All Pushbutton Reset all parameters to defaults Help Pushbutton Invoke this help topic Close Pushbutton Close the Power dialog box 202 ANALYSIS FUNCTIONS e Operation Enter the desired Title Sub Title Message message Position and Options Select the desired PSD Type Windowing Type Windowings or Windows and Avg or BW J Factor Enter the Carrier Frequency value for S f or f PSD types Use the Date Box Cursor Fit Pts and Info checkboxes to select the desired options Then press Plot to plot the power spectrum or Close to close the Power Spectrum dialog box The Auto Avg Factor selection uses a variable averaging factor for the periodogram PSD as described below Display of the FFT points and octave band fits are controlled by the Pts and Fit boxes and the Info box controls the display of the FFT information Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The Cursor option will activate the mouse during a plot to draw lines and display plot coordinates Use the Esc key to deactivate it before closing the plot Zero padd
213. ing is used if necessary to raise the of time series data points to the next larger power of two The PSD results Fourier frequency and Log PSD are written to a data file with the default filename PSD dat See the Special Characters help topic for information about adding subscripts superscripts Greek letters etc to power spectrum plot titles and subtitles e PSD Windowing Data windowing is the process of applying a weighting function that falls off smoothly at the beginning and end to avoid spectral leakage in an FFT analysis Without windowing bias will be introduced that can severely restrict the dynamic range of the PSD result The Stable32 program offers a choice of four windowing types None Hanning Hamming and Multitaper The classic Hanning and Hamming windows can be applied for 1 to 3 times e PSD Averaging Without filtering or averaging the variances of the PSD results are always equal to their values regardless of the size of the time domain data set More data provides finer frequency resolution not lower noise while the data sampling time determines the highest Fourier frequency Without averaging for white noise each spectral result has only 2 degrees of freedom Some sort of filtering or averaging is usually necessary to provide less noise in the PSD results This is accomplished in Stable32 by dividing the data into sections performing an FFT analysis on each section separately and then averaging those values to o
214. ion Because the plots have 8 X axis divisions it is best 1f the PlotSize value have a round number after division by 8 e g PlotSize 240 will provide a scale of 30 sec div Note The 5110Comm program is not included with all versions of the Stable32 software package INDEX Index 3 Comered m E 1 54 10 40 tuet mibi a t r htal koit h kepeh mb AE 101 5 RN 331 A Acknowledgments ls tel ie and salis idad 305 Add Function Automated Operation celeste cedet ee v u eee rto bacan cdi rola v e k 35 AutoPlot Autoregressive Nola id cat lease te aestus teles cia 194 Average Function ies PEE civ esta ees os es lp a cans a coe asta cH Pe UE gan 177 Averaging Time taU ociosa anadir lancia 90 Averaging Data 136 177 Averaging Large Files s csccccitsscsstescccsecsssucescesttcsndssdecstessubcsedectaconcestadsndesdasctscndecthsessecttoss 17 135 B Band Pass Band Stop IES REOR 95 A A EE A O PEA S A M SUE 194 Bitmap bmp Files A A staesbiveteeseshetestivences 327 Bitmaps s BLRAVO 105 223 Calendar Function Check Function Clear Data UTAR 0 Clear Function Clear Timetags Command Line Options hdr da ad 33 STABLE32 USER MANUAL Commas Instead of Decimal Points eese 18 Confidence Intetvals op Ie ii a rie se 89 Configuration File Configure
215. irectory name must be shortened to mydocu 1 An alternative file format conversion method for bitmaps and metafiles is to use the Edit Copy GraphiC menu command This is the easiest way to transfer a plot into another open document The best format for including GraphiC tkf plots in a Microsoft Word document is as a Windows metafile wmf GraphiC tkf plots can be included in web documents as gif files by first converting them into bitmaps and then using the free conversion program BMPTOGIF available on the Hamilton Technical Services web site This is the best format for including GraphiC plots in an html document Better looking data plot scales can be obtained by scaling the y axis to pp10 or standard units This will also eliminate duplicate scale markings and the colon that can appear in them This format is the default when the Smart Plot Scales configuration item is selected In the Y Axis Label edit control of the Plot Options dialog it is important to understand that brackets will create a superscript see Appendix II Problems have been reported while printing plots after reading data from read only network drives because the GraphiC functions are unable to write the temporary metafile needed for printing One solution to this problem is to copy the data file to a local drive for which you have write privileges before opening it for analysis Do not access the GraphiC menu items or resize the plot while it is drawing Problems h
216. is and plotting functions The confidence interval of an Allan variance estimate depends not only on the Allan variance type non overlapping overlapping modified or time and nominal value and on the averaging factor and number of data points but also on the statistical confidence factor desired and the type of noise e Simple Confidence Intervals The simplest confidence interval approximation with no consideration of the noise type sets the 10 68 error bars at 0 TAN where N is the number of freguency data points used to calculate the Allan deviation e Kn Noise Factor A more accurate determination of this confidence interval can be made by considering the noise type which can be estimated by the B1 bias function the ratio of the standard variance to the Allan variance That noise type is then be used to determine a multiplicative factor Kn to apply to the confidence interval These are the error bars shown by the Stable32 Variance and Run functions for the non overlapping Allan deviation Noise Type Kn Random Walk FM 0 75 Flicker FM 0 77 White FM 0 87 Flicker PM 0 99 White PM 0 99 e Overlapping Samples Better statistical confidence can be obtained by making maximum use of the available data by forming all possible frequency differences for a given averaging time Although these fully overlapping samples are not all statistically independent they nevertheless help to improve the confidence
217. isparate or correlated stability This problem is most likely to arise at long tau e 3 Cornered Hat Error Bars The error bars of the separated variances may be set using X statistics by first determining the reduced number of degrees of freedom associated with the 3 cornered hat process see References 11 and 12 below The fraction of remaining degrees of freedom for unit i as a result of performing a 3 cornered hat instead of measuring against a perfect reference is given by T 2 0 Q 0 62 02 62 024 02 02 The ratio of the number of degrees of freedom is 0 4 for three units having the same stability independent of the averaging time and noise type 101 STABLE32 USER MANUAL References The following references apply to the 3 cornered hat method for frequency stability analysis 1 10 11 12 13 102 The term 3 cornered hat was coined by J E Gray of NIST J E Gray and D W Allan A Method for Estimating the Freguency Stability of an Individual Oscillator Proceedings of the 28th Annual Symposium on Frequency Control May 1974 pp 243 246 J Groslambert D Fest M Oliver and J J Gagnepain Characterization of Frequency Fluctuations by Crosscorrelations and by Using Three or More Oscillators Proceedings of the 35th Annual Frequency Control Symposium May 1981 pp 458 462 S R Stein Frequency and Time Their Measurement and Characterization Chapter 12 Section 12 1 9 Separating t
218. l F Vernotte W J Riley and T K Peppler Enhancements to GPS Operations and Clock Evaluations Using a Total Hadamard Deviation JEEE Trans UFFC Vol 52 No 8 August 2005 V 78 STABLE32 USER MANUAL TIME DOMAIN STABILITY e Th o1 The Theoretical Variance 1 Th ol is a special purpose statistic for the estimation of long term frequency stability It produces results similar to the Allan variance for averaging factors out to nearly the full data length The Th o statistic is defined as follows 2 1 N m m 2 1 1 Theol m t N N mmr 0 75 52 m 2 6 x Ki m 2 x 7 Nir tm 2 Ji for averaging factor m even and 10 m lt N 1 where N is the number of phase data points It consists of N m outer sums and m 2 inner sums The Th ol deviation has the same power law noise tau dependence as the Allan deviation It is an unbiased estimator of the Allan deviation for white FM noise but requires bias corrections for the other power law noises An example of the sampling technique used by Th ol is shown in the figure below This figure shows the m 2 5 pairs of inner summation terms for N 11 phase data points at the largest averaging factor m 10 for its single outer summation i 1 Theo1 Schematic for nz 11 m 10 1ton m 1 5 0tom 2 1 4 x 1 2 3 4 5 6 7 8 9 10 11 EE ESA eee D nnn ie A oe oe A In general there are m 2 pairs of samples with spans ranging from m 2 to 1 al
219. l Allan and Hadamard variances the rounding down associated with successive averaging may reduce the With gaps the can depend on exactly where the gaps are In all cases the is counted dynamically during the calculation as the statistical sums are accumulated References 1l WJ Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18 European Frequency and Time Forum April 2004 2 D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proceedings of the 32nd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting pp 255 268 November 2000 93 94 STABLE32 USER MANUAL TIME DOMAIN STABILITY Bias Functions e Bias Functions Several bias functions are defined and used in the analysis of frequency stability These bias functions are defined below The Stable32 program uses the B1 the standard variance to Allan variance ratio and R n the modified Allan variance to normal Allan variance ratio bias functions for the identification of noise types e B1 Bias Function The B1 bias function is the ratio of the N sample standard variance to the 2 sample Allan variance with dead time ratio r T t where T time between measurements t averaging time and y exponent of t in Allan variance for a certain power law noise process BIN r u 0 N T t o Q T x e B2 Bias
220. l Services Stable32 PSD DAT Date 01 27 07 13 24 08 Type Fourier Freq Hz amp Phase Noise L f dBc Hz Avg Factor Auto Carrier Freg 1 000e 7 Points 63 Window 1 Hanning Fourier Freq PSD Avg Factor 1 95312500e 03 1 83080795e 02 2 00000000e 00 3 90625000e 03 1 84696045e 02 4 00000000e 00 7 81250000e 03 1 79434464e 02 8 00000000e 00 1 56250000e 02 1 72444656e 02 8 00000000e 00 2 34375000e 02 1 63880249e 02 8 00000000e 00 e Notes The carrier frequency parameter applies only to the Sf f and f PSD types The of Fourier frequency points is always the power of 2 greater than or equal to 1 2 of the of time domain data points n The spacing between Fourier frequency points is 1 nt and the highest Fourier frequency is 1 2t If averaging is done the value of n is reduced by the averaging factor The PSD fit is a least squares power law line through octave band PSD averages The Stable32 Power function is intended primarily for the analysis of noise not discrete components and includes the qualitative display of power law noise in common PSD units with weighted least squares fits a power law noise process The PSD line fit weighting is based on the of unaveraged PSD points used to determine each octave band average shown as circles on the PSD plot Amplitude corrections are made for the noise response of the windowing functions The amplitude of discrete components should be increased by the log of the BW Fourier fr
221. l special text characters The symbols and have special meanings Superscripts and subscripts may be entered into text strings as super and sub respectively Text color may be changed by entering N where N is the standard IBM color numbers shown below For example use 2 for green text to annotate a noise line The and symbols are not used by Stable32 To use the symbols and normally these characters should be preceded by For example use and to place and into the text GraphiC Colors Color 0 Black 1 Blue 2 Green 3 Cyan 4 Red 5 Magenta 6 Brown 7 White 8 Dark Gray 9 Light Blue 10 Light Green 11 Light Cyan 12 Light Red 13 Light Magenta 14 Yellow 15 Bright White Stable32 uses four special characters to control the font and symbol set used for plot labels These control characters are inserted into the label text for plot labels with NUM LOCK on by pressing the ALT key and using the numeric keypad to enter one of the 4 digit numbers shown in the following table Graphic Font Control Characters Font Code Character News 0200 Swiss 0201 E Newsgrm 0202 Simplex 0203 309 STABLE32 USER MANUAL The GraphiC News and Newsgrm fonts are used for all plot titles sub titles and axis labels For example to insert the lower case Greek letter t into a stablity plot x axis
222. l weighted the same The averaging time t associated with a Th ol value is t 0 75 m to where tp is the measurement interval Stable32 offers the Th ol deviation alone and in combination with the Allan deviation which provides stability data over the whole range of averaging times from the basic measurement interval to 75 of the record length 79 STABLE32 USER MANUAL e NewTh o1 The NewTh ol algorithm of Reference 2 provides a method of automatic bias correction for a Th ol estimation based on the average ratio of the Allan and Th ol variances over a range of averaging factors from 10 to N 30 3 where N is the of phase samples 1 Y Avar m 9 3i T N Th ol m Ta N n 15 Th ol m 12 4i 7 N NewTh ol m 7 N where n E 3 and denotes the floor function e Th oBR and Th oH The Th oBR Bias Removed algorithm of References 3 and 8 provides improved and faster methods of automatic bias correction Stable32 uses the latter method in the Th ol Run function when automatic noise identification is selected 1 5 Avar m 9 3i T N n 1 Th ol m 12 4i 7 N Th oBR m v N Th ol m To N where n P 3 and denotes the floor function Th oBR can be combined with the Allan variance to form the overlapping Allan and Th ol hybrid statistic Th oH that is available in Stable32 as the Th oH variance type Avar m ry N for 1 lt m lt E T Th oH m tp N A
223. latter is accomplished by using a reference channel 0 25 STABLE32 USER MANUAL e Archive File Records It is convenient to adopt the convention that while a gap in the data for all channels is a missing data point a gap in the data for an individual measurement channel represents the start of a new record Stable32 can process TSC archive data for a certain record for the last record for a span of MJD dates or from a particular starting MJD to the end of the file Archive File Indexing Locating the correct file and channel for a certain clock is easier with an index of the various measuring system transactions a list of the test start and end times channel s and record Zs for each clock under test Use the Index option of the Read Archive function to generate an index for TSC archive files This generates and displays an ASCII file named ARCINDEX DAT that may be printed and or searched for the desired clock data 26 GENERAL Filenames e Data Filenames Stable32 data filenames follow the usual DOS conventions While any names can be used the preferred extensions are DAT PHD and FRD for general phase and frequency data respectively A function that changes the data in memory optionally alters the extension to a number which is then incremented each time that the data is changed Phase data numerical extensions are even and those for frequency data are odd Automatic filename extension incrementing helps keep
224. lc Pushbutton Perform the Drift calculation Show Details Checkbox Select detailed Drift dialog box format Close Pushbutton Close the Drift dialog box Help Pushbutton Invoke this help topic Activating Show Details adds the following controls to the Drift dialog box 191 STABLE32 USER MANUAL Control Type Description Noise Model Text Noise model for the drift type Equations Groupbox Equations for the drift fit Results of drift fit These parameters use the Fit Parameters Text data point as the time units Thus the slope is per tau interval Copy Pushbutton Copy results to clipboard Show Details Checkbox Deselect detailed Drift dialog box format Averaging factor for noise fit calculation Avg Factor Edit Applies only to the log diffusion or autoregression drift types for freguency data e Operation Select the desired Drift Type and optionally check Remove Drift Then press OK to find and optionally remove the drift or Cancel to abort The Show Details checkbox changes the dialog box to a detailed format and the Help button invokes a Help screen A changed Drift Type clears the results e Detailed Drift Dialog Box The detailed Drift dialog box provides additional information about the drift analysis The Noise Model is the power law noise process corresponding to the selected drift type that provides white residuals The Equations box shows the eq
225. le opened None FregFile2 Full filename of 2nd from last freq file opened None PhaseFile3 Full filename of 3rd form last phase file opened None FregFile3 Full filename of 3rd from last freq file opened None Ext Additional file extension patterns None The Ext parameter takes the form Ext Label ext ext where the Label part defines the label for the pattern and ext defines the filename extension Both parts must end with a character These filename patterns will be added to the standard ones in the Open and Save functions e Preferences The Preferences section of the STABLE32 INI file can contain the following parameters Keyword Description Default ShowFileOpened Show the Opened dialog box whenever data file opened 0 UseFregPlotlni Use INI file data for freguency plot parameters 0 UsePhasePlotlni Use INI file data for phase plot parameters 0 UseSigmaPlotlni Use INI file data for sigma plot parameters 0 UseHistoPlotIni Use INI file data for histogram plot parameters 0 UseSpectPlotIni Use INI file data for spectrum plot parameters 0 UseAutoPlotIni Use INI file data for ACF plot parameters 0 UseDAVARPlotlni Use INI file data for DAVAR plot parameters 0 DataType Select Phase or Freq data Phase selects Phase Foo phase data any other text selects freq foo LabelPlot Add a label to plots 0 PlotLabel Label text for plots Null IncExtension
226. lepian functions to the entire data array The 1st function resembles a classic window function while the others sample other portions of the data The higher windows have larger amplitude at the ends that compensates for the denser sampling at the center These multiple tapering functions are defined by two parameters the order of the function J which affects the resolution bandwidth and the of windows which affects the variance The maximum allowable number of windows is equal to 2J 1 A higher J permits the use of more windows without introducing bias which provides more averaging lower variance at the expense of lower spectral resolution An example of seven of these functions for order J 4 is shown below Slepian DPSS Taper Functions J 4 7 Taper Amplitude 0 200 400 600 800 1000 Data Point The resolution BW is given by 2J Nt where N is the of data points sampled at time interval t An adaptive algorithm is used to weight the contributions of the individual tapers for lowest bias The multitaper PSD has a flat topped response for discrete spectral components that is nevertheless narrower than an averaged periodogram with the same variance It is therefore particularly useful for examining discrete components along with noise e Discrete Spectral Components Discrete spectral components spurs can be shown by heavy green lines on the PSD plot by activating the Spurs checkbox The dBc spur level is denoted by the to
227. liding time windows to perform an Allan DAVAR or Hadamard DHVAR analysis thereby showing changes nonstationarity in clock behavior versus time It is able to detect variations in clock stability noise bursts changes in noise level or type etc that would be difficult to see in an ordinary overall stability analysis and it can also show the portion of a run that has the best or worst stability The results of a dynamic stability analysis are presented as a 3D surface plot of log sigma versus log tau averaging factor as a function of time window Stable32 implements the DAVAR and DHVAR dynamic stability analyses in its Dynamic Stability function An example of a dynamic stability plot is shown below DYNAMIC STABILITY Analysis Windows 91 Windows of Size 100 amp Step Size 10 Time Spon 1 01 au Range 1 000e 00 ta 00e 01 e References The following references apply to the DAVAR statistic 1 L Galleani and P Tavella The Characterization of Clock Behavior with the Dynamic Allan Variance Proc 2003 Joint FCS EFTF Meeting pp 239 244 2 L Galleani and P Tavella Tracking Nonstationarities in Clock Noises Using the Dynamic Allan Variance Proc 2005 Joint FCS PTTI Meeting 87 88 STABLE32 USER MANUAL TIME DOMAIN STABILITY Confidence Intervals e Confidence Intervals Stable32 uses several different methods for setting the confidence intervals and error bars in its stability analys
228. ling rate WAV File Text Name of WAV file 52 GENERAL General Toolbuttons Plots Data Inputs Options General Toolbuttons Plots Data Inputs Options Audio r WAV File Playing Parameters Audio Player Sampling Rate 11025 Samples second C Program WAV File Files DevStudio MyProjects Stable32 Release table32 wav Enter the full path and filename of the desired audio player program and choose the sampling rate to be used for playing WAV files of selected phase or frequency data Kommi Tine 10 seconds Default 60 sec Enter the desired run calculation time threshold for offering DX an option to average the data before proceeding with the analysis A value of 0 will disable this feature A blank audio player filename causes the default player to be used and None will play the sound without an audio player The default sampling rate is 11 025 samples sec Page 7 Audio Page 8 Run e Run Page Controls The Run property sheet page contains a single edit control to enter the maximum Run calculation time limit before data averaging is automatically offered based on the estimated run time e Operation Select the page and options desired and press OK to accept them or Cancel to abort Help invokes the Configure HTML help file page Most options take effect immediately while the Read Plot Information options will apply when the S
229. llowing lines The MJD is a 18 character string comprised of a 5 digit integer part a decimal point and a 12 digit fractional part A sample line is as follows where the is in 1st column and is followed by a single space 48888 612500000000 The lines have 5 additional fields a 1 or 2 digit channel between 1 and N the of channels in the system a 20 character clock ID string and 3 numerical fields The 1st number is the nominal clock frequency in MHz for that channel It is expressed as a 1 or 2 digit integer part a decimal point and a 15 digit fractional part thus forming a 17 or 18 character string The 2nd and 3rd numbers are clock phase in cycles with respect to the offset reference oscillator The 2nd number is a rounded integer tag while the 3rd has the full precision with a decimal point and a 12 digit fractional part The integer parts of these numbers grow with the beat note cycles of the offset oscillator about 10 per second so a 9 digit field is sufficient for about 3 years Thus the 2nd number string can have 9 characters and the 3rd number string can have 22 characters The number fields are each separated by 2 spaces Including spaces the maximum length of a line is 79 characters A sample line is as follows where is in 1st column and is followed by a single space Clock S N 0123456789 5 000000000000000 12007355 12007354 000000000000 Raw clock time data in seconds is calculated by dividing th
230. llows Lin an ek Description Parameter Type None No line None Endpoints Line between certain endpoint values None Linear frequency data or quadratic Regression RO Frequency slope gr phase data regression line q yop Average Horizontal line at average value Average Marker Vertical line at certain x axis value None ix Frequency Plot Lines Line fi Up ZEE Endpoints OK Down Cancel Lines 1 anca Axis Y Axis Help 5 74890 01 Star 1 00000e 00 Start e Print End 00000e 03 End 7 26495e 01 Copy did Parameter Read Save Clear All e Controls The Plot Line dialog box contains the following controls Some parameters do not apply to all line types Control Type Description Line List Select the of the line to edit Up Pushbutton Increment line Down Pushbutton Decrement line Type Combo Select line type X Axis Groupbox X Axis line parameters Start Edit Enter x axis start of line End Edit Enter x axis end of line Y Axis Groupbox Y axis line parameters Start Edit Enter y axis start of line End Edit Enter y axis end of line Parameter Text Display line parameter 225 STABLE32 USER MANUAL Lines Text of lines entered Control Type Description Read Pushbutton Read line info from INI file Save Pushbutton Save lin
231. log box e Operation Enter the desired plot Title SubTitle Message Message Position and Options and select the desired Avg Factor and Lags Then press Plot to plot the autocorrelation sequence or Scatter to plot a lag scatter plot for the selected lag When done press Close to close the Autocorrelation dialog box Autocorrelation plot configurations may be read saved and reset with the Read Config Save Config and Reset All buttons The lag to be used for the scatter plot normally 1 can be entered in the Scatter Plot Lag box Display of the zero line is controlled by the Zero checkbox and the Lag k checkbox selects the insertion of a lag k scatter plot Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The Cursor option will activate the mouse during a plot to draw lines and display plot coordinates Use the Esc key to deactivate it before closing the plot e Noise Identification The Stable32 Autocorrelation function provides an estimate of the power law noise type white flicker random walk flicker walk or random run for the particular data type phase or frequency that is displayed as a message on the plot This estimate includes both the name of the closest power law noise type and the estimated alpha value based on the lag 1 autocorrelation value and is available for data sets of 30 and larger The estima
232. lotted during the same run Two types of time interval error statistic commonly used in the telecommunications industry are also available The overlapping Allan variance is recommended for most purposes The modified Allan variance is useful to distinguish between white and flicker phase noise the total variances provide better confidence at long averaging times and the Hadamard variance handles data with frequency drift 238 ANALYSIS FUNCTIONS Variance Type Abbreviation Symbol Normal AVAR 627 Overlapping AVAR o 1 Modified MVAR Mod o x Time TVAR 52 T Total TOTVAR total T Modified Total MTOTVAR Mod o total t Time Total TTOTVAR 0 X T Hadamard HVAR o u x Overlapping Hadamard HVAR o gu x Hadamard Total HTOTVAR CO Htotal T RMS Time Interval Error TIE rms Maximum Time Interval Error MTIE Theoretical Variance 1 Th ol Bias removed Th ol Th oBR AVAR and Th oBR Hybrid Th oH These are all functions of the averaging time t and each is usually expressed as its square root the deviation or sigma oy x Mod 6 t 6x T Ototal 1 ou t and O prota T These are abbreviated as ADEV MDEV TDEV TOTDEV MTOTDEV HDEV and HTOTDEV respectively The time error and Th ol functions are available only for phase data Manually enter the noise type to apply the appropriate Th o1 bias correction e Stability Results Table The table of results from the
233. ls Control Type Description Data Type Group Select data type Phase Radiobutton Use phase data array Frequency Radiobutton Use frequency data array The Open function also has a radiobutton to select archive data and an edit control to set the averaging factor to be used when reading the data The Save function has a checkbox to save timetags along with the phase or frequency data e Operation Select Phase Frequency or Archive data type enter the desired Avg By factor if applicable and perform the usual Windows file dialog box operations Opening a data file with multiple columns will invoke the Multicolumn Data function Attempting to open an oversize data file as determined by the Max Data File Size configuration value will invoke the Large Data File function and attempting to add excessive data will be trapped with an error message The results of an Open or Add operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function 119 STABLE32 USER MANUAL 120 Filenames Function e Purpose FILE FUNCTIONS Use the Filenames function to set the names of the various Stable32 data and plot files It is good practice to preset all the relevant filenames within this function before beginning an analysis m Plot Filenames Phase Freq Sigma Histo ACF 1 fe Stable32 PHASETIF OO Steble32 FREQTKF i
234. lso be used to accomplish that e GPCWIN The GPCWIN environment variable can be defined with the SET command to point to the directory where the GraphiC support files are located SET GPCWIN C Program Files Hamilton Technical Services Stable32 While normally unnecessary this can be used to share the same FNT files between several GraphiC applications See the help files for your particular operating system for information about how to use the SET command e Operation The default directory for all Stable32 operations is the one where it is installed and where the program is started That directory is where Stable32 looks for its support files and unless changed is where all output is written Thus regardless of where the current data is located the program will operate from its own directory This is particularly important when data is read from a floppy disk or read only media New Stable32 GraphiC plot files PHASE TKF FREQ TKF SIGMA TKF SPECTRUM TKF and HISTO TKF will overwrite the previous ones if any If it is desired to keep one of those files it is important to rename it either from within the Filenames function or corresponding dialog box before plotting or manually from the command line after the plotting operation The same rule applies to the SIGMA TAU stability data file the PSD DAT power spectrum data file the AUTO DAT autocorrelation data file and the XYZ DAT dynamic stability data file Those files are written
235. ly opens to offer averaging of the data when the calculation time is estimated to exceed a selected value default 60 sec That limit can be set by the Maximum Run Calculation Time item on the Run page of the Stable32 Configuration property sheet The Run calculation time coefficients are updated using recursive averaging each time a long variance run is performed and are saved in the Run section of the Stable32 ini configuration file Variance Tynes Approximate Run Default Data Point Limit yp Calculation Time sec Before Averaging Offered ADEV MDEV TDEV HDEV 2 5e 6 N Ms A 10 million TOTDEV TIE rms where N data points Th ol Th oH 2 0e 4 N log N 50 000 MTIE 1 5e 8 N 50 000 MTOT TTOT HTOT 1 5e 7 N 20 000 242 ANALYSIS FUNCTIONS Run Plot Function e Purpose Use the Run Plot function to generate a stability plot ES GraphiC Win sigma tkf Eile Edit Draw Convert Help TET 4 10 o 2 on Bt E 2 lo Palms 1 thru 100 of TI FREQUENCY STABILITY Sigma 2 92e 01 2 05e 01 1 49e 01 1 10e 01 5 24e 02 5 62e 02 3 25e 02 3 39e 02 ol 2 10 2 Averaging Time 1 Seconds 243 STABLE32 USER MANUAL 244 ANALYSIS FUNCTIONS Run Options Function e Purpose Use the Run Options function to control the attributes of the stability plot Run Plot Options x Title FREQUENCY STABILITY OK SubTitle PHASE DAT y f Message y
236. mal points in data values e Header An optional header can be written at the top of phase and frequency data files as shown below by checking the Header option in the Configure function File C Data PHASE DAT Date 04 08 01 17 37 59 Type Phase Points 8192 Tau 1 000000e 000 This information can help to identify the data and can be shown by pressing the Display button in the Data File Opened dialog box when the file is subsequently read The header lines are ignored when the actual data is read and are not displayed in the timetag and data column fields of that dialog box e Data Entry Data entry is generally done within edit controls in dialog boxes A default entry is usually presented and it generally represents an acceptable choice or a way to abort the current function The usual Windows editing keys apply e Gaps amp Outliers Stable32 includes provisions for handling gaps and outliers that often occur in time and frequency stability data A value of zero 0 is treated as a gap in a Stable32 data file unless it is the first or last point of phase data Stable32 data files are simple vectors of equally spaced phase seconds or fractional frequency dimensionless values Gaps should be included to maintain the proper implied time interval between measurements The Stable32 analysis functions will then produce meaningful results for data having gaps The analysis functions simply skip those points that involve a ga
237. me as the normal Allan variance for m 1 It includes an additional phase averaging operation and has the advantage of being able to distinguish between white and flicker PM noise The confidence interval of a modified Allan deviation determination is also dependent on the noise type but is often estimated as o t VN 65 66 STABLE32 USER MANUAL TIME DOMAIN STABILITY Time Variances e Time Variance The time variance TVAR is a measure of time stability based on the modified Allan variance It is defined as 67 7 22 3 Mod o x The time Allan variance is equal to the standard variance of the time deviations for white PM noise It is particularly useful for measuring the stability of a time distribution network It is usually given as its square root 0 t TDEV e Total Time Variance The total time variance TOTTVAR is a similar measure of time stability based on the total modified variance It is defined as O total 7 0 3 Mod ota T It is usually given as its square root o total t TOTTDEV 67 68 STABLE32 USER MANUAL TIME DOMAIN STABILITY Total Allan Variance e Total Allan Variance The total Allan variance TOTAVAR is similar to the 2 sample or Allan variance and has the same expected value but offers improved confidence at long averaging times Work on total variance began with the realization that the Allan variance can collapse at long averaging factors because of symmetry i
238. milar to the modified Allan variance but uses an uninverted even reflection method that improves its statistical confidence at large averaging factors Time Variance 0 T The time variance is based on the modified Allan variance It has units of seconds is given by o t C n 11 17 3 Mod o x sec where n B 1 Total Time Variance 0 T The total time variance in units of seconds is given by 0 totai t C n T 12 3 Mod o otai T sec where n B 1 Hadamard Variance Ho t The 3 sample Hadamard variance is used primarily as an alternative to the Allan variance for a frequency source having linear frequency drift or highly divergent a 4 or 5 noise It may be calculated by the non overlapping or overlapping method Total Hadamard Variance H0 a t The total Hadamard variance is similar to the Hadamard variance but uses a doubly reflected method that improves its statistical confidence at large averaging factors 112 FREQUENCY DOMAIN STABILITY e Sigma Tau Diagrams The following two diagrams show the relationship between the log o versus log t slopes for various power law noise processes for the normal and modified Allan variances Note that Mod o t is able to distinguish between white and flicker PM noise Sigma Tau Diagram p 2 oy t Sf f p a 1 eg N Flioker PM 31 1 1 1n Freq Drift oy x 0 2 4 6 8 10 log t Mod Sigma Tau Diag
239. mprising Section headings and Item string values These items may be edited directly with a text editor or preferably by using the Database Configure dialog box from within the Stable32 program which is invoked by pressing the Configure button The Database Configure dialog box is shown below Database Configure X Database Access HostIPAddes Database Name fisc2 0020022 User Guest 0002 Password v Stop tGap DK Cancel Enter configuration parameters and press OK to accept Control Type Description Database Access Groupbox Database connection parameters Host IP Address Edit Dot address or blank for localhost Database Name Edit tsc postgres is standard MMS database name User Edit tsc is standard MMS database user name Password Edit tsc is standard MMS database password StopAtGap Checkbox Stop reading data at gap OK Pushbutton Accept database configuration parameters Cancel Pushbutton Reject new configuration parameters Help Pushbutton Invoke help for this dialog box e Initial or Failed Launch When the Database function is launched the first time it is unlikely that the default database access parameters will be correct and the connection will fail This will bring up an error message followed by the Database Configure dialog that will allow the user to enter the correct access parameters Then after another error message the function c
240. multiplier 1 0 Y Offset Y axis scale offset 0 0 Y Mult Y axis scale multiplier 1 0 Y Min Y axis scale minimum value 0 0 Y Max Y axis scale maximum value 1 0 PPlotX Phase data plot x axis label 0 PXDefault Flag to set x axis scale to default 1 319 e SigmaPlot STABLE32 USER MANUAL The SigmaPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null PlotFile Plot TKF filename Null Position Message position 0 X Min X axis scale minimum value Null X Max X axis scale maximum value Null Y Min Y axis scale minimum value Null Y Max Y axis scale maximum value Null TablePos Table position 1 Wide Use wide plot line flag 0 X Label X axis tau label text Null Y Label Y axis sigma label text Null StabFile Stability data filename Null Date Date annotation flag 0 Box Draw box around plot flag 0 Table Draw sigma tau table on plot flag 1 ErrorBar Show error bars on stability plot flag 1 Fit Draw fit line flag 0 e SpectPlot The SpectPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null Position Message position 0 Wide Use wid
241. n The Domain dialog box may be cleared to its default values with the Clear All button and closed with the Close button 262 ANALYSIS FUNCTIONS e Recalculation Order Changing one of the Frequency group values updates the PSD items below it according to the corresponding sigma values Changing one of the Time group values updates the Sigma items below it according to the corresponding PSD values Changing a PSD or Sigma group value updates the corresponding item in the opposite domain Changing either the BW Hz or BW Factor updates the other value the BW factor depends on the tau value e Data Entry It is generally best to work from the top down setting constants like carrier frequency and BW first To activate the BW edit boxes enter a non zero PM noise value The PSD and sigma noise values can be entered at any convenient Fourier frequency or averaging time The PSD and sigma plot ranges should be set consistently approximately reciprocal frequency and tau ranges and within the range where the noise parameters apply e Title and Subtitle The PSD and Sigma plot titles are Frequency Domain Stability and Time Domain Stability respectively Their subtitles show the values of the non zero noise intensity parameters h of the spectral density of the fractional frequency fluctuations S f h f where a is the power law noise exponent In addition the carrier frequency and system bandwidth are shown at the bottom of the plots e
242. n Sort outliers by position Size Radiobutton Sort outliers by size Sigma Factor Edit Enter sigma factor Med Abs Dev Text Display MAD value Remove Outliers Group Choose type of outlier removal None Radiobutton Don t remove any outliers All Radiobutton Remove all outliers Largest Radiobutton Remove the largest outlier Selected Radiobutton Remove the selected outlier Print Pushbutton Print outliers Copy Pushbutton Copy outliers to clipboard e Operation Observe the of Outliers that meet the default 5o criterion Enter the desired outlier criterion in the Sigma Factor box and press Cale to find the of outliers that meet this criterion Optionally check the Remove All Outliers checkbox and press OK to replace them with gaps or press Close to abort the Check function The detailed Check dialog box also presents a list of the outliers allows a choice of sorting by Position or Size absolute deviation from median and removing None All the Largest or the Selected outliers Pressing Print will print a list of the outliers and Copy will copy them to the clipboard e Outlier Recognition Stable32 uses the median absolute deviation MAD as its means of outlier recognition The MAD is a robust statistic based of the median of the data It is the median of the scaled absolute deviations of the data points from their median value defined as MAD Median y i m 0 6745 y where m Median y 1 and the factor 0
243. n opened enter the correct Tau 0 value and then press OK to continue e Tau The Tau 0 value must be set to correspond to the basic measurement interval of the data in seconds to obtain correct analysis results It is preset to a value determined by the following order of precedence 1 a command line tau entry 2 a data file header tau entry 3 a STABLE32 INI Inputs value 4 the first timetag interval and 5 the default 1 0 137 STABLE32 USER MANUAL e Data Scaling The data scaling option uses phase or frequency data addend and multiplier values from the Inputs section of the STABLE32 INI configuration file Those values can be entered manually by editing the configuration file with a text editor such as Notepad or by pressing the Inputs button They default to 0 and 1 respectively and in that case the scaling option is disabled e Timetag Scaling The timetag scaling option uses the tag scale and tag offset values from the Inputs section of the STABLE32 INI configuration file Those values can be entered manually by editing the configuration file with a text editor such as Notepad or by pressing the Inputs button They default to 1 and 0 respectively Timetag scaling is done as the data file is read 138 FILE FUNCTIONS Inputs e Purpose Use the Inputs function to set the tau data addend and multiplier values and the timetag offset and scale factors for the current data type e Controls The Input
244. n the Phase or Freq button or plot to select the desired data type Enter the Tau value in seconds that applies to the current phase and frequency data Optionally enter values for the corresponding Start and End analysis point s if it is desired to restrict the analysis to a portion of the data Enter the title short filename of the phase or frequency data in the File edit box Right and left click on the Plot to zoom and un zoom the data display The Options Status Bar menu items may be used to select status bar controls from the keyboard e Limits The size of the phase and frequency data arrays is essentially unlimited and the maximum number of data points that can be processed is determined mainly by the computer memory and speed as set by the MaxSize configuration variable Only the top status bar message displays the full filename drive and path information The tau value must be positive and greater than zero The start and end analysis point s must be between 1 and the total of data points e Main Window The Stable32 main window may be resized and repositioned by the usual methods and these settings will be saved when the program is closed and reopened again A narrow main window width will cause the status plots to be eliminated and a very narrow setting will make it difficult to operate the status bar controls The toolbutton and status bar controls automatically update whenever the Windows system colors are changed e C
245. n the data An early idea was to shift the data by 1 4 of the record length and average the two resulting Allan variances 1 The next step was to wrap the data in a circular fashion and calculate the average of all the Allan variances at every basic measurement interval t 2 3 This technique is very effective in improving the confidence at long averaging factors but required end matching of the data A further improvement of the total variance concept was to extend the data by reflection first at one end of the record 4 and then at both ends 5 This latter technique called TOTAVAR gives a very significant confidence advantage at long averaging times and is an important new general statistical tool 6 TOTAVAR is defined for phase data as 1 Y 2 TORNA SEU S NEED ES i m 2x i EX m i 2 where t mt and the N phase values x measured at t x are extended by reflection about both endpoints to form a virtual sequence x from i 3 N to i 2N 2 of length 3N 4 The original data is in the center of x with i 1 to N and x x The reflected portions added at each end extend from j 1 to N 2 where x 2xj x and x yy 2Xy Xnj TOTAVAR can also be defined for frequency data as Tot var T xu DA nj i jal 7 y where the M N 1 fractional frequency values y measured at t t N phase values are extended by reflection at both ends to form a virtual array y The original data is in the center where y y for i
246. nce a small data set can easily be entered and analyzed manually A small data set is also an advantage for detecting off by one errors Table I NBS Monograph 140 Annex 8 E Test Data Frequency Normalized Frequency Phase 1 1 1 892 103 11111 0 00000 2 809 20 11111 103 11111 3 823 34 11111 123 22222 4 798 9 11111 157 33333 5 671 117 88889 166 44444 6 644 144 88889 48 55555 7 883 94 11111 96 33333 8 903 114 11111 2 22222 9 677 111 88889 111 88889 10 0 0000 295 STABLE32 USER MANUAL Table II NBS Monograph 140 Annex 8 E Test Data Statistics Averaging Factor 1 2 Data Points 9 4 Maximum 903 893 0 Minimum 644 657 5 Average 788 8889 802 875 Median 809 830 5 Linear Slope 10 20000 2 55 Intercept 839 8889 809 25 Standard Deviation 1 100 9770 102 6039 Normal Allan Deviation 91 22945 115 8082 Overlapping Allan Deviation 91 22945 85 95287 Modified Allan Deviation 91 22945 74 78849 Time Deviation 52 67135 86 35831 Hadamard Deviation 70 80607 116 7980 Overlap Hadamard Deviation 70 80607 85 61487 Total Hadamard Deviation 70 80607 91 16396 Total Deviation 91 22945 93 90379 Total modified Deviation 75 50203 75 83606 Time Total Deviation 43 59112 87 56794 Note 1 Sample not population standard deviation e 1000 Point Test Suite The larger frequency data test suite used here consists of 1000 pseudo
247. ncy data are filled to obtain phase continuity Two equal adjacent phase values will result in zero frequency which is treated as a gap unless the Adjust Zero Frequency option is used recommended see below e Zero Frequency The conversion of phase data having two equal adjacent values results in a fractional frequency value of zero While this is correct it will subsequently be treated as a gap in the frequency data That problem for which there is an optional warning during the reading of phase data can be avoided by using the Adjust Zero Frequency option during phase to frequency conversion which will adjust the frequency value to 1e 99 e Gaps Gaps in frequency data are filled in the converted phase data with values based on the average frequency e Timetags Transfer When the Transfer Timetags box is checked timetags will be transferred along with the converted data Three timetag types are available for converted frequency data equal to the first second or average value of the corresponding phase timetag This choice is set in the Freq Timetags section on the Data property sheet of the Configure function e Timetags as Tau The Use Timetags for Tau option allows the time difference between adjacent timetags to be used as the tau for each point s phase to frequency conversion This is not normally used except for non uniformly spaced data The tau units must be in seconds Timetags in other units e g MJD fractional days mus
248. ne Types and then choose the desired mask file from the File list that appears in the Masks group box The mask and its label will then be included on the stability plot The label can be edited on the Run Notes function Mask files may be created with a text editor according to the following format 1 2 No line shall exceed 80 characters An optional first line beginning with as the first character can contain a comment such as information about the name origin amp purpose of the mask for documentation purposes only A mandatory header line with four fields n x y 1 where int n mask data points double x label x position in stability plot units double y label y position in stability plot units char mask label string which must be enclosed in double quotes This label becomes a plot note and can be edited as a note before it appears on the plot The intent is for the label to automatically identify the mask on the plot An arbitrary number of following lines containing x y data in stability plot units defining the mask These tau sigma points must be in exactly n rows of two space delimited columns Plot lines will connect these points on the plot so they need only define the corners of the mask on log log axes Otherwise the points can be dense enough to draw a general smooth curve The last line should be terminated with a CR LF The mask filename shall have a msk extension and its name should relate in an obvious w
249. ne option For example to automatically opening a phd phase data file associate the phd extension with the phase action If a filename is entered on the command line without specifying the data type then Stable32 starts by invoking the Open Data File dialog box with that filename This feature may be used by associating an extension with the Stable32 program and clicking on any such file More than one association may be used The O SKIP option allows skipping display of the multicolumn and file opened dialog boxes when reading data with the F or P command It uses the default timetag 1 and data 2 columns for 2 column data and no scaling factor is applied Skipping is always done when a data file is opened with one of the three automation scripts 33 34 STABLE32 USER MANUAL GENERAL Automated Operation e Purpose Stable32 operation can be fully automated by using the WinBatch package from Wilson WindowWare Inc 5421 California Ave SW Seattle WA 98136 800 762 8383 www winbatch com e Operation WinBatch uses Windows Interface Language WIL WBT scripts These scripts can be created with a text editor or recorded automatically from a sequence of keystrokes They are then invoked from the command line or a menu to automate Stable32 operation by sending the series of keystrokes to the program An example of a WBT script to plot frequency data is shown below Main menu Plot Frequency command ALT P F
250. ng negative variances will have off scale points 270 MISCELLANEOUS FUNCTIONS Audio Function e Purpose Use the Audio function to listen to phase and frequency noise data as a WAV file on the computer sound system e Operation The sound file may be played on the default audio player e g Windows Media Player another specified audio player e g Quick Time Player or directly without a separate audio player program The sampling rate of the WAV file may be set to one of five standard values between 8 kHz and 44 1 kHz and has no relationship to the sampling period tau of the phase or frequency data The data is stored with 16 bit CD quality having a nominal 96 dB dynamic range The audio player and sampling rate are set on the Audio page of the Configure property sheet An example of a white FM frequency noise data displayed in Windows Media Player is shown below gt Library Rip Burn Sync Guide Stable32 0 06 Stable32 00 04 While of little analytical use this does provide another way to experience various noise types It works best with long data files several tens of thousands of points and with headphones or a sound system having good bass response The more divergent noise types are best observed at the highest sampling rate White PM frequency noise at the blue end of the audio spectrum sounds like frying bacon White FM frequency noise sounds like the white noise from a radio Random walk FM fr
251. nnect the TSC 5110A to a PC COM port using a null modem cable 2 Launch the 5110Comm program directly or from within Stable32 3 Verify that the COM port is open by observing the Open indicator or status message in the List box 4 Enter the desired filename for the data file Note If there is an existing file with this name it will be overwritten each time a new run is started 5 Enter the scale factor to convert cycles of the A channel frequency into seconds This is equal to the period of the A channel frequency e g 100 nsec or 1e 7 for 10 MHz 6 Press the Start button Data capture will begin immediately at 1 second intervals or as soon as the TSC 5110A is started 7 The captured data can be displayed as a listing a phase plot or a frequency plot by selecting the desired Radiobutton above the display area 8 The data listing shows the data point number the raw TSC 5110A data in cycles of the A channel frequency and the scaled data file values in seconds of phase difference as labeled below the listing 331 332 10 11 12 13 14 15 16 STABLE32 USER MANUAL For plots the annotation in the first line below the display shows the plot scales The X axis scale is shown in sec div The Y axis scale is shown as the maximum and minimum data values and the scale factor per division Phase plots have units of seconds while freguency plots show dimensionless fractional freguency For plots the ave
252. not apply to all line types Control Type Description Line Edit Enter of line to edit Up Pushbutton Increment line Down Pushbutton Decrement line Type Combo Select line type Tau Groupbox X Axis line parameters Start Combo Enter x axis start of line End Combo Enter x axis end of line Sigma Groupbox Y axis line parameters Start Edit Enter y axis start of line End Edit Enter y axis end of line 249 STABLE32 USER MANUAL Enter the desired plot lines and press OK to accept them Print to print them or Cancel to abort Press Clear All to clear all lines or use the Read and Save buttons to retrieve and A particular line can be chosen with either a Line entry or the Up Down buttons Up to 12 lines may be entered The line type is then selected from the Type list which varies according to the sigma type that is being run Most of the line types require a combination of Tau and Sigma Start and End values which may be either entered into an edit box or in the case of noise lines chosen from a list Noise lines also require a Slope choice that is appropriate for the particular sigma type and power law noise process The Sigma 1 value is shown for the noise fit The total of active Lines is also displayed store line information Control Type Description Noise Line or Masks Groupbox Noise line parameters or mask files Slope or
253. nputs Configure page contains edit controls for entering parameters that are applied to set and scale input data Separate sets of input values apply to phase and frequency data The Tau input value sets the measurement interval of the data in accordance with the following order of precedence It must have units of seconds 1 Manual entry 2 Command line 3 File header 4 INI Inputs 5 Timetag interval 6 Default 1 second The Addend and Multiplier values modify the phase or frequency data as it is being read The data is scaled according to the following equation scaled value original value multiplier addend The Tag Scale and Tag Offset values modify the data timetags as they are being read A common use is to set the tag scale to 86 400 to convert MJD timetags into seconds e Options The Relative Max AF Absolute Max AF and LF Points to Skip values apply to the PSD Auto AF option of the Power function See the Power function section for more information about those parameters The Weight PSD Fit checkbox activates weighting of the semilog power law noise fit on a smoothed PSD plot The Smoothing Points Octave edit box controls the number of smoothed PSD points per octave of Fourier frequency The Many Tau checkbox determines whether the faster many tau method is used instead of an all tau Run stability analysis With the Many Tau option a selectable subset of the possible tau values is used to provide a qua
254. ntains the following controls Control Type Description Start Edit Enter starting timetag value Increment Edit Enter timetag increment if applicable Data Type Groupbox Data type choices Phase Radio Button Phase data Frequency Radio Button Frequency data Units Groupbox Timetag units choices Seconds Radio Button Use t timetag units in seconds Days Radio Button Use 1 86400 timetag units in days Other Radio Button Use arbitrary timetag units and increment as entered OK Pushbutton Perform the Timetag function amp close dialog box Cancel Pushbutton Abort the Timetag function amp close dialog box Help Pushbutton Invoke this help topic e Operation Select the applicable data type Phase or Frequency Enter the desired Start timetag value and units Seconds Days or Other If Other arbitrary units is chosen enter the desired timetag Increment Otherwise if Seconds or Days units are chosen the increment will be determined by the t value Press OK to generate the timetags or Cancel to abort the Timetags function 229 STABLE32 USER MANUAL e Caution Use caution when generating timetags for data that is not regular Do not confuse these artificially generated timetags with actual ones Such timetags can be useful to identify the position of data interruptions but gaps should be manually inserted into the data to provide regularity and the timetags
255. o 2 pp 105 120 May 1971 C A Greenhall Does Allan Variance Determine the Spectrum Proc 1997 Intl Freq Cont Symp pp 358 365 June 1997 C A Greenhall Spectral Ambiguity of Allan Variance JEEE Trans Instrum Meas Vol IM 47 No 3 pp 623 627 June 1998 D A Howe Interpreting Oscillatory Frequency Stability Plots Proc 2000 IEEE Freq Contrl Symp pp 725 732 May 2002 Modified Allan Variance D W Allan and J A Barnes A Modified Allan Variance with Increased Oscillator Characterization Ability Proc 35th Symp on Freq Contrl pp 470 474 May 1981 P Lesage and T Ayi Characterization of Frequency Stability Analysis of the Modified Allan Variance and Properties of Its Estimate JEEE Trans Instrum Meas Vol IM 33 No 4 pp 332 336 Dec 1984 C A Greenhall A Shortcut for Computing the Modified Allan Variance Proc 1992 IEEE Freq Contrl Symp pp 262 264 May 1992 C A Greenhall Estimating the Modified Allan Variance Proc IEEE 1995 Freq Contrl Symp pp 346 353 May 1995 C A Greenhall The Third Difference Approach to Modified Allan Variance JEEE Trans Instrum Meas Vol IM 46 No 3 pp 696 703 June 1997 OTHER INFORMATION Time Variance D W Allan and H Hellwig Time Deviation and Time Prediction Error for Clock Specification Characterization and Application March 1981 D W Allan D D Davis J Levine M A Weiss N Hironaka and D Okayama New
256. ocorrelation histogram and dynamic stability plots The GraphiC plotting package also includes the Play program for replotting the TKF graphics files produced by Stable32 not available in the Student Version of Stable32 e Controls The GraphiC plot screen contains the following menu items and commands the commands marked with an apply only to the Play program GraphiC and Play Commands Menu Command Description The File menu s Open command will display a dialog box for the user to Open select a new TKF file to open and display When the file is opened the first plot will be drawn in the user s window The File menu s Print Setup command calls the printer driver s setup dialog Printer Setu box to allow the printer to be setup without going to the Windows Control P Panel The changes you make to the printer driver s setup will not be retained once Play is terminated started The File menu s Preferences command opens the preferences dialog box to allow the user to select preferences in printing The current options are Preferences printing an all white background even if the screen background is non white printing black lines in place of white lines on the screen and printing The File menu s Print command will print the currently displayed TKF plot to the currently selected printer device The printer may be setup using the Print Printer Setup command A dialog box is displayed while the printer output is being genera
257. oefficient for Th oH 2 0e 4 MTIETime Run calculation time estimate coefficient for MTIE 1 5e 8 RunTime Selected maximum run calculation time limit seconds 60 326 APPENDICES Appendix V Hints and Notes 1 Launching Stable32 Stable32 can be launched like any Windows application from the Start menu from the Run dialog or via an icon on the desktop By associating Stable32 with a filename extension such as dat Stable32 may also be launched by clicking on a data file or by dragging a data file to the Stable32 icon on the desktop Main Window The Stable32 main window has the best appearance and functionality with XGA 1024x768 or higher screen resolution and with the main window adjusted for nearly full width This allows the use of the mini data plots in the Stable32 status bar and all the toolbuttons If only a lower screen resolution is available use the Configure function to choose the desired toolbuttons and use the Stats function as an alternate way to observe the current data The position of the main window is saved between runs GraphiC Plots When performing a metafile file format conversion for a GraphiC plot within Stable32 make sure that the target path and filename comply with DOS filename conventions e g no more than 8 characters Otherwise the file creation process will produce an error and the conversion will fail For example to use the operating system default path C My Documents the d
258. of the Stable32 analysis functions 146 FILE FUNCTIONS The parameters for the database access can be set by pressing the Configure button see the Database Configure Help topic These settings will take effect the next time the Database function is opened The clock names and records can be reset with the Reset button useful if the database may have changed since opening the Database function e Symmetricom MMS System The Symmetricom previously Timing Solutions Corporation Multi Channel Measuring System MMS is a multiple mixer clock measurement system It measures the phase differences between the clocks under test and an offset reference that is common to all measurment channels These phase differences and the time of the measurement are stored in the MMS database When data is read from the database reference and measurement channels must be selected that were measured on the same system over the same time span Timetagged clock data is then written to a file where it may be used with Stable32 to perform an analysis e MMS Data The data output from a MMS in the form of time differences x are obtained by dividing the measured phase differences of the measurement and reference channels by their respective nominal frequencies and then subtracting them to remove the effect of the common offset reference x Ab meas Vmeas Abres Vier The x values have units of time in seconds The x t time fluctuations are related to the ph
259. of the resulting Allan deviation estimate Furthermore Chi squared statistics can be applied to calculate single and double sided confidence intervals at any desired confidence factor These calculations based on a determination of the number of degrees of freedom for the estimated noise type are the confidence intervals used by the Stable32 Variance function for the overlapping Allan deviation The same method is used by the Run function to show 10 error bars for its overlapping Allan deviation plot The error bars for the modified Allan and time variances are also determined by Chi squared Statistics using the number of MVAR degrees of freedom for the particular noise type averaging factor and number of data points During the Run function noise type estimates are made at each averaging factor except the last where the noise type of the previous averaging factor is used 89 STABLE32 USER MANUAL e Noise Identification It is necessary to identify the spectral characteristics of the dominant noise process in order to set the confidence interval show the error bars and where appropriate apply a bias correction to the results of a time domain frequency stability analysis Stable32 uses two methods for power law noise identification based respectively on the lag 1 autocorrelation and the B1 bias factor The former method is preferred and is used when there are at least 30 analysis data points The lag 1 autocorrelation is an effectiv
260. oise process and the p is the o t log log slope See the Noise Processes and Noise Spectra Help screens for more information about those subjects Confidence Interval information is displayed in the center group box The Kn value is used to determine the confidence limits for the nno overlapping sigma Chi squared statistics are used for the overlapping modified time and total sigmas and the X value is displayed A bias correction is applied automatically as needed to the total sigma and Theol value Activating the Set Noise checkbox opens a Noise combo box that allows selection of a particular noise type or the r1 and Alpha lag 1 ACF noise ID parameters are shown and may be Appl y ied to determine the noise type e Allan Variance The non overlapping Allan variance function calculates the original o t and the standard deviation and uses their ratio to estimate the noise type and the confidence interval of the Allan deviation e Overlapping Allan Variance The overlapping Allan variance function also calculates and displays o t using fully overlapping samples It also estimates the noise type and uses that to determine the of degrees of freedom It then establishes single or double sided confidence intervals for the Allan deviation based on a certain confidence factor e Modified Allan Variance The modified Allan variance function requests the averaging factor and bandwidth factor for the measuring system BW 2nf ty where f is
261. ol has appeared in the status bar indicating that the data has changed Also if enabled in the Configure box the filename extension will have been changed to 001 Close the Drift dialog box by pressing Close Select the Statistics function Notice that the plot now shows only noise Close the Statistics box Choose the Scale function Change the data so it more closely resembles actual stability data by entering a Multiplier of 1 0e 11 and pressing OK If you wish examine the data again with the Edit function to see how it has changed Go to the Sigma function Accept the default Normal sigma type and Averaging Factor 1 Then press Calc to calculate the sigma value about 2 99e 10 Try the Show Details option and some other sigma types and averaging factors for this sample of white FM noise Go to the Run function Select the desired Variance Type and press Calc to produce a table of stability data Then press Plot to see it plotted or Print to send it to your printer Try the Options Lines and Notes functions if you wish to add a noise line or otherwise customize the stability plot GraphiC Win c 146 sigma tkf nIx File Edit Drew Convert Help Dole 01 08 06 Time 18 46 50 Dolo Points 1 thru 512 of 512 1 0000000e 00 File SAMPLE OO FREQUENCY STABILITY Line 1 W FM Samalt 3 022e4 01 f Tau Sigma i 2 99e 01 10 2 2 08e 01 4 1496 01 8 9 95e 00 16 7 65e 00 32 5 52e 00 64 3 80e 00 128 2 85e 0
262. ols Control Type Description Find What Combo Search type Edit Search value Replace With Edit Replacement value Direction Group Search direction controls Up Radiobutton Search upwards Down Radiobutton Search downwards Find Next Pushbutton Perform a Find operation Replace Next Pushbutton Perform a Replace operation for one point Replace All Pushbutton Perform a Replace operation for all points Confirm Checkbox Confirm each replacement Close Pushbutton Abort Replace function amp close dialog box Help Pushbutton Invoke the Replace help topic 171 STABLE32 USER MANUAL e Operation Select the search criterion with the two Find What controls The numeric value also determines the search precision Enter the value that it is to be Replaced With Set the search direction with the Up and Down buttons and press one of the Find Next Replace Next or Replace All buttons The result of a successful search is displayed in the Edit dialog box Additional searches may be conducted with the Find Next button and additional replacements with the Replace Next or Replace All buttons Close the Replace dialog with the Cancel button or by closing the Edit dialog box 172 EDITING FUNCTIONS Convert Function e Purpose Use the Convert function to convert between phase and frequency data Conversion OK Phase to Frequency Bequency ta Phase v Adjvet zero Frequency Help Trans
263. onfigure dialog box to set defaults for the Read Archive function Read Archive Configure E Defaults Channels Meas Chan Ref Chan Enter defaults for Read Archive function e Controls The Read Archive Configure dialog box contains the following controls Control Type Description Defaults Group Read Archive default values Channels Edit Set the maximum of channels Meas Chan Edit Set the default measurement channel Ref Chan Edit Set the default reference channel OK Pushbutton Perform the Read Archive Configure function amp close dialog box Cancel Pushbutton Abort the Read Archive Configure function amp close dialog box Help Pushbutton Invoke the Read Archive Configure help topic e Operation Use the Channels Meas Ch and Ref Chan edit controls to set default values for the Read Archive function Then press OK to accept or Cancel to reject these values The new of channels will take effect immediately in the Read Archive function 127 STABLE32 USER MANUAL 128 FILE FUNCTIONS Multicolumn Data e Purpose The Multicolumn Data function supports the reading of data files with multiple columns It is a sub function of the Open and Add functions Use the Multicolumn Data function to select the desired columns of phase or frequency and optional timetag data This dialog box opens automatically during an Open or Add operation
264. ons that are shown on the toolbar below the menu Select as many of these as will fit across your screen omitting as necessary those least used The order of the toolbuttons cannot be changed Menu items are also available to access all toolbutton functions e Plots The Phase Frequency Sigma Dynamic Stability Histogram Spectrum and Autocorrelation checkboxes control automatic reading and saving of plot options lines and notes when the Stable32 program is opened and closed This can be convenient for repetitive manual analysis or batch operations Otherwise it is probably better to control the retrieving and storing of plot information manually with the individual Save and Read buttons of the Plot and Run function Options Lines and Notes dialog boxes The Use Smart Scales checkbox activates Y Axis data plot scales with units applied For example a phase plot with values in the 10 range will be shown as nanoseconds The Plot Labels checkbox and Label edit box are used to add organization and other such labels at the lower right corner of all plots e Data The Max Data File Size value default 999999 is not a program limitation but rather an option to deliberately bound the size of the data arrays This is useful to tailor the program to personal preferences or computer memory and speed limits The Max Data File Size value limits the number of data points that can be generated by the Noise function and controls the opening of the Large
265. op left of the calendar when applicable This number is used by the Global Positioning System to measure its system time It has an origin time zero of 00 00 00 UTC 6 January 1980 Julian Day 2 444 244 500 MJD 44244 A GPS week cycle is 1024 weeks 276 MISCELLANEOUS FUNCTIONS Pad e Purpose Use the Pad function to invoke Windows Notepad or an alternative text editor program Ed phase dat Notepad File Edit Search p 000000000000000e 00 8 511601033439709e 02 204754825860608e 01 470741798514836e 01 417563029461325e 01 145763378402094e 01 512799857208863e 01 798670993851 792e 01 938636382882 760e 01 840701657650369e 01 355546508103378e 01 856719903110837e 01 581741624819895e 01 525590220324474e 01 229270669703960e 00 172310267951015e 00 892151893271170e 01 160605940601602e 00 153397939900557e 01 575908768589536e 01 019178375517534e 01 555233845694533e 01 Help e Operation N 4 The current data file is automatically opened when the Pad function is invoked Consult the Notepad help topics for information regarding that program Use the Notepad item in the Preferences section of the STABLE32 INI configuration file to set the name of the text editor program to be invoked e Caution Opening of the current data file may be prohibited as a file sharing violation 277 STABLE32 USER MANUAL 278 MISCELLANEOUS FUNCTIONS Play e Purpose Use the Play function to invoke th
266. or the Index button to show a listing of all clock transactions in the archive file Enter the desired Measurement and Reference channel s that correspond to the clock to be analyzed Entering a Reference channel of 0 will select the offset LO as the reference Entering a negative Measurement channel will cause the sense of the measurement and reference channels to be reversed this is useful in the case of a LO that is above rather than the below the nominal frequency as is normal Reversal of the Measurement and Reference channel s will also accomplish this but the ID information displayed after processing the data will be that of the other channel Then select either the Record or Start MJD button as the method for defining the time span for the data If Record is selected either enter the desired Record or check the Last record checkbox If Start MJD is selected as the time span method enter the Start MJD value in the corresponding edit box This will extract the data for the selected clock from that time to the end of the file If it is desired to also set the End MJD then check the End MJD checkbox and enter that value into its corresponding edit box Then press OK to extract the clock data or Cancel to abort the Read Archive function The Configure button brings up another dialog box that allows setting certain defaults for the Read Archive function 126 FILE FUNCTIONS Read Archive Configure e Purpose Use the Read Archive C
267. ose Set Pushbutton Set all filenames to new path Reset Pushbutton Reset all filenames to default path Cancel Pushbutton Abort Filenames function amp close Help Pushbutton Invoke the Filenames help topic e Operation Enter the path for the filenames and press the Set button Then enter the individual plot and data filenames Press OK to apply the new filenames Reset to use the default path or Cancel to restore the original filenames e Note A valid filename cannot be blank or contain the characters A lt gt or 122 FILE FUNCTIONS Open Function e Purpose Use the Open function to read a phase or frequency data file from disk Open Data File xl Lookin Stable32 Jj emet 122100 dat PHASENOHEAD DAT 523809 DAT CQFREQNOHEAD DAT EQPSD DAT Ex da Archive dat gd FREOTAG DAT ES RandomWalk dat data8 dat gd GAP DAT gd SAMPLE DAT error dat Cd messages DAT Eg Sine dat Flicker dat CQNBS DAT tour dat Flicker1 dat GA NEW DAT E TSC DATA DAT Flicker2 dat PHASE DAT EdTST SUIT DAT File name PHASE DAT Files of type Data Fies aay mg Cancel Data Type Phase Freq Archive Avg By Poo Help e Controls The Open dialog box contains the standard Windows file open controls plus the following custom controls Control Type Description Data Type Groupbox Controls to choose the data type Phase Radiobutton Read data into the pha
268. otal Variance D A Howe An Extension of the Allan Variance with Increased Confidence at Long Term Proc 1995 IEEE Int Freq Cont Symp pp 321 329 June 1995 D A Howe and K J Lainson Simulation Study Using a New Type of Sample Variance Proc 1995 PTTI Meeting pp 279 290 Dec 1995 D A Howe and K J Lainson Effect of Drift on TOTALDEV Proc 1996 Intl Freq Cont Symp pp 883 889 June 1996 D A Howe Methods of Improving the Estimation of Long term Frequency Variance Proc 1997 European Frequency and Time Forum pp 91 99 March 1997 D A Howe amp C A Greenhall Total Variance A Progress Report on a New Frequency Stability Characterization pp 39 48 Proc 1997 PTTI Meeting Dec 1997 D B Percival and D A Howe Total Variance as an Exact Analysis of the Sample Variance Proc 1997 PTTI Meeting Dec 1997 C A Greenhall D A Howe and D B Percival Total Variance an Estimator of Long Term Frequency Stability ZEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 46 No 5 pp 1183 1191 Sept 1999 D A Howe Total Variance Explained Proc 1999 Joint Meeting of the European Freq and Time Forum and the IEEE Freq Contrl Symp pp 1093 1099 April 1999 287 10 288 STABLE32 USER MANUAL D A Howe The Total Deviation Approach to Long Term Characterization of Frequency Stability ZEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 47 No 5 pp
269. ower Law Identifier That Uses Lag 1 Autocorrelation private communication August 28 2003 5 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Frequency and Time Forum EFTF April 2004 Session 6B 103 STABLE32 USER MANUAL 104 FREQUENCY DOMAIN STABILITY Frequency Jump Detection e Frequency Jump Detection Stable32 has a choice of two methods for frequency jump detection using either a block averaging BLKAVG or a sequential averaging SEQAVG algorithm both supplemented by the classic cumulative sum CUSUM method for analyzing data for changes in mean e BLKAVG Frequency Jump Detection The Block Average BLKAVG frequency jump detection algorithm compares the difference between the average values within a pair of adjacent windows of adjustable length against a selectable jump threshold That threshold can be either an absolute fractional frequency limit or a sigma factor based on the Allan deviation at an averaging factor equal to the window length over the entire data set The start of the data windows can be offset between zero and the record length modulo the window size The BLKAVG jump detection algorithm is shown in the following flowchart Start Group size Igth lim canbe set manually Set igth lt Default Igth npts 10 on basis of either absolute fractional freq or sigma factor Calc lim Default lim 3 0 c at AF npt
270. p For example in the calculation of the Allan variance for frequency data if either of the two points involved in the first difference is a gap that Allan variance point is skipped in the summation Stable32 also has provisions for filling gaps in phase or frequency data by replacing them with interpolated values Use the Fill function for this purpose Fill first removes any leading and trailing gaps It then uses the two values immediately before and after any interior gaps to determine linearly interpolated values within the gap Filling is recommended before using the modified and time Allan variance functions especially for frequency data because these calculations are much faster for gapless data 18 GENERAL Stable32 has a Check function for locating and removing outliers from frequency data While the definition of an outlier is somewhat a matter of judgment it is important to find and remove such points in order to use the rest of the data Stable32 defines an outlier on the basis of its deviation from the median of the data The user may enter a deviation limit in terms of the median absolute deviation A 56 limit is the default This is a robust way to determine an outlier which is then replaced by a gap Automatic outlier removal is also provided which iteratively applies this method to remove all outliers It should be an adjunct to and not a substitute for visual inspection of the data A message controlled by the WarnZero
271. p of this line which may start at either the bottom of the plot or at the power law PSD fit and complete spur detection information is written to the Windows clipboard The spurs may optionally be removed from the PSD plot replaced by faint yellow lines and or the time domain data by checking either or both of the Remove Spurs checkboxes Press Plot again to see the resulting spur removed PSD plot see example below The spur detection threshold in dB 204 ANALYSIS FUNCTIONS above the PSD fit line is set by the Spur Threshold value on the Options page of the Configure property sheet which may be accessed by pressing the Options button POWER SPECTRUM Discrete3 004 POWER SPECTRUM Discrete3 002 9988 03 1ude 67 08 dBc 30 l Spurs Removed st 60 B n My Phase Noise L f dBc Hz 8 Phase Noise L f dBc Hz bas i 1507 107 1 97 107 10 Fourier Freguency f Hz 1507 107 107 107 10 Fourier Frequency f Hz L f PSD Plot with Spurs Shown L f PSD Plot with Spurs Removed e PSD Data File A data file comprising a header and rows of 2 or 3 columns of Fourier frequency PSD and optionally AF values is written each time a power spectrum plot is generated This file which has a default name PSD DAT must be manually renamed before the next plot to save it An example of the first few lines of a PSD dat file is shown below File C Program Files Hamilton Technica
272. parameters the items are repeated for each line as indicated by the index 1 171 to 12 Keyword Description Default Typeli Line type 0 5 0 None 0 X Start i X axis start point 0 0 X End i X axis end point 0 0 Y Start i Y axis start point 0 0 Y End i Y axis end point 0 0 Slope i Line slope 0 5 0 MaskFile i Mask filename Null e FreqNotes The FreqNotes section of the STABLE32 INI file can contain the following parameters the items are repeated for each note as indicated by the index i i 1 to 8 Keyword Description Default Size i Font point size 8 Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text i Note text Null 322 e PhaseNotes APPENDICES The PhaseNotes section of the STABLE32 INI file can contain the following parameters the items are repeated for each note as indicated by the index i i 1 to 8 Keyword Description Default Size i Font point size 8 Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text i Note text Null e SigmaNotes The SigmaNotes section of the STABLE32 INI file can contain the following parameters the items are repeated for each note as indicated by the index 1 i 1 to 8 Keyword Description Default Size i Font point size 8
273. perations and Clock Evaluations Using a Total Hadamard Deviation IEEE Trans UFFC Vol 52 No 8 August 2005 T N Tassert D A Howe and D B Percival Th ol Confidence Intervals Unpublished paper 2004 T N Tasset Th oH Unpublished private communication July 2004 TIME DOMAIN STABILITY Dead Time e Dead Time Dead time can occur in frequency measurements because of instrumentation delay between successive measurements or because of a deliberate wait between measurements It can have a significant effect on the results of a stability analysis especially for the case of large dead time e g frequency data taken for 100 seconds once per hour Stable32 includes provisions for making dead time corrections in the Sigma and Run functions for normal and overlapping Allan deviations where the noise type is known These corrections use the B2 and B3 bias functions to handle single and multiple distributed measurement dead time respectively The dead time is entered as the ratio r T t where t is the measurement time and T is the longer time between measurements 1 1 for no dead time Measurement Dead Measurement Dead Time Time Time Time The corrections are applied by dividing the calculated sigma by the square root of the product of B2 and B3 These corrections are particularly important for non white FM noise with a large dead time ratio Restricting the dead time corrections to Allan deviations is a conservative approach
274. pes for the same averaging factor 2 This method of noise identification is reasonably effective in most cases The main limitations are 1 its inability to distinguish between white and flicker PM noise and 2 its limited precision at large averaging factors where there are few analysis points The former limitation can be overcome by supplementing the B1 ratio test with one based on R n the ratio of the modified Allan variance to the normal Allan variance That technique is applied to members of the modified family of variances MVAR TVAR and TOTMVAR The second limitation is avoided by using the previous noise type estimate at the longest averaging time of an analysis run One further limitation is that the R n ratio is not meaningful at a unity averaging factor A description of the power law noise identification method used in Stable32 can be found in Reference 2 e AVAR EDF The equivalent of X degrees of freedom edf for the fully overlapping Allan variance AVAR is determined by the following approximation formulae for each power low noise type 90 TIME DOMAIN STABILITY Power Law AVAR edf where Noise Type N phase data points m averaging factor t t W PM N V N 2m 2 N m 1 2 FPM ella N 1 In 2m 1 N 1 2m e 3 N 1 2 N 2 4m 2m N Am 5 F FM AN 2 For m 1 2 3N 49 soe For m 1 4m N 3m RW EM N 2 N 1 3m N 1 4m m N 3
275. ppang Error Bars for Three Cornered Hats JEEE Trans UFFC Vol 53 No 5 pp 876 879 May 2006 W J Riley Application of the 3 Cornered Hat Method to the Analysis of Frequency Stability Hamilton Technical Services TIME DOMAIN STABILITY Autocorrelation e Autocorrelation The theoretical autocorrelation function is defined as CA CA TES where E is the expectation operator z is the time series m is its mean and s is its variance A common estimate of the autocorrelation function is y ME E 20 n0 2 hh T zy 22 Ne where 1 N Z zZ Ney and where the lags are k 0 1 2 K and K is lt N 1 An equivalent and faster estimate can be made for the summation in the numerator as the product of the Fourier transforms of the two terms based on the fact that convolution in the time domain is equivalent to multiplication in the frequency domain e Noise Identification The lag 1 autocorrelation can provide an estimate of the power law noise type as described in Reference 5 below e References W H Press B P Flannery S A Teukolsky and W T Vetterling Numercial Recipes in C Cambridge University Press 1988 ISBN 0 521 35465 X Section 13 2 2 G Box and G Jenkins Time Series Analysis Holden Day Inc 1976 ISBN 0 8162 1104 3 3 DB Percival and A T Walden Spectral Analysis for Physical Applications Cambridge University Press 1993 ISBN 0 521 43541 2 4 C A Greenhall Another P
276. r 49 STABLE32 USER MANUAL Control Type Description Show Splash Checkbox Show splash screen when Stable32 opens Text Editor Groupbox Choose text editor to use Notepad Edit Enter filename of test editor program Printer Groupbox Printer settings Point Size List Select printer text point size e Toolbuttons Page Controls The Toolbuttons property sheet page contains the following controls Control Type Description Select Active Groupbox Select desired toolbuttons to appear on toolbar Toolbuttons List Multiple selection list box Configure x1 Configure x General Toolbuttons Data Inputs Options Audio Run General Toolbuttons Plots inputs Options Audio Run r Read Plot Information r Plot Settings Phase and Freq Data Reading Settings F Freq Timetags T Phase IV Use Smart Plat Scales Max Data File Size 99999999 Use selected TE IV Weight Sigma Plot Noise Fit oia Frequency IM t it Y iy 5 quency Weight Sigma Plot Noise Fil Nor Numerics to Skip 0 e m Signa ee Use comma as decimal point C Avg D ic Stabilit Selecting the read plot info items T Dynamic stabit will cause their stored settings to T War for Zero Freq Data C 2nd Hist be loaded automatically The AE plot label can show your Phase and Freq Data Writing Settings organization name Restore Default Values T Spe
277. r FM modulation rate in Edit Rate Hz Hz Also equal to sideband freq of spectral component Spurious Level Phase Grou Result for sine vibration random vibration or sine FM Noise or FM SB Level P respectively L 1 dBc or dBc Hz Text Result of calculation Spurious level dBc Phase noise dBc Hz or FM SB level dBc 273 STABLE32 USER MANUAL Control Type Description Calc Pushbutton Perform the Vibra calculation Copy Checkbox Copy results to clipboard Close Pushbutton Close the Vibra dialog box Help Pushbutton Invoke this help topic Sine Vib Radiobutton Choose sinusoidal vibration calculation Random Vib Radiobutton Choose random vibration calculation Sine FM Radiobutton Choose sinusoidal FM calculation Note Some controls change along with calculation type Choose the desired calculation type and enter the relevant parameters Then press Calc to perform the calculation and Copy to copy the results to the Windows clipboard When finished press Close to exit the Vibra dialog box Use the Help button to invoke this help topic e Discussion The level of the spectral components discrete or noise sidebands is determined by the standard formula for sinusoidal FM modulation Sideband Level dBc 20 log Af 2 finoa where Af is the peak frequency deviation in Hz and f 4 is the modulation rate and SB frequency For sinusoidal vibration this formula for dis
278. r Plot File field in the Plot Options dialog box When the SmartScale configuration option is on the default y axis phase data plot scales are whenever possible set to standard units like microseconds and nanoseconds and the frequency scales to pplO XX notation Checking the Cursor option activates crosshairs on the plot whose position is indicated at the right end of the GraphiC menu bar please ignore the strange characters This option also activates a line drawing feature The right mouse button starts a line and the right button ends it The line can be extended with another right button click or a new line started with the left button The lines can be deleted with the Del key Press the Esc key to deactivate the cursor function Checking the Wide option causes the data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations See Appendix II for information about adding subscripts superscripts Greek letters etc to data plot titles subtitles and labels e Time Scales The X Axis Label control offers several choices for the data plot x axis time scale as shown in the following table X Axis Label Units Remarks Data Point Data point Data Point x1000 Data point 1000 Time Milliseconds Milliseconds Tau x 1000 Time Seconds Seconds Tau Time Minutes Minutes Tau 60 Time Hours Hours Tau 3600 Time Days Days Tau 86400 Time W
279. r the selected data or Cancel to abort e Caution There is no confirmation after OK is pressed the selected data is cleared and cannot be recovered It is possible to clear the phase or frequency data and retain the corresponding timetags but this is an unusual thing to do 235 STABLE32 USER MANUAL 236 ANALYSIS FUNCTIONS Run Function e Purpose Use the Run function to calculate and optionally plot or print Allan total or Hadamard variance statistics for the selected portion of the current phase or frequency data over a series of averaging times The averaging times may be selected in octave or sub decade increments or at every possible tau out to a reasonable fraction of the record length The Sigma function is available for performing this calculation at a single averaging time Frequency drift may be removed and 1 of 2 unit scaling may be applied as options Variance Type Overlapping E Alpha Automatic Confidence Factor 0 683 Calc AF Tau Alpha Min Sigma Sigma Max Sigma Close 1 1 0000e 00 999 0 2 8458e 01 2 9223e 01 3 0054e 01 2 2 0000e 00 997 0 1 9535e 01 2 0102e 01 2 0721e 01 4 4 0000e 00 993 D 1 3961e 01 1 4479e 01 1 5059e 01 8 8 0000e 00 985 0 1 0060e 01 1 0570e 01 1 1168e 01 16 1 6000e 01 969 0 5 7798e 02 6 1915e 02 6 7057e 02 32 3 2000e 01 937 0 4 3715e 02 4 8082e 02 5 4088e 02 Copy 64 6 4000e 01 873 D 3 1771e 02 3 5237e 02 4 3338e 02 Options 128 1 2800e 02 745 0 2 3073e 02 2 7674e 02 3 6911
280. rage fractional freguency and its standard error are shown on the lower line The current data point number is shown in the text box above the plot This number is useful for tagging purposes if a measurement condition such as supply voltage is changed During data capture all the controls in the 5110Comm dialog box are disabled except for the display selection window minimization and the Stop button If the 5110Comm dialog box is minimized its icon in the system tray displays the data point number to show the progress of the run It is OK to read data from the 5110Comm data file into Stable32 on the fly during a run In that way a preliminary analysis of the results can be performed while continuing to capture data Access to the help file during a run can be obtained by launching another instance of 5119Comm After a run the on screen portion of the listing phase plot and frequency plot can be examined And of course the data file can be read into Stable32 for a complete analysis The 5110Comm program uses a standard Windows initialization file 5110Comm ini to hold configuration information about the program This file retains the previous COM port data filename scale factor and display mode It can also be manually edited with a text editor such as Notepad to change those and other parameters In particular the number of listing and plot points can be set with the ListSize and PlotSize items in the Preferences sect
281. ram Mod oy x E Sf w a 1 A A uie log i e Mod bo Eh Mu cuu NU EE E Drift oy 0 2 4 6 8 10 log 113 STABLE32 USER MANUAL 114 FREQUENCY DOMAIN STABILITY Noise Spectra e Noise Spectra The random phase and frequency fluctuations of a frequency source can be modeled by power law spectral densities of the form S f h a f where S f one sided power spectral density of the fractional frequency fluctuations 1 Hz f Fourier or sideband frequency Hz h a intensity coefficient a exponent of the power law noise process The most commonly encountered noise spectra are White Random Walk f Flicker f Flicker Walk f For examples showing the appearance of these noise types use the Play program to display the file NOISEPIX TKF Power law spectral models can be applied to both phase and frequency power spectral densities PSD Phase is the time integral of frequency so the relationship between them is as 1 f Saf S f 2nfP where S PSD of the time fluctuations sec Hz Two other quantities are also commonly used to measure phase noise Sy PSD of the phase fluctuations rad Hz and its logarithmic equivalent f dBc Hz The relationship between these is S4 f Qvo Sx f 10 logis S O where vo is the carrier frequency Hz The power law exponent of the phase noise power spectral densities is B a 2 These fr
282. rans Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 2 P Tavella A Godone amp S Leschiutta The Range Covered by a Random Process and the New Definition of MTIE Proc 28th PTTI Meeting Dec 1996 pp 119 124 3 P Tavella and D Meo The Range Covered by a Clock Error in the Case of White FM Proc 30th PTTI Meeting pp 49 60 Dec 1998 4 S Bregni and S Maccabruni Fast Computation of Maximum Time Interval Error by Binary Decomposition IEEE Trans I amp M Vol 49 No 6 Dec 2000 pp 1240 1244 83 84 STABLE32 USER MANUAL TIME DOMAIN STABILITY TIE rms e TIE rms The rms time interval error TIR rms is another clock statistic commonly used by the telecommunications industry TIE rms is defined by the expression where n 1 2 N 1 and N phase data points For no frequency offset TIE rms is approximately equal to the standard deviation of the fractional frequency fluctuations multiplied by the averaging time It is therefore similar in behavior to TDEV although the latter is better suited for divergent noise types e References The following reference applies to the TIE rms statistic S Bregni Clock Stability Characterization and Measurement in Telecommunications JEEE Trans Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 85 86 STABLE32 USER MANUAL TIME DOMAIN STABILITY Dynamic Stability e Dynamic Stability A dynamic stability analysis uses a sequence of s
283. requency Max Text Maximum Fourier frequency Min Text Minimum Fourier frequency OK Pushbutton Perform the filtering amp close dialog box Cancel Pushbutton Abort the Filter function close dialog box Help Pushbutton Invoke the Filter help topic e Operation Select the desired filter type and enter the desired cutoff frequency or frequencies Then press OK to perform the filtering or Cancel to abort e Cutoff Frequencies The range of Fourier frequencies for the phase or frequency data set extends from the frequency bin size of fin 1 N t to the Nyquist frequency fax 1 2 t where t is the sampling interval of the data and N is the number of data points extended as necessary by zero padding to the next larger power of 2 Low pass filtration has a pass band that extends from fmin to an upper cutoff frequency fhig High pass filtration has a pass band that extends from a lower cutoff frequency fi to fmax Band pass filtration has a pass band between flow to fhigh While band stop filtration has a stop band between those frequencies 186 ANALYSIS FUNCTIONS Statistics Function e Purpose Use the Statistics function to display basic statistics for and a simple plot of phase or frequency data The full filename and the following statistics are displayed Point Range Points Gaps Minimum Maximum Average Median Std Dev Sigma Noise Type File PHASE gt Phase Data 1e D0 diw Zoom 2 0X Points 228 730 Point
284. responding item in the Inputs section of the INI file the default value is used Otherwise the one in the INI file overrides that value The tau number can be changed in the Opened dialog box or by editing the value in the status bar The addend and multiplier values do not take effect unless the Scale function is executed These items are very useful for setting the tau to a standard measurement interval time for adding a frequency offset and for scaling the data by a particular factor e g microseconds If there is timetag data and no tau Input then the spacing of the first two timetags scaled by the TagScale value is used as the default tau when a data file is opened The TagOffset is applied as the data file is read e Archive The Archive section of the STABLE32 INI file can contain the following parameters Keyword Description Default Num Channels 4 Meas Measurement Channel 2 Ref Reference Channel 1 The Archive section of the INI file contains the default values set by the Read Archive Configure function 324 e Database The Database section of the STABLE32 INI file can contain the following parameters APPENDICES Keyword Description Default Host Host ID address 1 Database Database name tsc postgres User User name tsc Password Password tsc encrypted e Auto f The Auto sections where 1 3 of the STABLE32 INI file can contain the following
285. rint Function e Purpose Use the Print function to print a listing of all or a portion of the current phase or frequency data Data Type C Phase DK Frequency Copy r Data Range Start fi End 51 2 Help Timetaus AllData Press OK to print the selected data or Copy to copy it to the clipboard Controls The Print dialog box contains the following controls Control Type Description Data Type Group Data type Phase Radiobutton Select phase data Frequency Radiobutton Select frequency data Data Range Group Data range Start Edit Enter first point to print End Edit Enter last point to print Timetags Checkbox Print timetag data AII Data Checkbox Print all data OK Pushbutton Perform the Print function amp close dialog box Copy Pushbutton Copy selected data to clipboard Cancel Pushbutton Abort the Print function amp close dialog box Help Pushbutton Invoke the Print help topic 163 STABLE32 USER MANUAL e Operation Choose Phase or Frequency data and enter the Start and End points to print or check All Data to print all the data Check Timetags to also print the corresponding timetag data Then press OK to print Copy to copy or Cancel to abort 164 EDITING FUNCTIONS Edit Function e Purpose Use the Edit function to display search and edit the current phase or frequency data The primary purpose o
286. rmat gif Files etmtenreoneenenneenneoneeneennenneenneeneennene 327 H Hadamard Variance scq epe eee rg ai esee rer d esee eei puede aeg eoo 59 73 195 237 Hamilton Technical Services cccccccccssscccsescecesscececssececesccecsessececssseecsseceesseeecssseecseseeceeaaees ii 2 Help Biles T dis 3 High Pass Hints and Notes eras tias 327 Histogram Function eee cette ettet rettet enne ese ndn es ses ves eae aen esee dedo ene gie ei 211 I Inputs from Configuration File Insert Gaps eene pee aee Insert Plot is ado cordialidad oa e ene Oeo ED at Installations 5a oem isse i ler OR GRO o sd nte edad AA DO vb J Julian Dit it Dee dti ae rec iet ier diia i ne INE S 276 K Keys Editing AERE A 315 L Lag 1 Autocorrelation esses eere enne trennen enne tnter entente nnne enne nennen 93 Large Data Files 135 Launching ae Sl TAGSASEE A not ad E O 2 Ti GIR TAM EDI EM ON E 45 EOW P ssaste kitsa 185 M Man With OW T saad rts Dalai n A da dadas 7 MASK A A A A GE 251 Mean Value id da 175 STABLE32 USER MANUAL Medi t a dada Menu Ti it t e DIEN OBI Ce debe A late P iat MIL O 55310B E Modified Allan Variance cccccccecsccesssscecssscecessseceessececeseeeceessececsssseceeseeceesseeecsseeceesaeesesaeees 65 Modified Julian Date MID isidro eet e tee e ege dettes 275 276 Modified Total V
287. rten the file reading process but will make the subsequent analysis faster Several configuration options can be set to alter the behavior of the file reading operation See the Configuration section of this User Manual for more information about these settings Configuration Item Description Show File Opened Show data plot and other information when file opened Status Plots Show mini data plots in status bar Max Data FileSize Set maximum data file size to read without averaging Non Numerics to Skip Set non numeric characters to skip at beginning of each row of data Use Comma as Decimal Point Use comma instead of decimal point for input data Warn for Zero Freq Data Display warning if two adjacent phase data points are equal 124 FILE FUNCTIONS Read Archive Function e Purpose Use the Read Archive function to extract clock data from a TSC archive file This function will read the information produced by a Timing Solutions Corporation now Symmetricom clock measuring system and convert it into time tagged phase and frequency data for analysis by the Stable32 program Controls are available for selecting the desired data file measurement channels and time span for analysis Read Archive E File archive dat Tau 900 First MJD 51026 00000000 mS i Last MJD 51078 51041667 Display Channel Index Measurement c ij Configure Beference E nee Time Span Record Iv Last C
288. rum and the IEEE Freq Contrl Symp pp 1093 1099 April 1999 D A Howe private communication March 2000 C A Greenhall Recipes for Degrees of Freedom of Frequency Stability Estimators IEEE Trans Instrum Meas Vol 40 No 6 pp 994 999 December 1991 D A Howe Methods of Improving the Estimation of Long Term Frequency Variance Proc 11th European Freq and Time Forum pp 91 99 March 1997 J A Barnes and D W Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 C A Greenhall private communication May 2000 D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proceedings of the 32nd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting pp 255 268 November 2000 C Greenhall and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 2003 PTTI Meeting December 2003 D A Howe and T K Peppler Very Long Term Frequency Stability Estimation Using a Special Purpose Statistic Proceedings of the 2003 IEEE International Frequency Control Symposium pp 233 238 May 2003 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Frequency and Time Forum EFTF April 2004 Session 6B D A Howe R L Beard C A Greenhall F Vernotte W J Riley and T K Peppler Enhancements to GPS O
289. ry of the Allan and Hadamard families of time domain stability measures can be found in the reference below which categorizes then according the following parameters Parameter Symbol Value Variance Remarks Order of phase d 2 Allan difference 3 Hadamard Allowable power a gt 1 2d gt 3 Allan W PM thru RW law noise FM noise exponent gt 5 Hadamard W PM thru RR FM noise Filter factor F m Unmodified m averaging 1 Modified factor t ty Stride factor S 1 Non overlapped estimator Stride 1 S m Overlapped estimator Reference C Greenhall and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 2003 PTTI Meeting December 2003 60 TIME DOMAIN STABILITY Allan Variance e Allan Variance The Allan or 2 sample variance AVAR is the most common time domain measure of frequency stability Its non overlapping version is defined as 2 0 r UE 1 rn AA Yi ie where y i is the ith of M fractional frequency values averaged over the measurement interval Te In terms of phase data the Allan variance may be calculated as N 2 o T 2x TX i 7 AN EX annet i 2 i l ls where x 1 is the ith of the N M 1 phase values spaced by the measurement interval t The result is usually expressed as the square root o t the Allan deviation ADEV The Allan variance is the same as the ordinary variance for white FM noise but has the advantage
290. s Igth y All Data Tested o Loop thru all data gt Done y Calc next pair of avgs Jump Limit Aavg gt lim Calc diff between avgs Yes No Limit Record jump Exceeded An example of a BLKAVG plot is shown below 105 STABLE32 USER MANUAL Date 02 27 08 Time 15 40 45 Data Paints 1 thru 100 of 100 Tou 1 0000000e 00 File NEW FRD FREQUENCY DATA EA PA 80 T 7 Largest Jump 4 886095e 01 at Point 49 UM mm TES JA i X CN iti u TN 20 Ele NEW FRD BLKAVG Jump Detection Results Window Length 10 10 Window Offset 0 Jump Threshold 3 507280e 01 OF 4 Jumps 1 Largest Jump 4 886095e 01 Point Jump Size 49 4 886095e 01 Scaled Cumulative Sum Results 20 Min 2 021790e 004 at Point 100 E Max 1 277337e 003 at Point 4 49 Single Jump Estimate 30 Hump 5 174156e 001 at Point 49 onfidence Factor gt 99 9 40 i i i i ii i i 0 10 20 30 40 50 60 70 80 90 100 Data Point BLKAVG Freq Jump Detection Window Length 10 Window Offset 0 Jump Threshold 3 507280e 01 3 000 sigma Jumps 1 x JEEN Freguency Stables e SEQAVG Frequency Jump Detection The Sequential Average SEQAVG method is similar but instead of dividing the frequency record into fixed blocks it examines the data sequentially If
291. s 503 Gaps 0 Maximum 2 794732e 00 1 Minimum 3 609595e 00 L W an W A Average 190 QU 1 A Median 5 133007e 01 Std Dev 2 881059e 02 p 2 pp A Sigma 2 913097e 02 Noise W FM a 0 m Track copv Ai lt H i Point 682 Basic Statistics 199295 Vajua 18725788 00 for Plotted Data e E WEE e Controls The Statistics dialog box contains the following controls Control Type Description File Text lt gt Pushbutton Swap data type Plot Title Text Statistics Text Plot Graphic Data plot Scrollbar Scrollbar Data selection Point Text Zoom Text Box Zoom factor Track Checkbox Enable scroll tracking Copy Pushbutton Copy plot to clipboard Timetags Combo All Pushbutton Select all data Close Pushbutton Close the Statistics dialog box Help Pushbutton Invoke the Statistics help topic 187 STABLE32 USER MANUAL e Operation Use the mouse cursor to select data points for numeric display and the scrollbar to select them for statistics and plotting Zoom and un zoom the plot with the R and L mouse buttons The Track checkbox determines if the plot updates during scrolling Disable tracking for large data sets and or slow computers Use the Timetags box to select the timetag display for data that has them The All button selects all the data and disables the scrollbar and the lt gt button switches between phase and frequency data
292. s Checkbox Check to label plots at bottom left Label Edit Enter text to appear as plot label e Data Page Controls The Data property sheet page contains the following controls Control Type Description Data Reading Settings Groupbox Settings for reading phase and frequency data Max Data File Size Edit Set maximum data file size to read without averaging Non Numerics to Edit Set non numeric characters to skip at beginning of Skip each row of data Use Comma as DP Checkbox Use comma instead of decimal point for input data Warn for Zero Freq Checkbox Display warning if two adjacent phase data points are Data equal Freq Timetags Groupbox Settings for frequency data timetags 1 Radiobutton Use 1 phase timetag for corresponding freq data Avg Radiobutton Use average phase timetag for corresponding freq data 2 Radiobutton Use 2 phase timetag for corresponding freq data Data Writing Settings Groupbox Settings for writing phase and frequency data Write Header Checkbox Add header to data files Reset Pushbutton Restore default values max size amp non numerics General Toolbuttons Plots Data ptions Audio Run y General Toolbuttons Plots Data Inputs Data Input Scaling Values Audio Run Phase Data Frequency Data Addend 0 0000000000000e 00 Tau 1 0000000000000e 00 1 0000000000000e 00 0 0000000000000
293. s are included for ignoring a selected of non numeric characters from the beginning of each row of phase or frequency data as it is read The NonNums configuration variable sets the of non numeric characters that are skipped at the beginning of each line of data This value normally 0 can be used to read data files that contain non numeric markers at the start of each line This value can be set in either the Configure dialog box or the STABLE32 INI configuration file Data files are parsed for numeric values one line at a time and a non numeric character normally terminates the reading of the current line While this is desirable to reject comments it will also prevent the reading of a line of actual data Thus if the data lines contain non numeric characters the NonNums feature will allow them to be read The MaxSize configuration variable sets the maximum number of data points that can be read without averaging An attempt to load a file that is either larger or too small lt 3 points will generate an error message A larger file can be processed with the Large Data File dialog box either by averaging it or by loading only the first or last portion A file that is smaller than 3 data points cannot be meaningfully processed and is not read 17 STABLE32 USER MANUAL Setting the Comma configuration variable with the Configure function or directly in the Preferences section of the STABLE32 INI file allows commas to be substituted for deci
294. s dialog box contains the following controls Tau 7 0000000000000e 00 Addend 0 0000000000000e 00 Cancel Multiplier 7 0000000000000e 00 Help Tag Scale 8 6400000000000e 04 Tag offsetis applied as file Tag Offset 0 00000000000008 00 mom Press OK to set values stored in Inputs section of Stable32 ini configuration file for phase data Control Type Description Tau Edit Enter the tau value Addend Edit Enter the addend scaling value Multiplier Edit Enter the multiplier scaling value Tag Scale Edit Enter the timetag scale multiplier Tag Offset Edit Enter the timetag offset value OK Pushbutton Store values amp close dialog box Cancel Pushbutton Abort amp close dialog box Help Pushbutton Invoke this help topic e Operation Invoking the Inputs dialog box displays the current Tau Addend Multiplier Tag Scale and Tag Offset values from the Inputs section of the STABLE32 INI configuration file for the current phase or frequency data type These values may be edited and saved by using the corresponding edit control s and pressing OK or any changes made may be aborted by pressing the Cancel button 139 STABLE32 USER MANUAL e inputs Values There are separate Tau Addend Multiplier Tag Scale and Tag Offset inputs values for phase and frequency data The Tau value should be set to the measurement interval of the data in seconds The Multiplier value s
295. s of data The Multicolumn Details dialog can help to understand this data file reading process It is available after the first pass which uses the contents of its last active numeric line to determine the number of data file columns Data File and Line Parsing Flowcharts for the Stable32 data file and data line parsing are shown on the following page e Caution The MJD value is correct only if the right date and time formats are supported and selected Timetag generation using the start MJD value in the Timetags function requires that the data be equally spaced without missing points If there are missing points it may be possible to first use another timetag type from the data along with the Regularize function to insert placeholder gaps into the data and then change the timetags to MJD e See Also Multicolumn Data Function and Timetags Function 133 Inc Line Count Inc Rejected Line Count STABLE32 USER MANUAL Start Read Next Line Done UNIX style comment in 1st char of line controlled by UnixComment read only item in Preferences section of configuration file No Yes Digit in Line Conv Slashes Colons Tabs amp Bars To Spaces Skip nSkipChar Non Numeric Chars Skip Leading Whitespace Digit is 0 9 Conv Commas To Spaces nSkipChar set in 3t Non Numerics to Skip item on Data tab of Configuration Property Sheet Numeric character is 0 9 e or
296. se array Frequency Radiobutton Read data into the frequency array Archive Radiobutton Read TSC archive file Avg By Edit Averaging factor to apply when reading data e Operation Select Phase Frequency or Archive data type and perform the usual file dialog box operations Opening a data file with multiple columns will invoke the Multicolumn Data function The data may be averaged as it is read by entering a non unity Avg By value Attempting to open an oversize data file as set by the Max Data File Size configuration parameter will invoke the Large Data File function The results of an Open operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function e Filename Extensions The Open function supports DAT general data PHD phase data FRD frequency and all filename extensions Selecting PHD or FRD file types automatically selects the corresponding data type 123 STABLE32 USER MANUAL e Notes The data are read twice first to determine their size and layout and then to read the desired portion averaging and columns Commas are converted to spaces and the resulting whitespace spaces and tabs is used to divide the lines into columns The data are scanned by lines using an array of 8 le fields Non numeric input characters are ignored as are characters in excess of 8 fields Using a non unity averaging factor does not sho
297. select an appropriate variance for the stability analysis The overlapping Allan variance is recommended in most cases especially where the frequency drift is small or has been removed The Allan variance is the most widely used time domain stability measure and the overlapping form provides better confidence than the original non overlapping version The total variances and Th ol can be used for even better confidence at large averaging factors at the expense of longer computation time The modified Allan variance is recommended to distinguish between white and flicker PM noise and again a total form of it is available for better confidence at long tau The time variance provides a good measure of the time dispersion of a clock due to noise while MTIE measures the peak time deviations TIE rms can also be used to assess clock performance but TVAR is generally preferred Finally the overlapping Hadamard variance is recommended over its non overlapping form for analyzing stability in the presence of divergent noise or frequency drift In all cases the results are reported in terms of the deviations The choice of tau interval depends mainly on whether interference mechanisms are suspected which cause the stability to vary periodically Normally octave spacing will be used with decade spacing available to analyze tau multiples of ten The all tau option can be useful as a form of spectral analysis to detect cyclic disturbances such as temperatur
298. should then be cleared The Regularize function cannot accomplish this with artificially generated timetags 230 ANALYSIS FUNCTIONS Noise Function e Purpose Use the Noise function to function to generate simulated power law clock noise Noise Parameters Alpha Noise OK Random Walk FM o 00000e 00 2 parameter Cancel is Allan Elicker FM 0 00000e 00 1 deviation at Copy Tau 1 sec White FM Jo 000002 00 0 Help Points Flicker PM 0 00000e 00 1 Num 513 White PM 0 00000e 00 2 Tau 1 000008 00 Fractional Frequency Parameters Offset 0 000006 00 Drift per Tau Interval 0 000008 00 Sine peak o 00000e 00 Sine Period sec o 00000e 00 E Press OK to generate simulated power law clock noise e Controls The Noise dialog box contains the following controls Control Type Description Noise Params Group Power law noise parameters RW FM Edit Enter random walk FM noise coefficient o 1 Flicker FM Edit Enter flicker FM noise coefficient o 1 White FM Edit Enter white FM noise coefficient o 1 Flicker PM Edit Enter flicker PM noise coefficient o 1 White PM Edit Enter white PM noise coefficient o 1 Points Group Points and t interval Num Edit Enter points Tau Edit Enter t sampling interval Freg Params Group Fractional freguency parameters Offset Edit Enter fractional freguency offset Drift Edit Enter fractional fre
299. si uniform distribution of points on the stability plot adequate to give the appearance of a complete set which can provide much faster calculating plotting and printing The Size edit box sets the approximate number of points used for the many tau analysis default 500 The two Reset pushbuttons restore the defaults for the PSD or many tau parameters Notes 1 The display of data plots on the status bar applies only for XGA and higher screen resolutions 2 The Inputs parameters may also be set with the Inputs function e See Also Configuration File Inputs Function 55 56 STABLE32 USER MANUAL GENERAL Configuration File e Description The STABLE32 INI file holds all the configuration data for the Stable32 program The format of this file is that of a standard Windows INI file such as WIN INI The Section items define the sections of this file while the Keyword String items define the configuration information Each keyword is set equal to a string which may be either a Boolean value 0 or 1 or an unterminated string of characters which may contain spaces See Appendix IV for more information about the STABLE32 INI configuration file e Operation Ordinarily the reading and writing of STABLE32 INI is automatic and it is not necessary to edit it directly However manual editing is useful in batch file automation and can be done from within the Stable32 program using the Pad function The changes will take effe
300. spectral density of the time fluctuations and S f rad Hz the power spectral density of the phase fluctuations The Stable32 program can plot any of these from the appropriate phase or frequency data 109 STABLE32 USER MANUAL 110 FREQUENCY DOMAIN STABILITY Noise Processes e Power Law Noise Processes The spectral characteristics of the power law noise processes commonly used to describe the performance of frequency sources are shown in the following table Spectral Characteristics of Power Law Noise Processes Noise Type a B p w n White PM 2 0 2 3 1 Flicker PM 1 1 2 2 0 White FM 0 2 1 1 1 Flicker FM 1 3 0 0 2 Random Walk FM 2 4 1 1 3 e Power Spectral Densities Four types of power spectral density PSD are commonly used to describe the stability of a frequency source PSD of Frequency Fluctuations S f The power spectral density PSD of the fractional frequency fluctuations y t in units of 1 Hz is given by S f h a where f sideband frequency Hz PSD of Phase Fluctuations S f The PSD of the phase fluctuations in units of rad Hz is given by S f 2nvo gt S f where Vo carrier frequency Hz PSD of Time Fluctuations S f The PSD of the time fluctuations x t in units of sec Hz is given by S f h B S D 2nf where B a 2 The time fluctuations are related to the phase fluctuations by x t o t 2mvo9 Both are commonly
301. ssi i sSSCS CABIbleSASIGMATKE OOO CAStable3AHISTOTRE O Spectrum C Stable32 SPECTRUMTKF 00000 CAStable3MAUTOTKE SSCS DAVAR C Steble32 DAVARTKF O O O el Reset Cancel Help m Data Filenames mii Phase _ C Stable32 PHASE DAT A 3 Enter plot amp Freq C Stable32 FREQ DAT ee Stability C Stable32 SIGMA TAU names Set paths or PSD C Stable32 PSD DAT Reset them to defaults ACF 2 C Stable32 AUTO DAT Path CAStable32 e Controls The Filenames dialog box contains the following controls Stability Edit Control Type Description Plot Filenames Groupbox Controls to set plot filenames Phase Edit Enter phase plot filename Freq Edit Enter frequency plot filename Sigma Edit Enter sigma plot filename Histo Edit Enter histogram plot filename Spectrum Edit Enter power spectrum plot filename ACF 1 Edit Enter autocorrelation plot filename DAVAR Edit Enter dynamic stability plot filename Data Filenames Groupbox Controls to set data filenames Phase Edit Enter phase data filename Freq Edit Enter frequency data filename Enter stability data filename PSD Edit Enter power spectrum data filename 121 STABLE32 USER MANUAL Control Type Description ACF 2 Edit Enter autocorrelation data filename Path Edit Enter the filename path OK Pushbutton Apply filenames amp cl
302. t O Pushbutton Enter initial parameter values Type Combo Choose line options Date Checkbox Show date on plot Box 5 Checkbox Draw box around plot Fit 6 Checkbox Show fit parameters at bottom of plot Wide Checkbox Use wide lines for data plot Cur 9 Checkbox Activate mouse cursor Plot File Edit Enter plot filename Read Config 1 Pushbutton Read plot configuration data from STABLE32 INI Save Config 2 Pushbutton Save plot configuration data in STABLE32 INI Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke this help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort Press Reset All to reset all attributes to their default values Both of the Stable32 phase and frequency data plots have defaults that give reasonable plots automatically Common changes are to modify the Subtitle Title to add a Message and to Scale and re Label the axes Standard and previous titles subtitles and messages may be selected from their combo box controls Several curve fits are available from the Options box as described in the Drift function The X axis is rescaled automatically when new time units are selected Since the x axis time scale is determined automatically use the X Divs
303. t a longer tau which corresponds to frequency averaging Do not confuse this process with actual averaging of the phase data such as is done when computing the modified Allan variance e Frequency Averaging Frequency averaging is done by finding the mean value of the data points being averaged e Gaps Gaps 0s are ignored and the average will be a gap if all points in the group being averaged are gaps 177 STABLE32 USER MANUAL 178 EDITING FUNCTIONS Fill Function e Purpose Use the Fill function to fill gaps in the selected portion of phase or frequency data with interpolated values Leading and trailing gaps are removed the of data points is adjusted and the analysis limits are reset Gaps 2 Press OK to fill gaps in data with interpolated values e Controls The Fill dialog box contains the following controls Control Type Description Gaps Text Display gaps in data OK Pushbutton Perform the Fill function amp close dialog box Cancel Pushbutton Abort the Fill function amp close dialog box Help Pushbutton Invoke the Fill help topic e Operation Press OK To abort press Cancel or OK if gaps 0 e Caution The data inserted are simply interpolated values using the closest non gap data points at either side of each gap No attempt is made to simulate noise and the resulting statistics are not necessarily valid It is generally better practice to
304. t be scaled to seconds e g 86400 by the PhaseTagScale multiplier in the STABLE32 INI which can be entered from the Inputs function accessed via the Data File Opened dialog box or the Utilities menu The average timetag interval is used as the tau value for the converted frequency data e Notes The conversion of phase data having two equal adjacent values results in a fractional frequency value of zero While this is correct it would subsequently be treated as a gap in the frequency data That problem can be avoided by using the Adjust Zero Frequency option during the phase to frequency conversion which will adjust the frequency value to 1e 99 e Cautions Gaps in frequency data are converted to phase data by linear interpolation using the average frequency value which can cause a discontinuity in the resulting phase data The Use Timetags for Tau option will fail generating an error message if two adjacent timetags are equal Frequency data converted from unequally spaced phase data using the Use Timetags for Tau option will be correct but must have approximately the same tau to support subsequent analysis 174 EDITING FUNCTIONS Normalize Function e Purpose Use the Normalize function to remove the average value from phase or frequency data This normalizes the data to have a mean value of zero 5 403683e 01 Average Press OK to normalize data by X 0 removing the average value from each point
305. t interval by the expression 3 1 M 3m j m 1 2 H um SA eo o T 6m M 3m 1 2 2 Pos Yun Xil where y is the ith of M fractional frequency values at each measurement time In terms of phase data the overlapping Hadamard variance can be estimated from a set of N M 1 time measurements as 1 N 3m Ho t 6 N 3m r las m 3X on BX eam E el i l where x is the ith of N M 1 phase values at each measurement time Computation of the overlapping Hadamard variance is more efficient for phase data where the averaging is accomplished by simply choosing the appropriate interval For frequency data an inner averaging loop over m frequency values is necessary The result is usually expressed as the square root Ho t the Hadamard deviation HDEV The expected value of the overlapping statistic is the same as the normal one described above but the confidence interval of the estimation is better Even though all the additional overlapping differences are not statistically independent they nevertheless increase the number of degrees of freedom and thus improve the confidence in the estimation Analytical methods are available for calculating the number of degrees of freedom for an overlapping Allan variance estimation and that same theory can be used to establish reasonable single or double sided confidence intervals for an overlapping Hadamard variance estimate with a certain confidence factor based on Chi squared statist
306. t squares linear regression to the frequency data y t a bt where a intercept b slope y t This is the optimum method for white FM noise The second method computes the drift from the frequency averages over the first and last halves of the data slope 2 y 2nd half y 1st half Nx where N points This bisection method is optimum for white and random walk FM noise The third method a log model of the form see MIL O 55310B y t a In bt 1 where slope y t ab bt 1 which applies to freguency stabilization It is available in the Plot function for freguency data The fourth frequency drift method is a diffusion Vt model of the form 1 2 y t a b t c where slope y t 4 b t cy It is also available in the Plot function for freguency data In addition there is an autoregression method that can fit and optionally remove AR 1 autoregressive noise from freguency data according to the eguation y t y t 1 r 1 y t where r 1 is the lag 1 autocorrelation coefficient That method calculates r 1 for a selected averaging factor and uses it to remove a first order AR 1 noise process It is useful for prewhitening data before a jump analysis Auto Calc A drift analysis can be done automatically when the Drift function is invoked by setting the AutoCalc item in the Configure function 194 ANALYSIS FUNCTIONS Sigma Function e Purpose Use the Sigma fun
307. table32 program is restarted All of these options may also be changed by editing the STABLE32 INI configuration file e General The Write Sigma File checkbox controls the option to write the stability data to a file after a Run Use the Filenames function to set the stability data filename to a name other than its default SIGMA TAU before performing a Run The Autoinc Filename Ext checkbox controls the option to automatically increment the data filename after it changes Phase data has an even filename extension number while frequency data has an odd extension number The Show File Opened checkbox controls the option to show a data plot and other information when a data file is opened This also allows the data file to be displayed and the data and timetags to be scaled as it is read The AutoCalc checkbox controls the option to automatically perform a default calculation upon entry to the Sigma and Run function The AutoPlot checkbox controls the option to automatically do a default phase or frequency data plot upon entry to the Plot function The Show Status Plots checkbox controls the option to display small phase and frequency data plots on the status bar at the bottom of the screen This option is offered because it can take a significant amount of time to redraw these plots for large data files 53 STABLE32 USER MANUAL e Toolbuttons The Toolbuttons Configure page contains a multiple selection list box to select the Toolbutt
308. ted frequency data is averaged Remove Remove bad data points Use the Check or Edit Outliers must be removed to Outliers function perform meaningful analysis Fill Gaps Eliminate gaps Replace gaps with Gap filling is necessary for interpolated values some analysis procedures but can cause bias Regularize Establish uniform data Use Regularize function Timetags required Data spacing 300 OTHER INFORMATION What Why How Remarks Remove Offset Obtain better plot scale improve dynamic range Use Normalize or Scale function or combine with drift removal Removing an offset may be necessary to produce data plot and can help with other aspects of analysis Remove Drift Remove drift before analyzing noise Use the Drift or Scale function It is usually best to first analyze and remove frequency drift before performing a noise analysis Remove AR 1 Autoregressive Fit Prewhiten data Use autogression option of frequency Drift function Prewhitening can help to distinguish frequency jumps from divergent noise Remove Functional Fit Fit data to an arbitrary function and optionally remove it Use function fit option of data Plot function Remove sinusoidal or other fit not otherwise supported Detect and Delete Spurs Look for and optionally remove Use spur detection feature of Power Discrete components can interfere wit
309. ted alpha value is particularly helpful for mixed noises because it indicates the approximate proportions of the two dominant noise types e g alpha 1 50 indicates an equal mixture of white and flicker PM noise e Lag Scatter Plot The Lag k checkbox inserts a scatter plot of the phase or frequency data plotted against itself with a lag of k The data at time t k is plotted on the y axis versus the value at time t on the x axis This plot is another way of showing the degree of correlation in the data and the slope of a linear fit to these points is closely related to the lag k autocorrelation 208 ANALYSIS FUNCTIONS The lag scatter plot is a cluster of uncorrelated points for white noise and has a linear shape for the more correlated flicker and random walk noises It will assume a circular form for noise having a sinusoidal component when the lag is at or near one quarter of its period Boxes showing the one two and three sigma error bounds are drawn on the lag scatter plot with dashed lines Not all of these boxes may be visible The lag scatter plot can take a considerable time to draw and the normal filled dot symbol is replaced with a cross when the of analysis points is 10 000 and higher The subtitle of the lag scatter plot is the same as the autocorrelation plot e ACF Data File A data file comprising rows of 2 columns of lag and ACF values is written each time a dynamic stability plot is generated This file which has a d
310. ted and allows the user to Abort printing before the output is File to fill the entire page instead of a 9 x 6 884 inch region The user may also select whether preference options will be saved upon exiting Play Stop The File menu s Stop command will stop the plotting of the current TKF SP plot An alt s from the keyboard can also be used to stop the current plot The File menu s Exit command will close the currently opened TKF file and Exit ask Windows to terminate the current instance of Play Windows Help will be terminated if left open when the user exits Play 41 Draw 42 STABLE32 USER MANUAL Copy Bitmap Copy Metafile Go To Plot The Edit menu s Copy Bitmap command will make a bitmap of the user s client area and copy it to the Windows clipboard for importing into another application The Edit menu s Copy Metafile command will make a metafile of the current plot and copy it to the Windows clipboard for importing into another application Note The Copy Metafile can be used only once after Stable32 is launched and a Copy Metafile not available message will appear thereafter Use the Convert Metafile function instead The Draw menu s Draw Next command is used to start the drawing of the next plot in the currently opened TKF file A return key from the keyboard will also generate a Draw Next command Note This does not apply to Stable32 plots The Draw menu s Redraw command is used to redraw t
311. termined by the difference between the first two timetags If this value is not correct edit the data file with a text editor before executing the Regularize function The Regularize function operates on the full data array 259 STABLE32 USER MANUAL 260 ANALYSIS FUNCTIONS Domain Function e Purpose Use the Domain function to perform basic time and frequency domain conversions for power law noise processes Domain FI Close Copy 1 Clear All Help KA Time Domain Sigma Type Normal y Tau Sec 1 000008 00 Frequency Domain PSD Type up dBc Hz y SB Freg Hz 00000e 00 Carrier Freq 1 00000e 01 Avg Factor n oo ronnonn Bwraeor 263156 Power Law Noise Power Law Noise Type dB dec PSD Type Mu Sigma BWFM 4 None BWFM 1 f0 00000e 00 EFM 30 None EPM oo000e 00 WFM 20 eo r00000e131 FEM 1 None ron000e 00 WPM o0 L2328te 12 All 80 0 1 00757e 11 PSD Plot Sigma Plot BESO Start Freq 1 00000e 00 Start Tau 1 00000e 03 Porso End Freg 1 00000e 03 End Tau 1 00000e 00 Enter parameters to denotes none BW applies only to W amp F PM noise e Controls The Domain dialog box contains the following controls Control Type Description Sigma Type Combo Choose sigma
312. ters Start Freq Edit Enter PSD plot start frequency End Freg Edit Enter PSD plot end freguency Sigma Plot Groupbox Sigma plot parameters Start Tau Edit Enter sigma plot start tau End Tau Edit Enter sigma plot end tau Plot PSD Pushbutton Show PSD plot Plot Sigma Pushbutton Show sigma plot e Operation The Domain function is a flexible spreadsheet like tool that performs a variety of conversions as values are entered Begin by entering values for the domain being converted from Choose the desired PSD or Sigma Type and the associated basic parameters in the upper panels These are the SB and Carrier Freq for the frequency domain or Tau and Avg Factor for the time domain The BW and BW Factor applies only to white and flicker PM noise and may be entered later Then enter the PSD or Sigma power law noise parameters for any combination of RW FM F FM W FM F PM and W PM noise The corresponding parameters for the other domain are updated automatically as is the total noise for each domain Besides these domain conversions other common operations are changing the PSD Type to perform units conversions changing the SB Freq to obtain the phase noise versus sideband frequency and changing the Avg Factor to obtain sigma versus averaging time It all cases the overall display is automatically updated in a consistent manner To plot the PSD or sigma results enter the respective Start and End plot limits and press the respective Plot butto
313. th the coefficients as follows Power Law HVAR edf Noise Type coefficients a0 al W FM 7 9 1 2 F FM 1 00 0 62 RW FM 31 30 17 28 FW FM 1 06 0 53 RR FM 1 30 0 54 e TOTMVAR EDF The edf for the total modified variance TOTMVAR is given by the formula b T t c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table Power Law TOTMVAR edf Noise Type coefficients b c W PM 1 90 2 10 F PM 1 20 1 40 W FM 1 10 1 20 F FM 0 85 0 50 RW FM 0 75 0 31 e Th ol EDF See the Th ol section of this User Manual for a discussion of the Th ol edf and confidence intervals e Analysis Points The in the Run stability table and the Analysis Pts in the detailed Sigma dialog box is the number of analysis points the of 2nd or 3rd differences summed in the sigma calculation This number is used in determining the confidence intervals Without gaps the s are equal to the following 92 TIME DOMAIN STABILITY Sigma Type Normal Allan M m 1 Overlapping Allan M 2m 1 N 2m Modified amp Time M 3m 2 N 3m 1 Total M m N m 1 Mod amp Time Total M 3m 2 N 3m 1 Hadamard M m 2 Overlapping Hadamard M 3m 1 N 3m where N phase data points M 1 M frequency data points m AF averaging factor For the norma
314. the following controls Control Type Description Plot Pushbutton Plot autocorrelation Scatter Pushbutton Plot lag scatter plot Title Combo Edit or select plot title SubTitle Combo Edit or select plot subtitle Message Combo Edit or select plot message Position List Select message position Avg Factor Edit Averaging factor for autocorrelation Tau Text Averaging time for autocorrelation Read Config Pushbutton Read configuration data from INI file Save Config Pushbutton Save configuration data to INI file ACF File Edit Enter autocorrelation function data filename Plot File Edit Enter autocorrelation plot filename Lag Edit Scatter plot lag X Axis Groupbox X axis parameters X Label Text X axis label Lag Lags Edit of autocorrelation lag points 207 STABLE32 USER MANUAL Control Type Description Y Axis Groupbox Y axis parameters Y Label Text Y axis label Autocorrelation Options Groupbox Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Cursor Checkbox Activate mouse cursor for plot Zero Checkbox Draw horizontal line at zero Lag k Checkbox Show lag k scatter plot Wide Checkbox Use wide lines for spectrum plot Reset All Pushbutton Reset all parameters to defaults Help Pushbutton Invoke this help topic Close Pushbutton Close the Power dia
315. the page the top of the plot is to appear The default is the top The Convert menu s TIFF command is used to display a TIFF conversion dialog box to select the filename and resolution of the TIFF file to be produced The user is asked to select one of four TIFF image resolutions and the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The Convert menu s CGM command is used to display a CGM conversion dialog box to select the filename and page orientation of the CGM Computer Graphics Metafile file to be produced The user is asked to select the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The Convert menu s GEM command is used to display a GEM conversion dialog box to select the filename and page orientation of the GEM file to be produced The user is asked to select the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top 43 STABLE32 USER MANUAL The Convert menu s PIC command is used to display a PIC conversion dialog box to select the filename and page orientation of the PIC file to be produced The user is asked to select the page orientation The page orientation refers to which side left right or top of the page the top of t
316. their respective plots This row also shows the total of points in each data file The next row shows the file titles and the of analysis points The file title may be edited The bottom row shows the tau value and the analysis start and end points Those parameters may also be changed by entering the desired values into their corresponding edit boxes The Stable32 status bar optionally shows small plots of the phase and frequency data Those plots are activated by the Status Plots checkbox of the Configure function The active status bar plot is red and the inactive one is black which can be made the active data type by clicking with the L mouse button The active plot may be zoomed in centered on the position of the mouse cursor with the R mouse button and un zoomed out with the L mouse button The analysis limits change accordingly The status plots are available only with XGA 1024x768 or higher screen resolution and then only if the main window width is large enough The status bar also displays bitmaps for each data type to indicate 1 the data has changed and is unsaved 2 the data has corresponding timetags and 3 the analysis limits are restricted The full analysis limits may be restored by clicking on the small button next to the analysis limit bitmap A blue bitmap at the top center of the status bar indicates when the two data arrays contain corresponding data CAstable32phase dat Date 02 26 98 MJD 50870 P
317. til at least one result is displayed The analysis point being processed is repeated if the run is stopped so the most efficient time to interrupt a run is immediately after a point is completed It may take a little while for the program to respond to the Stop button during a run with a large data set It may take a while for the progress bar to indicate anything when starting a run with a large data set The progress bar shows each point during a TOTMDEV TOTTDEV or MTIE octave or decade run and the overall progress during an all tau run During the latter the current averaging factor is displayed on the status bar 329 STABLE32 USER MANUAL 330 APPENDICES Appendix VI 5110Comm Communications Program e 5110Comm 5110Comm is a program to capture data from the Timing Solutions Corporation TSC now Symmetricom Model 5110A Time Interval Analyzer for analysis by Stable32 It may be launched from within Stable32 by clicking on its toolbutton or the TSC 5110A item in the Utilities menu TSC 5110A Communications Program Bie E3 comz O Open 9600 8 1N i E M Filename c stable32 comm dat Close iius Press Startto Scale Factor 0000000000e 09 Help read data inta file via comm C List C PlotPhase PlotFreq 1161 port l TET ibd id L X Axis 30 sec div Y Axis 1 917e 11 to 1 270e 12 3 480e 12 div Avg Freq 9 99261e 12 2 711e 13 scaled e Condensed Operating Instructions 1 Co
318. tion 1 396338e 01 3 752293e 01 1 320847e 00 Notes 1 Expected value 0 5 2 All slopes are per interval 3 Least sguares linear fit 4 Exact results will depend on iterative algorithm used Data not suited to log fit 5 Sample not population standard deviation Expected value 1 V12 0 2886751 6 Expected value egual to standard deviation for white FM noise 7 Equal to normal Allan deviation for averaging factor 1 8 Calculated with listed averaging factors from the basic t 1 data set 297 STABLE32 USER MANUAL Table IV Error Bars for n 1000 Point 1 Data Set with Avg Factor 10 Allan Deviation Sigma Value Confidence Interval X for Type Points Noise Type amp Ratio 95 CF Normal 9 965736e 02 CI 8 713870e 03 2 3 99 W FM 1 B1 0 870 16 CI 6 Overlapping 9 159953e 02 Max 0 1 1 014923e 01 7 119 07 981 W FM Max o x 1 035201e 01 8 114 45 X df 146 177 Min o t 8 223942e 02 8 181 34 Modified 4 6 172376e 02 Max o 1 7 044412e 02 7 72 64 972 W FM 5 R n 0 384 Max o 1 7 224944e 02 8 69 06 y df 94 620 Min o 1 5 41996 1e 02 8 122 71 Notes 1 Theoretical B1 1 000 for W FM noise and 0 667 for F and W PM noise 2 Simple noise independent CI estimate o XN 1 001594e 02 3 This CI includes k a factor that depends on noise type Noise a x a WPM 2 0 99 F PM 1 0 99 WFM 0 0 87 FFM l 0
319. to divergent noise drift or wandering in order to better see and analyze the high frequency noise This is particularly effective when the drift or wandering does not fit a function to allow its removal Band pass filtration can be useful for analyzing the amplitude variations of a discrete interfering component Its function resembles that of a classic wave analyzer Band stop filtration can be useful for removing a discrete interfering component By repeating this operation multiple components may be removed without significantly affecting the underlying behavior m Filter Type C High Pass C Low Pass Cancel Band Pass Help C Band Stop High 2 00000e 01 5 00000e 01 Low h 00000e 01 Min 1 95313e03 m Cutoff Frequency Hz Select filter type and enter cutoff frequencies Then press OK to apply filtering e Controls The Filter dialog box contains the following controls Control Type Description Filter Type Groupbox Filter types High Pass Radiobutton Select high pass filter Low Pass Radiobutton Select low pass filter Band Pass Radiobutton Select band pass filter Band Stop Radiobutton Select band stop filter Cutoff Frequency Groupbox Filter cutoff frequencies Hz High or Cutoff Edit Enter upper cutoff frequency 185 STABLE32 USER MANUAL Control Type Description Low or Cutoff Edit Enter lower cutoff f
320. togram dialog box Reset All Pushbutton Reset all parameters to defaults Help Pushbutton Invoke this help topic e Operation Enter the desired Title Sub Title Message message Position and Options Check Normalize to remove the mean value from the data This may be required if the data has relatively small variations around a large average value Normalization does not permanently affect the data in memory If the Normalize checkbox is grayed normalization is required and will be done automatically and the mean value removed will be displayed as the default message The original data is not affected The Fill control can be used to eliminate the filled histogram bars for better printouts Then press Plot to plot the histogram or Close to close the Histogram dialog box e Example An example of a histogram plot is shown below i GraphiC Win histo tkf Eile Edit Draw Convert Help Doe 02 27 35 ilme 701023 Dolo Palms 1 thru 1007 af 001 Tou 1 0009000e 00 Fhe obose dol HISTOGRA 150 phase dat El ES a g E 212 Plot Function e Purpose Use the Plot function to control the plotting of the current phase or frequency data e Controls The Plot dialog box contains the following controls ANALYSIS FUNCTIONS e Operation Simply press the button for the desired plotting function e Auto Plot Plotting can be done automatically bypassing the Plot function dialog box by
321. type Tau sec Edit Enter basic measurement time Avg Factor Edit Enter averaging factor BW Factor Edit Enter bandwidth factor PSD Type Combo Choose power spectral density type SB Freq Hz Edit Enter the sideband frequency in Hz Carrier Freq Edit Enter the carrier frequency in MHz BW Hz Edit Enter the measuring system bandwidth PSD Label Use ALT P to access PSD parameters PSD RWFM Edit Enter or read the random walk FM PSD noise parameter PSD FFM Edit Enter or read the flicker FM PSD noise parameter 261 STABLE32 USER MANUAL Control Type Description PSD WFM Edit Enter or read the white FM PSD noise parameter PSD FPM Edit Enter or read the flicker PM PSD noise parameter PSD WPM Edit Enter or read the white PM PSD noise parameter Sigma Label Use ALT G to access sigma parameters Sigma RWFM Edit Enter or read the random walk FM sigma noise param Sigma EFM Edit Enter or read the flicker FM sigma noise parameter Sigma WFM Edit Enter or read the white FM sigma noise parameter Sigma FPM Edit Enter or read the flicker PM sigma noise parameter Sigma WPM Edit Enter or read the white PM sigma noise parameter Clear All Pushbutton Restore all parameters to their default values Copy 1 Pushbutton Copy results to clipboard Close Pushbutton End the Domain function close dialog box Help Pushbutton Invoke this help topic PSD Plot Groupbox PSD plot parame
322. uations for the noise fit while the Fit Parameters box shows the values of the all the fit parameters e Drift Analysis Methods Several drift methods are available for both phase or frequency data as described below The best method depends on the quality of the fit which can be judged by the randomness of the residuals Drift Analysis Methods Data Method Noise Model Quadratic Fit W PM Avg of 2nd Diffs RW FM bide 3 Point Fit W amp RW FM Linear Freq Offset Avg of 1st Diffs Freq Offset Endpoints Freq Offset Linear Fit W FM Bisection Fit W amp RW FM Freq Log Fit Stabilization Diffusion Fit Diffusion Autoregression AR 1 192 ANALYSIS FUNCTIONS e Averaging Factor The detailed Drift dialog box also has an Avg Factor edit control when either the log or diffusion drift type is selected for frequency data The averaging factor for these fit calculations can be set larger than the normal value of 1 to provide a better fit in the presence of noise This is especially useful for large data sets having a short measurement interval where both the short term noise and drift are high compared with the flicker floor In that case an averaging factor sufficient to show the drift is suggested perhaps up to VN where N is the of data points A larger averaging factor also speeds up the iterative fit calculation Phase Data Three drift methods are available to analyze frequency drift in phase
323. uggestions Cosmo Little for many helpful discussions about spectral analysis Thanks all those who have contributed ideas toward and reported bugs for the Stable32 program I hope this latest version will also prove useful 306 APPENDICES Appendix I Stable32 Functions e Stable32 Functions The Stable32 program includes the following functions File Functions Editing Open Function Read Archive Multicolumn Data Large Data File Data File Opened Add Function Save Function Database Function Read Function Print Function Functions Edit Function Find Function Replace Function Fill Function Scale Function Part Function Regularize Function Timetags Function Normalize Function Average Function Clear Function Conversion Functions Convert Function Domain Function Plot Functions Plot Function Plot Options Plot Lines Plot Notes Analysis Functions Sigma Function Run Function Run Options Run Lines Run Notes Dynamic Stability Function Check Function Statistics Function Drift Function Plot Function 307 STABLE32 USER MANUAL Analysis Functions Con t Autocorrelation Function Power Function Histogram Function Miscellaneous Functions 308 Calendar Noise Function Configure Filenames Autor 3 Cornered Hat Function Audio Function Vibra Function APPENDICES Appendix II Special Characters e Special Characters The Stable32 GraphiC graphics functions make use of severa
324. ull down Convert and select the file type to convert the currently displayed TKF plot Drag and Drop Play uses the drag and drop feature of Windows to allow a TKF file to be dropped into the Play window to start the displaying of that TKF file Alternatively the user may associate TKF files with Play by defining a link between TKF files and Play Play supports the use of command line arguments and assumes the first argument to be a TKF file name to open and display Exiting GraphiC and Play may be terminated by selecting the File Exit menu or by entering an ALT X from the keyboard 44 Log File e Log File A STABLE32 LOG file is automatically written to record a synopsis of all program activity during each run This ASCII text file contains a line for each major function called It gives a summary of the operation performed and thus can be used to document the steps performed during an analysis An example of a STABLE32 LOG file is shown below 01 17 99 01 17 99 01 17 99 01 17 99 01 17 99 The first two 113 des T1 11 115 GENERAL 08 Stable32 Version 1 46 Log File 08 Freq Data Opened FREQ DAT 09 Freq Sigma Type Overlapping AF 1 Sigma 2 922319e 01 09 Freq Data Plot C Stable32 FREQ TKF 09 Stable32 Closed columns show the date and time in MM DD YY and HH MM format respectively The text on each line describes the operation performed and as appropriate a summary of the results obtained A new log file is
325. values are shown in the text box below the plot when the mouse cursor is in the plot region Phase data is read at the points while freq data is read on the horizontal lines that show the averaging time Timetags can also be displayed for the selected data point in MJD DOY Date or general exponential formats e Data Type Switching Use the lt gt button to switch between equivalent phase and frequency data at the same zoom factor Caution The Statistics function can be slow when processing frequency data having many repeated values because of the function used to find the median value 188 ANALYSIS FUNCTIONS Check Function e Purpose Use the Check function to check for and remove outliers from frequency data e Controls The Check dialog box contains the following controls Sigma Factor Edit Enter desired outlier criterion Outliers Text Display the of outliers Remove All Checkbox Remove all frequency outliers Show Details Checkbox Show detailed Check dialog box Calc Pushbutton Perform Check function amp close dialog box Close Pushbutton Abort Check function amp close dialog box Help Pushbutton Invoke the Check help topic Activating the Show Details option adds the following controls to the Check dialog box 189 STABLE32 USER MANUAL Control Type Description Sort Order Group Choose sort order Position Radiobutto
326. voked in this way the automation script is executed immediately without requiring that it be started with the Go button e Automation Scripts Three separate automation scripts are stored in the STABLE32 INI configuration file under the Auto sections Each of these sections has the same items that define the analysis steps for each automated analysis While it is possible to edit these configuration file items directly it is recommended that the corresponding Auto dialog box be used to avoid errors e Analysis Methods The Stable32 automation script feature is intended as a convenient way to quickly produce basic stability analysis information It is not intended to replace either manual analysis or complete batch files The former has the advantage of close user integration and insight while the latter can harness the full capabilities of the program including plot customization and annotation e Caution While considerable effort has been taken to make this automation process robust and useful many factors including data size hardware speed and concurrent programs can affect the script execution and successful operation cannot be guaranteed 267 STABLE32 USER MANUAL 268 e Purpose Use the 3 Cornered Hat function to separate variances from 3 sets of stability data e Controls MISCELLANEOUS FUNCTIONS 3 Comered Hat Function The 3 Cornered Hat dialog box contains the following controls 3 Cornered Hat x
327. welcome screen 1 CheckDetails Flag for detailed check box 0 DriftDetails Flag for detailed drift box 0 SigmaDetails Flag for detailed sigma box 0 WideEdit Flag for wide edit box 0 NormFreg Flag to normalize freguency during conversion 0 XferTags Flag to transfer timetags during conversion 0 ManyTau Flag for many tau run 1 ManySize Many tau parameter 500 UseTags Flag to use timetags for tau 0 Weight Flag for weighted stability plot noise fit lines 1 Smooth Flag to apply smoothing to PSD plot 0 PSDAvgSize Relative max PSD automatic averaging factor 64 PSDAvgMax Absolute max PSD automatic averaging factor 256 PSDLFSkip low frequency PSD points to skip 1 PSDSmoothPPO PSD smoothing points octave 64 PSDLine Weight Flag to weight smoothed PSD semilog fit 1 PointSzie Point size for printouts 9 MaxTheoBRPts Max phase points used for Th oBR bias calc 3000 ZeroPad Flag to use zero padding in PSD FFT cales 1 FreqTagType Code for freq timetag type 0 PSDSpurLimit Spur detection threshold dB above PSD fit line 20 ExtendSpurRange Extra FFT points removed each side of spur 2 UnixComment Flag to skip line in data file that starts with character 1 Read only FreqPlot The FreqPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null X Label X axis time label text Null Y Label Y axis freq label text Null PlotFile
328. whenever multicolumn data is detected The contents of the last line of the data file are displayed at the bottom of the dialog box to assist in selecting the desired timetags and data column Select destination array s for multicolumn data DK Destination Array Column Ue JAS ae Ts Timetags O wu on Y Details Data 9 O E E Help LastLine 75093 1 2008 02 23 05 40 41 0000006577 6 of File BAT e Controls The Multicolumn Data dialog box contains the following controls Control Type Description Timetags Radiobutton Choose column of timetag data to be read Data Radiobutton Choose column of phase or frequency data to be read Ist Line of File Text Display of the 1st line of the data file OK Pushbutton Perform the read operation close dialog box Cancel Pushbutton Abort the read function close dialog box Details Pushbutton Open Multicolumn Details dialog box Help Pushbutton Invoke Multicolumn Read help topic e Operation Select the desired column for the optional Timetags and Data and then press OK to read the data or Cancel to abort Press the Details button to see detailed information about the data file e Limits Up to 8 columns may be processed from the data file with this Multicolumn Data dialog box If the data file has more than 8 columns an alternate Multicolumn Data dialog box opens instead which can handle up to 32 columns 129 STABLE32 USER MANUAL
329. written each time Stable32 is started so the previous one must be renamed in order to preserve it 45 46 STABLE32 USER MANUAL GENERAL Special Versions e Student Version A Student Version of Stable32 is available at a significantly reduced price It is identical in all respects to the standard version except for the following differences 1 No printed User Manual is included 2 The maximum data array size is limited to 513 points 3 The Play and 5110Comm programs are not included 4 The automation function is not supported 5 Printouts cannot be made of data stability power spectrum and histogram plots e Demo Version A Demo Version of Stable32 identical in all respects to the standard version may be available for a free 30 day evaluation period Please contact Hamilton Technical Services for further information 47 48 STABLE32 USER MANUAL GENERAL Configure Function e Purpose Use the Configure function to set certain options of the Stable32 program These options are stored in the STABLE32 INI configuration file The Configure function has six property sheet pages as shown and described below e Property Sheet Controls The main Configure property sheet contains the following controls Control Type Description OK Pushbutton Accept the configuration changes close dialog box Cancel Pushbutton Abort the Configure function close dialog box Help Pushbutton
330. x Title HISTOGRAM SubTitle phase dat S Message y Help Message Position Top Left Read Config Save Config Plot Filename Castable321HISTO TKF Reset All X Axis fees Label Data Value Label Points Per Bin m Options Iv Date Y Box Cursor v Fit Normalize e Controls The Histogram dialog box contains the following controls Control Type Description Plot Pushbutton Plot histogram Title Combo Enter or select plot title SubTitle Combo Enter or select plot subtitle Message Combo Enter or select plot message Position List Select message location on plot Read Config Pushbutton Read configuration data from INI file Save Config Pushbutton Save configuration data to INI file Plot Filename Edit Enter plot filename X Axis Groupbox X axis parameters Label Text X axis label Y Axis Groupbox Y axis parameters Label Text Y axis label Options Groupbox Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Cursor Checkbox Activate mouse cursor for plot Fit Checkbox Draw normal curve fit on plot Norm Checkbox Normalize plot data for zero mean Fill Checkbox Fill histogram bars Mean Removed Text Average value removed from data 211 STABLE32 USER MANUAL Control Type Description Close Pushbutton Close the His
331. ximum value of the time deviation over a moving window It can be calculated for phase data only e Th ol Th ol is a special purpose statistic used to estimate the Allan variance at large averaging factors e Power Law Noise Type Estimates The power law noise type is estimated for each of the variance types by using either the lag 1 autocorrelation the B1 ratio the ratio of the standard variance to the Allan variance for zero dead time or R n the ratio of the modified to normal Allan variances The bandwidth factor BW 2nf t where f is the measuring system bandwidth in Hz applies to the R n calculation for flicker PM noise e Bias Correction Bias corrections are applied to the total variances and Th ol based on the estimated noise type e Confidence Intervals Single or double sided confidence intervals are determined using the of analysis points estimated noise type and the equivalent of X degrees of freedom for the particular variance type These are then used to calculate the corresponding maximum and optionally minimum sigma values e Auto Calc A sigma calculation can be done automatically when the Sigma function is invoked by setting the AutoCalc item in the Configure function 199 STABLE32 USER MANUAL 200 ANALYSIS FUNCTIONS Power Function e Purpose Use the Power function to plot the power spectral density of the current phase or frequency data Power Spectrum Plot X Tile POWER SPECTRUM
332. y Estimation Using a Special Purpose Statistic Proc 2003 IEEE International Frequency Control Symposium pp 233 238 May 2003 2 T N Tasset and D A Howe A Practical Th ol Algorithm Unpublished private communication October 2003 3 T N Tasset Th oH Unpublished private communication July 2004 4 T N Tasset D A Howe and D B Percival Th ol Confidence Intervals Proc 2004 IEEE International Frequency Control Symposium pp 725 728 August 2004 5 D A Howe and T N Tasset Th ol Characterization of Very Long Term Frequency Stability Proc 18 European Frequency and Time Forum April 2004 6 D A Howe Th oH A Hybrid High Confidence Statistic that Improves on the Allan Deviation Metrolog a No 43 pp 322 331 August 2006 7 D A Howe et al Th oH Bias Removal Method Proc 2006 IEEE International Frequency Control Symposium pp 788 792 June 2006 8 J A Taylor and D A Howe Fast Th oBR A Method for Long Data Set Stability Analysis to be published 81 82 STABLE32 USER MANUAL TIME DOMAIN STABILITY MTIE e MTIE The maximum time interval error MTIE is a measure of the maximum time error of a clock over a particular time interval This statistic is very commonly used in the telecommunications industry It is calculated by moving an n point n t t window through the phase time error data and finding the difference between the maximum and minimum values range
333. y timetags gaps and outliers and can perform several search and replace functions which you can explore later For now exit the Edit function by pressing Cancel 11 Select the Plot function by clicking on its toolbutton 12 Press the Plot button to produce a GraphiC plot of the frequency data The plot shows white frequency noise plus drift Close the plot by double clicking on its system menu icon If you wish you can try pressing the plot Options button to change the plot title or add a linear regression line and slope message to the plot Then leave the overall plot function GraphiC Win freg tkf n x Eile Edit Draw Convert Help Dole 01 08 08 Time 1E3127 FREQUE NCY DA TA Tie SLT SAMPLE DAT 6 00 5 50 E Slope Tau Interval 1 014e 00 5 00 4 50 oor d 3 50 3 9 3 00 E 3 2 50 2 200 1 50 1 00 0 50 0 00 i i i i 0 50 100 150 200 250 300 350 400 450 500 550 Data Point Lineor Fl y t o bt Intereepi 0 4 5868560e 01 Slope b 1 0125908e 00 iss 13 Select the Drift function from the Analysis menu or toolbar Notice that you have the option to Show Details for this function 293 14 15 16 17 18 19 20 21 22 294 STABLE32 USER MANUAL Choose Linear drift and check the Remove Drift box Then press Calc to calculate and remove the linear drift of about 1 0 per tau interval from the frequency data Notice that the unsaved symb
334. y be installed on any number of computers within the immediate user group that purchased it and backup copies may be made but only one copy of the program may be used at any time Additional copies may not be distributed to others This program has been extensively tested but it is never possible to declare a program completely bug free No warranty is made nor is any liability assumed in connection with the use of the program e Release Notes This document describes the Stable32 program as of the version and date shown on page ii of this User Manual Please see the User Manual Addendum if any for more recent changes and the Readme txt file for a more complete revision history Also please use the context sensitive help topics for more detailed information about any new features e Support Support for the Stable32 program is available from W J Riley Telephone Hamilton Technical Services 843 525 6495 650 Distant Island Drive Fax 843 525 0251 Beaufort SC 29907 USA E Mail stable32 wriley com On line support including tutorial papers test data and updates is available from the Hamilton Technical Services web site at http www wriley com and http www stable32 com GENERAL Installation e Installation Stable32 is distributed with a standard Windows installation program called SETUP EXE which should start automatically when the CD ROM is inserted into the drive To install Stable32 manually use the Add Remove Pro
335. y edited stability results from one or more previous Run operations The main purpose of the Read function is to allow stability data from multiple runs with different basic averaging times to be combined onto a composite stability plot Stability File SIGMA TAU Sigma Type Normal v Min Sigma Sigma Close 9 000e 02 3 158e 04 3 247e 04 3 336e 04 1 800e 03 2 190e 04 2 279e 04 2 368e 04 3 600e 03 1 569e 04 1 660e 04 1 752e 04 7 200e 03 1 128e 04 1 224e 04 1 319e 04 Plot 1 440e 04 6 159e 05 6 331e 05 7 703e 05 5 256e 05 6 248e 05 7 241e 05 Options 2 776e 05 3 617e 05 4 458e 05 EEE te Help 1 152e 05 2 426e 05 3 762e 05 5 098e 05 mum Notes Print n Elo Select sigma type Then Read stability data file and Plot or Print e Controls The Open dialog box contains the following controls Control Type Description Stability File Text Stability data filename Sigma Type Combo Select sigma type Stability Data Table Display of stability data Read Pushbutton Read stability data from disk Close Pushbutton Close the Read dialog box Help Pushbutton Invoke the Open help topic Plot Pushbutton Plot the stability data Options Pushbutton Enter plot options Lines Pushbutton Enter plot lines Notes Pushbutton Enter plot annotations Print Pushbutton Print the stability data e Operation Choose the Sigma Type to be read and press the Read button
336. y set the tau value e Timetag Types Three timetag types are available for converted frequency data equal to the first second or average value of the corresponding phase timetag This choice is set in the Freq Timetags section on the Data property sheet of the Configure function e Timetag Editing Timetag editing is not supported by the Stable32 program but may be accomplished by an external ASCII text editing program such as Windows Notepad e Timetag Processing Timetags are processed automatically by the Average and Part functions to yield the correct values that correspond to the averaged or remaining data e See Also Configure Function 29 30 STABLE32 USER MANUAL GENERAL Launching e Launching The Stable32 program can be launched in several ways Like any Windows application it can be launched from the Start menu from the Run dialog by clicking on its program file Stable32 exe in Windows Explorer or via an icon on the desktop or taskbar By associating Stable32 with a filename extension Stable32 may also be launched by clicking on a data file or by dragging a data file to the Stable32 icon on the desktop The dat phd and frd filename extensions are associated with Stable32 during its installation e Data File Selection The data file to be opened may be entered in the Open Data File dialog box or selected from the list of the three most recently opened phase or frequency data files in the File menu Be
337. ybrid Th oH Combined Allan and Th oBR RMS Time Interval Error TIE rms RMS value of time deviations Max Time Interval Error MTIE Max time deviation within window e Allan Variances The most common time domain stability measure is the Allan variance AVAR o x which gives a value for the fractional frequency fluctuations as a function of averaging time t The other common time domain statistics are the modified Allan variance MVAR Mod o t and the time variance o 1 The modified Allan variance is better able to distinguish between white and flicker phase noise The time variance TVAR o7 t measures the time fluctuations of a source or time distribution system All of these quantities are usually expressed as their square roots ADEV o t MDEV Mod o t and TDEV o t They are dimensionless except for the latter which has units of seconds The Allan variance can be calculated by either the non overlapping or overlapping method The latter provides better statistical confidence at the expense of a slight increase in computation time The results can be shown for a single t over a range of octave or decade t spacing or at every t for which there is sufficient data The total Allan and total modified Allan variances TOTAVAR and TOTMVAR are similar in purpose and expected value to the Allan and modified Allan variances respectively but use extended data sets to provide improved confidence at larger averaging
338. ysis for Physical Applications Cambridge University Press 1993 ISBN 0 521 43541 2 4 J M Lees and J Park A C Subroutine for Computing Multi Taper Spectral Analysis Computers in Geosciences Vol 21 1995 pp 195 236 5 Help File for the AutoSignal program for spectral analysis AISN Software Inc 1999 6 W J Riley Spur Detection Analysis and Removal in Stable32 Hamilton Technical Services 206 ANALYSIS FUNCTIONS Autocorrelation Function e Purpose Use the Autocorrelation function to plot the autocorrelation function ACF of the current phase or frequency data The primary purpose of the Autocorrelation function is to provide insight into the degree of correlation or non whiteness of the phase or frequency fluctuations and to provide an estimate of the power law noise type Title AUTOCORRELATION 00000000 gg Plot Sume PHASEDAT 09090900 gg Scatter Message White FM Estimated alpha 0 05 y Close Message Position TopLer H Avg Factor fi Save Config Help Scatter Plot Lag NEN Tau 000000400 Read Config Reset All ACFEile C Stable32 AUTODAT PlotFile C Stable32 AUTO TKF Axis Label Lag Lags 500 LAU Y Axis of 500 All Y Label Autocorrelation 1 0 987 Options Ie Date M Box Cursor V Zero M Lagk M Wide Eg Press Plotfor Autocorrelation plot Controls The Autocorrelation dialog box contains

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