Calibration of the Tektronix TDS 2014 Digital Oscilloscope
Contents
1. display area The vertical lines of the grid are used to represent a quantity of time and the horizontal lines are used to represent voltage levels Vertical scale Measured in Volts per division the vertical scale determines the voltage represented by a single division along the y axis Vertical position Used to offset the input of a particular channel by a fixed DC voltage This is useful to view large voltages which would fall out of range of the screen e Vertical resolution The smallest distinguishable voltage increment along the vertical axis e Regression line Line of best fit A mathematical equation used to represent a set of data as closely as possible This document only discusses linear regression lines These are lines which can be described by the equation y ax b where a and b are constants Coefficient of determination R A numerical indication of the variability between a set of data and a statistical model of the data The coefficient page 1 of 5 of determination can take any value between zero and one If R 1 all variability in the data set is explained in the statistical model and if R 0 there is no relationship between the data set and model III TESTBED SPECIFICATIONS This section will introduce the specifications of the equipment used in our calibration experiments Tektronix TDS 2014 Digital Storage Oscilloscope This is the oscilloscope we wish to calibrate It has an 8 bit2. 15 5 l l i i 15 5 16 16 5 17 17 5 18 18 5 19 Oscilloscope CH1 Reading Volts Fig 2 Calibration Scatter Plot Test 1 0 015 0 01 0 005 wn E ll I ke 0 z Ep M 0 005 t 0 01 0 015 i i i 15 5 16 16 5 17 17 5 18 18 5 19 Oscilloscope CH1 Reading Volts Fig 3 Residual Bar Plot Test 1 TABLE II CALIBRATION RESULTS FROM TEST 1 Channel Equation y ax b Err Volts R 1 y 0 99452 0 0882 0 015 0 999963 2 y 0 99632 0 0345 0 014 0 999964 3 y 0 9940x 0 1291 0 013 0 999980 4 y 0 9924x 0 1003 0 016 0 999958 TABLE III CALIBRATION RESULTS FROM TEST 2 Channel Equation y ax b Err Volts R 1 y 0 9948x 0 0737 0 013 0 999965 2 y 0 9965x 0 0465 0 013 0 999976 3 y 0 9935x 0 1344 0 014 0 999954 4 y 0 9927x 0 0983 0 012 0 999975 page 3 of 5 TABLE IV CALIBRATION RESULTS FROM TEST 3 Channel Equation y ax b Err Volts R 1 y 0 9936z 0 0915 0 012 0 999984 2 y 0 99702 0 0296 0 013 0 999968 3 y 0 99362 0 1329 0 014 0 999950 4 y 0 99182 0 1135 0 014 0 999959 based on the distance between the data points and the regression line see Figure 2 The maximum distance or residual can be used as a conservative error estimation of the regression equation A less conservative approach may be to choose the 90 percentile of the residuals D Limitations and Future Work Some future w
3. ADC resolution and four separate input channels The oscilloscope has ten horizontal divisions along the y axis and ten vertical divisions along the x axis Note that only eight of the ten horizontal divisions are visible on the display The oscilloscope has a vertical position setting which allows the user to offset the input voltage by a specified quantity If the vertical scale is configured between 2mV div and 200mV div the maximum configurable vertical position is 2V If the vertical scale is set in the range 202mV div to 5V div the maximum vertical position is 50V Instek GPC 1850D This is used to supply a variable DC voltage to the oscilloscope Fluke 189 digital multimeter The multimeter is used to accurately measure the power supply s output voltage The multimeter has a 45 digit display and a DC accuracy of 0 025 5 digits the error is 0 025 of the reading plus 5 counts of the least significant digit 2 IV OSCILLOSCOPE CALIBRATION When recording quantitative measurements it is neces sary to consider the potential error in the measuring de vices Manufacturers usually provide error specifications for their products but in some cases the error margin is quite conservative By calibrating a device we can justify the accuracy of the measurements as well as produce a tighter error specification There are several variables which may alter the out come of a calibration test e Vertical scale The vertical s
4. Calibration of the Tektronix TDS 2014 Digital Oscilloscope Adam Black Thuy Nguyen Centre for Advanced Internet Architectures Technical Report 071008A Swinburne University of Technology Melbourne Australia adamblack swin edu au tnguyen swin edu au Abstract The Tektronix TDS 2014 is a four channel Digital Storage Oscilloscope DSO with 8 bit analogue to digital converter This document reports on the calibration of the equipment for voltage measurements A precise multimeter was used to calibrate the DSO The calibration was performed by applying various DC voltages to the DSO and comparing the measurement results reported by the DSO and the multimeter We were able to establish a regression line for the multimeter and DSO readings which could be used to estimate the real input voltage in future measurements recorded with the oscilloscope We established there may be several factors which when altered could affect the outcome of a calibration These factors include some of the DSO s display settings such as the vertical position and vertical scale Due to the results obtained we recommend that individual calibration tests must be conducted for different DSO settings I INTRODUCTION Calibration is the process of determining or rectifying the graduations of any instrument which returns quan titative measurements 1 There are several reasons to calibrate an oscilloscope Firstly we can improve the ac curacy of measurement
5. cale determines the resolution of the oscilloscope A large vertical scale results in low resolution voltage measurements and conversely a small vertical scale results in high resolution measurements This means the oscillo scope s vertical scale setting can affect the results of a calibration test Vertical position In Section V we have experimen tally tested whether varying the vertical position CAIA Technical Report 071008A October 2007 affects the output of the oscilloscope and therefore the results of a calibration e Temperature The user manual 3 recommends that the oscilloscope s self calibration function should be used if the ambient temperature changes by 5 C or more since the last calibration It is recommended that the oscilloscope is re calibrated for any changes in the above variables Measurement of a voltage range may require a partic ular combination of vertical scale and position settings This section discusses the calibration process of the Tektronix TDS 2014 oscilloscope for three different voltage ranges Similar method can be applied to other settings and measurements A Equipment e Tektronix TDS 2014 DSO and cables e GPC 1850D Power Supply Unit PSU e Fluke 189 digital multimeter e PC with serial port B Method Connect the PSU s variable DC voltage output to the oscilloscope s channels and the digital multimeter in parallel Adjust the PSU to the lowest voltage level we wish t
6. ing generally has minimal effect regarding the consistency of voltage measurements however as the vertical position decreases shifts further away from zero negatively the measurements do seem to become less consistent This result means the oscilloscope should be re calibrated for different vertical position settings VI CONCLUSION In Section III we listed the various equipment con sisting of the testbed We had a Tektronix TDS 2014 os cilloscope which we wanted to calibrate a GPC 1850D DC power supply and a Fluke 189 digital multimeter CAIA Technical Report 071008A October 2007 Section IV discussed how we calibrated the oscillo scope The calibration was performed by connecting a DC signal into the oscilloscope and measuring the signal using the oscilloscope and a precise multimeter The output voltage of the oscilloscope was plotted against the multimeter s reading and a linear regression equation was fitted to the data Section V investigated whether changing the vertical position affects the output of the oscilloscope We found that as the vertical position decreases the voltage mea sured by the oscilloscope can slightly change To sum marise the oscilloscope should be calibrated for different vertical position settings used to record measurements REFERENCES 1 Dictionary com Calibration Viewed 27 August 2007 http dictionary reference com browse Calibration 2 Fluke Understanding specificat
7. ions for precision multimeters Viewed 08 October 2007 _ http support fluke com calibration sales Download Asset 2547797_6200_ENG_A_ W PDF 3 Tektronix TDS 1000 and TDS 2000 Series User Manual Viewed 24 August 2007 http courses washington edu phys334 datasheets Tek2kUserManual pdf page 5 of 5
8. o calibrate and capture a record of 2500 samples also keep a log containing the multimeter s reading Increment the power supply s voltage and repeat the acquisition process until the required range of voltages have been calibrated Figure 1 shows the described testbed configuration In this experiment we calibrated the oscilloscope with three different vertical positions as displayed in Table I These values were chosen to measure the voltage of various ADSL modems in a separate experiment The VRange column displays the voltage range used to calibrate the oscilloscope for the particular vertical scale and position The PSU was adjusted in increments of 100mV beginning from the lower bounds of Vrange For the three tests shown in Table I a timebase of 25ms div was used TABLE I CALIBRATION TEST CONFIGURATION Test Vertical scale Vertical position Vrange 1 57 300 15 5 18 5 2 41 300 10 8 13 8 3 43 300 11 4 14 4 page 2 of 5 TDS 2014 Oscilloscope L E tA e a 20 7 58 CH1 CH2 4 CH3 Fluke 189 CH4 Multimeter GPC 1850D Power Supply Fig 1 Testbed Setup C Results Figure 2 shows the calibration scatter plot for Test 1 using channel one of the oscilloscope The values along the x axis represent the oscilloscope s median voltage over 2500 samples and the y axis values represent the multimeter s reading Under ideal circumstances the os cilloscope and multimeter readings sho
9. ork may include investigating the ef fects ambient temperature has upon the oscilloscope s output E Conclusion We have demonstrated an oscilloscope can be cal ibrated by inputting a controlled voltage into one or more channels and recording the voltage using a precise multimeter and the oscilloscope The multimeter voltage can then be plotted against the oscilloscope voltage and a regression equation can be formed to optimise the accuracy of future measurements V VARYING THE VERTICAL POSITION The Tektronix TDS 2014 has the ability to offset an input signal in order to make large voltages visible on the screen In this section we investigate whether varying the vertical position has any affect upon the consistency of the oscilloscope s measurements From this experiment we should be able to determine whether the oscilloscope needs to be calibrated for different vertical positions A Equipment e Tektronix TDS 2014 DSO and cables e GPC 1850D power supply e PC with serial port B Method Connect the power supply s variable DC output to channel four of the TDS 2014 and set the output voltage to 1VDC Configure channel four of the oscilloscope with a vertical scale of 200mV div and set the timebase to 25ms Adjust the vertical position to O divisions and capture ten records of 2500 samples then decrease the position by one division and repeat the measurements CAIA Technical Report 071008A October 2007 for all po
10. s by justifying the oscilloscope s output in our case applying a regression equation to the oscilloscope s output to estimate the true input voltage It is also likely that we are able reduce the manufacturer s error specification The report is structured as follows Section II lists the definitions of important terms which have been used throughout the report Section II con tains the specifications of the various hardware consisting of our testbed In Section IV the report describes how the TDS 2014 oscilloscope can be calibrated and contains the results from several calibration tests we performed Section V investigates whether varying the vertical po sition of the oscilloscope can affect the consistency of voltage measurements The report is concluded in CAIA Technical Report 071008A October 2007 Section VI and the references are listed at the end of the document Il TERMINOLOGY This section introduces some important terminology used throughout the report e ADC analogue to digital converter Converts an analogue voltage level into a discrete digital repre sentation The granularity of an ADC can be deter mined from the number of bits it uses For example an 8 bit ADC can digitally represent an analogue signal using 28 256 unique voltage levels The more bits an ADC uses the less uncertainty exists in the digital representation Division The oscilloscope s display has a grid superimposed on the waveform
11. sitions up to and including 10 divisions The testbed configuration is shown in Figure 4 TDS 2014 Oscilloscope oo NV a0 CH4 PC 9 Pin RS232 GPC 1850D Power Supply Fig 4 Testbed Setup C Results 1 107 1 08 E ear 2 Cia S L 1 04 a gee go tare gee eae ee ee ae ee eerie roe S 1 02 sneousttsnesuatnsenttcr desu ana aesuathsnatis data eeehe seee 00a eeee e e e e e e e e e 7 e e e 0 98 too oto oot 0 1 2 3 4 5 6 7 8 9 10 Vertical Position Divisions Fig 5 Varying the Vertical Position Figure 5 shows the median voltage of 25 000 samples which were measured using channel four of the oscillo scope The graph shows the median voltage was 0 992V when the vertical position was configured between 0 divisions and 6 divisions When the vertical position was configured in the range 7 divisions to 9 divisions the median voltage decreased by 8mV and when the vertical position was set to 10 divisions the median voltage was 1 08V This results suggest the consistency of the oscilloscope can be affected as the vertical position decreases page 4 of 5 NB For a vertical scale of 200mV div the maximum configurable vertical position is 10 divisions D Limitations and Future Work Future work may including running similar tests using vertical scale settings other than 200mV div E Conclusion We found that changing the oscilloscope s vertical position sett
12. uld be identical In reality we do not expect this to be true because both devices have some degree of error in their measurements Tables II III and IV display the regression equations for the tests shown in Table I In the Equation column the x variable represents the voltage from the oscillo scope and the y variable is the calibrated voltage The R column contains the coefficient of determination There are several important factors to consider when performing calibration tests one of them is the channel used to perform the calibration The oscilloscope has four independent input channels and they do not all have identical characteristics therefore it is important to calibrate each channel individually It is also reasonable to assume the regression equation is only applicable when the oscilloscope s display settings used for voltage measurements are the same as the settings used during the calibration In Tables II II and IV we can see the regression equations slightly differ from the theoretical mapping y x The coefficient of determination is very close to one for all the regression lines which mean they have very strong linear correlation The error values shown in Tables II III and IV are CAIA Technical Report 071008A 197 October 2007 18 5 A g f y 0 9945x 0 08823 D 17 5H 8 174 cc 16 5 Q el
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