Radar Emitter Simulation Using the E8267C
Contents
1. seperation zeros 1 128 Define variables counting variable no units ramp from 1 to almost 1 used to build sine waves raised cosine pulse rise time definition samples pulse on time definition samples raised cosine pulse fall time definition samples pulse off time definition samples in phase modulation signal samples quadrature modulation signal samples complex array containing both i and q waveform samples array containing markers for Event Markers 1 and 2 array containing the time separation between the pulses defines the number of points in the rise time amp fall time ramp from 1 to almost 1 over n points defines the raised cos rise time shape defines the on time characteristics defines the raised cos fall time shape defines the off time sample points defines the seperation between the pulses ae dh oe dP oe define arrays which contain the pulse envelope for each pulse pulsel rise on fall pulse2 5 rise on fall concatenate and scale the pulses i pulsel seperation pulse2 off plot the i samples and scale the plot plot i axis 0 length i 2 2 set the q samples to all zeroes q zeros 1 length i 20 Appendix B Pulse doublet continued oe IQData o Markers Markers 1 define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant Teak J eg al 9 define a marker matrix2. agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData nlfm sampclk play no_normscale Markers Turn on modulation status status_description agt_sendcommand io OUTPut MODulation STATe ON Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON Online The source code for the examples used in this paper along with Download Assistant for MATLAB 6 5 or later can be downloaded from the Agilent Web site www agilent com find psg 31 MATLAB is a U S registered trademark of The Math Works Inc Agilent Technologies Test and Measurement Support Services and Assistance Agilent Technologies aims to maximize the value you receive while minimizing your risk and problems We strive to ensure that you get the test and measurement capabilities you paid for and obtain the support you need Our extensive support resources and services can help you choose the right Agilent products for your applications and apply them successfully Every instrument and system we sell has a global warranty Support is available for at least five years beyond the production life of the product Two concepts underlie Agilent s overall support policy Our Promise and Your Advantage Our Promise Our Promise means your Agilent test and measurem
3. set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 verify that communication with the PSG has been established status status_description query_result agt_query io idn if status lt 0 return end preset the instrument status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Download Assistant status status_description agt_sendcommand io SOURce FREQuency 1e9 status status_description agt_sendcommand io POWer 0 put the ALC into manual control and set the IQ real time scaling status status_description agt_sendcommand io POWer ALC STATe OFF status status_description agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData phase_offset sampclk play no_normscale Markers Turn on modulation status status_description agt_sendcommand io OUTPut MODulation STATe ON Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON Appendix D Pulse with doppler frequency offset Script file Doppler m Purpose To calculate and download an arbitrary waveform file that simulates a simple pulse signal with a fixed doppler frequency offset from the
4. 2 off zeros 1 900 defines the defines the defines the defines the dP dP dP dP cP cP defines the number of points in the rise amp fall time ramp from 1 to almost 1 over n points raised cos rise time shape on time characteristics raised cos fall time shape off time sample points concatenate the parts of the amplitude of the pulse into a single array am rise on fall off plot the am samples and scale the plot plot am axis 0 length am 2 2 23 24 Appendix D Pulse with doppler frequency offset continued define an array which contains the the doppler freq in each sample fm doppler_freq ones 1 length am use an intergral to translate from fm to pm pm 2 pi sampclk cumsum fm convert am and pm to i and q i am cos pm q am sin pm define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant IQData i j q define a marker matrix and activate a marker to indicate the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1 set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 verify that communication with the PSG has been established status status_description query_result agt_query io idn if status lt 0 return end preset the instrument
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6. status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Downlaod Assistant status status_description agt_sendcommand io SOURce FREQuency 1e9 status status_description agt_sendcommand io POWer 0 put the ALC into manual control and set the IQ real time scaling status status_description agt_sendcommand io POWer ALC STATe OFF status status_description agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData doppler sampclk play no_normscale Markers Turn on modulation status status_description agt_sendcommand io OUTPut MODulation STATe ON Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON Appendix E Pulse with barker code de oe Purpose dP dP dP oe g w ct oO oe l l l l 4 15 2002 8 14 2002 9 4 2002 6 26 2003 dP dP dP AP dP oe n Sok ramp ches rise vs on fall off oa i aoa q SS pm ve sampclk on neg_pos pos_neg SE pos_pos S neg_neg ines pos neg dP dP dP AP DP dP DP AP GP dP DP OP oe sampclk 100e6 Script file Barker m Record of revisions Programmer Randal Burnette John Hutmacher Randal Burnette Randal Burnette Define pulse variable
7. Building Pulse Compression Signals Having provided examples of simple pulsed waveforms with control of the amplitude and phase of the pulse the next step will be to produce modulation within the pulse Both phase and frequency modulation are used by radar systems to improve range and resolu tion Radar systems that use modulation within the pulse are referred to as pulse com pression radar systems The radar range equation points out a basic engineering trade off between range and res olution and the need for pulse compression To build a long range radar or for the radar to see a great distance the radar needs high average output power To obtain good resolu tion the radar needs a narrow pulse that reduces the average output power Pulse com pression provides a path around this trade off Pulse compression radars will transmit a long pulse with modulation inside the pulse The returns are processed through a filter that is matched to the characteristics of the modulation compressing the pulse in time This compression allows the radar to separate overlapping returns while transmitting a high average power It is important for elint and radar warning receivers to correctly process these types of signals The modulation type and deviation of the signals provide important information about the purpose and intent of an observed system It is often difficult to obtain a signal source with the appropriate characteristics to verify the perfo
8. Vector Signal Analyzer z F Ete Edit Control Source Input MeasSetup Display Trace Markers Utilities Help C Chl Main Time Range 316 2278 miv 316 2 my LinMag 31 62 mi div ol y Start 0 Sec Stop 12 717 uSec Trig Ch Delay 0 Sec Trig Lvl 2 V shi Main Time 3 Measurement paused INT REF Figure 8 Demodulated signal To demonstrate a linear fm chirp signal the objective is to build an fm waveform that will linearly sweep the frequency across a known deviation This example uses the technique introduced in the doppler example that integrates the fm waveform to produce a pm waveform which can be converted over to IQ The advantage of this process is that it allows the user to build waveforms in frequency versus time to create arbitrary fm wave forms that can be converted and downloaded into the signal generator As the code below illustrates the fm chirp is built using a ramp that starts at exactly 1 and ends at exactly 1 This allows the user to easily scale the waveform by multiplying by the desired frequency deviation divided by two Note that the frequency will sweep both above and below the carrier frequency Using the internal arbitrary waveform syn thesizer the signal generator can produce up to an 80 MHz chirp To eliminate an unnec essary frequency step at the beginning and end of the chirp the fm waveform is held at the frequency of the chirp endpoints during the rise time and fall time
9. chirp_dev 2 ones 1 n nonlinear 1 2 length on 1 1 ones 1 n ones 1 length off plot the fm samples and scale the plot plot fm axis 0 length fm 10e6 10e6 use an integral to translate from fm to pm pm 2 pi sampclk cumsum fm oe convert am and pm to i and q and scale amplitude am cos pm am sin pm i i Q l define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant IQData i j q o define a marker matrix and activate a marker to indicate the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1 set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 verify that communication with the PSG has been established status status_description query_result agt_query io idn if status lt 0 return end preset the instrument status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Download Assistant status status_description agt_sendcommand io SOURce FREQuency 1e9 status status_description agt_sendcommand io POWer 0 put the ALC into manual control and set the IQ real time scaling status status_description agt_sendcommand io POWer ALC STATe OFF status status_description
10. com ponents a microwave signal generator capable of producing the signals required for the test and a microwave spectrum analyzer capable of verifying the signal s characteristics The equipment should cover a frequency range of 0 5 18 GHz If the receiving system must process phase or frequency coded pulses then the generator must be able to pro duce these signals Vector signal generator The Agilent E8267C vector signal generator that covers 250 KHz to 20 GHz meets the needs for a general purpose signal source to test radar warning receivers and elint systems The generator is a member of the ESG PSG line and provides excellent output power low phase noise option analog modulation and digital communication modulation common to that line The generator also provides 0 modulation with an internal arbitrary waveform generator providing 80 MHz of modulation bandwidth The E8267C s internal arbitrary waveform generator to produce complex radar signals Software programming tools Creating custom radar signals requires a software programming tool capable of dealing with complex array math and displaying the information in a usable format While there are several tools available MATLAB is widely used and commonly available Agilent has chosen to support MATLAB as a waveform builder for the PSG To move the digital waveforms from MATLAB into the arbitrary waveform generator inside the PSG vector signal generator Agilent has developed Dow
11. common pulse parameter and can easily be measured using standard test equipment Given that the rising and falling edges of the pulse are built from raised cosine functions it can be shown that the 10 to 90 rise time is equal to 59 times the 0 to 100 rise time In this case the 10 to 90 rise time would equal 59 ns Thus the rise time of the pulse can be set and very accurately calculated by setting the value of n and smplclk In general to insure the final output signal s rise time is controlled by the calculated waveform and not the rise time of the anti alias filters following the arbitrary waveform generator in the signal generator when the sample clock is set to its maximum value of 100 MHz use four or more points in the rise time waveform Pulse width and repetition The pulse width and pulse repetition interval can easily be calculated Typically the pulse width is calculated based on the points 0 5 down from the amplitude of the pulse in a linear display or 6 dB down from the amplitude of the pulse in a log display Because the raised cosine function is symmetric around this point the number of points in the 6 dB pulse width can be exactly calculated as the on time plus half of the rise time plus half of the fall time The equation to calculate the pulse width in seconds would be pulse_width length rise 2 length on length fall 2 smplclk The number of points in the pulse repetition interval is the rise time plus the
12. of the pulse In Figure 9 note the demodulated fm waveform in the lower right hand plot The chirp is linear and the deviation is equal to the 10 MHz defined in the program 5 MHz The values in the fm demodulator are only defined during the on time of the pulse In the upper right hand plot note that the amplitude of the pulse is flat during the pulse on time Because the signal is being swept across a 10 MHz frequency span this indicates the 10 modulator within the signal generator provides a flat frequency response across that bandwidth The spiral effect in the IQ plot in the lower left hand corner is due to the fre quency offset from the carrier during the rise and fall time of the pulse af Agilent 89600 Vector Signal Analyzer E B x File Edit Control Source Input MeasSetup Display Trace Markers Utilities Help u e IG DOQ wt ya o lil j TEDE S m amp i pec ian Start 0 Sec Stop 12 717 uSec Trig Ch1 Delay 0 Sec Trig Lvl 2 V D Chi Main Time Range 316 2278 mv 0 h Stat 0 Sec Stop 12 717 uSec Trig Ch1 Delay 0 Sec Trig Lvl 2 jeasurement pause Ai M d INT REF CAL OK Figure 9 FM chirp signal The following block contains a subset of the code in LFM_Chirp m chirp_dev 10e6 defines the total chirp deviation in Hz define an array which contains the chirp waveform fm chirp_dev 2 ones 1 n 1 2 length on 1 1 ones 1 n ones 1 length off use an integral t
13. on time plus the fall time plus the off time The equation to calculate the pulse width in seconds would be pulse_repetiton_interval length rise length on length fall length off smplclk This is an exact calculation and can be used as a standard when evaluating the performance of the signal processing within a receiver Controlling output power To test a receiver s performance it is critical to have known pulse power at the receiver input Controlling the output power of the PSG from MATLAB is straightforward When Vag 1 the output power of the signal generator will equal the front panel power level For pur poses of this paper refer to the power level set at the front panel as the reference power level For our example waveform that sets the pulse amplitude in the real array to one and in the imaginary array to zero If we set the output power of the signal generator to 0 dBm then the peak power of the pulse will equal 0 dBm The command from MATLAB which uses Download Assistant to set the output power is status status _description agt_sendcommand io POWer 0 Reducing the amplitude of the waveform below one will reduce the output power However there are several scaling factors that must be addressed Automatic loop control The first issue to deal with is automatic loop control ALC in the output of the signal gen erator This feedback loop is used during the normal operation of a continuous wave CW source
14. the negative of the rising edge The amplitude envelop of the final pulse is built by concatenating the four arrays using the equation i rise on fall off 4 Figure No 1 Ed 10 x File Edit Tools Window Help Joa mSlrAAs aOR A 3 LL 0 10 20 30 40 50 60 70 80 90 100 Figure 2 Final pulse plot Because the phase of the pulse will be constant in this example the imaginary portion of the array is set to zero using the formula q zeros 1 length i A single complex array is built from the two arrays using the formula 10Data i j q Note that multiplying by 7 in this equation is the equivalent of multiplying by the square root of 1 This infers that q is the imaginary portion of the waveform The waveform is now ready to be downloaded into the signal generator Setting the clock The variable smplclk 100e6 is used to set the clock frequency for the arbitrary waveform generator to 100 MHz This allows time to be associated with each point in the waveform Each point within the waveform will occupy 1 smplclk or 10 ns of time The important timing characteristics of the pulse can be calculated using this information The 0 to 100 rise time and fall time of the pulse is 10 ns n or 100 ns where n describes the number of points in the arrays rise or fall While the 0 to 100 is useful during the construction of the waveform it cannot be measured accurately on the microwave pulse The 10 to 90 rise time is a
15. the user to specify the doppler offset frequency in hertz versus time and given the sample clock in hertz calculate the pm waveform This is very powerful While this example produces a static doppler offset within a single pulse the technique can easily be extended to produce a doppler trajectory for a moving emitter The primary limitation of the technique is the 64 MSa of memory within the signal generator to play the waveforms With 100 MHz sample clock the of memory will allow the production of 640 ms of unique signal The following block contains a subset of the code in Doppler m doppler_freq 100e3 defines the doppler offset freq in Hz define an array which contains the doppler freq in each sample fm doppler_freq ones 1 length am use an integral to translate from fm to pm pm 2 pi sampclk cumsum fm convert am and pm to i and q and scale amplitude i 707 am cos pm q 707 am sin pm Now to discuss the two vector displays of the doppler signal Figure 6 shows the vector signal analyzer tuned to the exact center frequency of the signal generator The phase versus time plot in the lower right hand corner shows a ramp in phase versus time during the on time of the pulse The IQ display in the lower left hand corner shows an arc of phase From the parameters in the doppler m MATLAB program the pulse width can be calculated to be 1 ms and the doppler shift set to 100 KHz The phase shift generated b
16. Introduction Historically simulating radar emitters has been an expensive and time consuming process However using off the shelf vector signal generators it is now possible to produce the complex pulsed waveforms The advent of microwave signal generators and spectrum analyzers with vector capa bility allows engineers to generate pulsed microwave signals with precise control over output power amplitude envelope and modulation within the pulse These precision signals can be used as a standard to evaluate the performance of subsystems and to troubleshoot system problems The devices to be tested are typically radar warning receivers and elint receivers The purpose of this application note is to help the design engineer generate and evaluate complex radar signals using standard microwave test equipment This application note shows how MATLAB and the Agilent E8267C PSG vector signal generator can be used to create signals and simulate complex radar emitters The appendices contain the complete MATLAB code for generating the pulse signals described in this application note Experience has shown that this type of series of complex pulse patterns will enable the user to perform roughly 80 of the tests necessary to evaluate the per formance of an electronic warfare system The final 20 of the receiver testing is typically done on a test range using real emitters Radar Emitter Simulation Using The E8267C PSG Vector Signal G
17. Turn on RF output power tatus_description agt_sendcommand io OUTPut STATe ON Appendix C Pulse doublet with phase offset oe Script file Phase_Offset_Doublet m oe oe Purpose To calculate and download an arbitrary waveform file to generate a doublet two simple pulses within a single PRI and that has pi 2 or 90 deg phase offset between the pulses af dP dP dP oe Record of revisions oe Date Programmer Description of change 4 15 2002 Randal Burnette Initial version for 2002 AD Symposium 8 14 2002 John Hutmacher Added comments and Download Assistant 9 4 2002 Randal Burnette Added Preset turned ALC off and IQ Scaling 6 26 2003 Randal Burnette Added Modulation ON oe oe Define variables oe n counting variable no units ramp ramp from 1 to almost 1 used to build sine waves rise raised cosine pulse rise time definition samples on pulse on time definition samples fall raised cosine pulse fall time definition samples off pulse off time definition samples i in phase modulation signal samples q quadrature modulation signal samples IQData complex array containing both i and q waveform samples Markers array containing markers for Event Markers 1 and 2 separation array containing the time separation between the pulses am amplitude envelope for the pulse linear units pm phase of
18. _sendcommand io POWer 0 put the ALC into manual control status status_description agt_sendcommand io POWer ALC STATe OFF set the IQ real time scaling to 70 7 or 3dB status status_description agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData pulse sampclk play no_normscale Markers Turn on modulation Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON status status_description agt_sendcommand io OUTPut MODulation STATe ON Appendix B Pulse doublet Script file Doublet m Purpose To calculate and download an arbitrary waveform file to generate a doublet two simple pulses within a single PRI with the PSG vector signal generator Record of revisions Date Programmer Description of change 4 15 2002 Randal Burnette Initial version for 2002 AD Symposium 8 14 2002 John Hutmacher Added comments and Download Assistant 9 4 2002 Randal Burnette Added Preset turned ALC off and IQ Scaling 6 26 2003 Randal Burnette Added Modulation ON n ramp rise on fall off i q IQData Markers seperation dP dP dP AP P P P ADP BP GDP dP AP AP GP AP oP dP dP dP dP n 4 ramp 1 2 n 1 2 n rise 1 sin ramp pi 2 2 on ones 1 120 fall 1 sin ramp pi 2 2 off zeros 1 640
19. and activate a marker to indicate the beginning of the waveform zeros 2 length IQData fill Marker array with zero ie no markers set 1 10 1 set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 o verify t status s if status preset t status s status s status s put the status s status s defines sampclk o status status status hat communication with the PSG has been established tatus_description query_result agt_query io idn lt 0 return end he instrument tatus_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Downlaod Assistant _sendcommand io SOURce FREQuency 1e9 _sendcommand io POWer 0 tatus_description ag tatus_description ag ct ct ALC into manual control and set the IQ real time scaling tatus_description agt_sendcommand io POWer ALC STATe OFF tatus_description agt_sendcommand io RADio ARB RSCaling 70 7 cd ct the ARB Sample Clock for playback 100000000 download the iq waveform the PSG baseband generator for playback status_description agt_waveformload io IQData doublet sampclk play no_normscale Markers Turn on modulation status_description agt_sendcommand io OUTPut MODulation STATe ON Ss
20. c 00 kHz i Trig Ch1 Delay 0 Sec Trig Lvl 2 V Chi Main Time _ ge 3 ELOA D Chi Main Time _ Range 316 2278 mv 18 Ilr dh a LW PT Start 0 Sec Stop 12 Trig Ch Delay 0 Sec Trig Lvl 2 Measurement paused INT REF CAL OK a Figure 5 Screen capture of phase shift between pulses 7 uSec The following block contains a subset of the code in PM_Doublet m rc set the phase of the two pulses pm 0 ones 1 length pulsel separation pi 2 ones 1 length pulsel off convert am and pm to i and q i 707 am cos pm q 707 am sin pm Creating Doppler Shift Doppler m Creating a pulsed waveform with a constant doppler frequency shift requires the introduc tion of a new technique The idea is to build a waveform that contains the doppler offset frequency from the carrier versus time then integrate the waveform to produce phase versus time Remember that phase is simply the integral of frequency In Figure 7 an array fm is produced that contains a constant offset frequency in hertz The length of the array is equal to the entire am pulsed waveform The fm waveform is integrated using the func tion cumsum which is the cumulative sum of the elements of the array The new array must be scaled by 2 x sampclk to obtain units of radians The am and pm waveforms are converted into IQ and scaled for downloading into the signal generator Note that the math shown in the block below allows
21. center frequency of the signal generator using IQ modulation Record of revisions Date Programmer Description of change 4 15 2002 Randal Burnette Initial version for 2002 AD Symposium 8 14 2002 John Hutmacher Added comments and Download Assistant 9 4 2002 Randal Burnette Added Preset turned ALC off and IQ Scaling 6 26 2003 Randal Burnette Added Modulation ON Define variables n counting variable no units ramp ramp from 1 to almost 1 used to build sine waves rise raised cosine pulse rise time definition samples on pulse on time definition samples fall raised cosine pulse fall time definition samples off pulse off time definition samples i in phase modulation signal samples q quadrature modulation signal samples IQData complex array containing both i and q waveform samples Markers array containing markers for Event Markers 1 and 2 am amplitude envelope for the pulse linear units pm phase of the pulse vs time in rads fm offset frequency from carrier vs time in Hz sampclk clock freq for the D A converters in the IQ modulator doppler_freq doppler offset frequency in Hz sampclk 100e6 defines the ARB Sample Clock for playback doppler_freq 100e3 defines the doppler offset freq in Hz n 4 ramp 1 2 n 1 2 n rise 1 sin ramp pi 2 2 on ones 1 92 fall 1 sin ramp pi 2
22. enerator Application Note Table of Contents INtrOdUCHION vy cise oa Se tks vehi EE Been hal Sade aed Equipment Configuration 0 ccc cece cent eee eens Vector performance signal generator Software programming tools Performance Spectrum Analyzer Generating a Simple Pulse 0 2 000 c eee e eee eee Generating a signal Setting the clock Pulse width and repetition Controlling output power 00 ccc cece eee eee e ees Automatic loop control Scaling factor Calibration Running Pulse m Generating a Pulse Doublet Doublet m 0 000 c cee ees Generating Phase Shift Between Pulses PM_Doublet m Creating Doppler Shift Doppler m 002 20 cece eee Building Pulse Compression Signals 00 0000eeeeeeeee Generating a Barker Coded Pulse Barker m 0000e eee ee Generating a Linear FM Chirp LFM_Chirp m 005 Generating a Non Linear FM Chirp NLFM_Chirp m APPENdic S i e sao eas ees Mitscal TEE ete ede ph ohn ek A Simple pulse B Pulse doublet C Pulse doublet with phase offset D Pulse with doppler frequency offset E Pulse with barker code F Pulse with linear fm chirp G Pulse with non linear fm chirp w e j Agilent Technologies e s0e e Equipment Configuration Generating a Simple Pulse The general purpose test equipment needed to evaluate a receiver requires two key
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24. es to create the signal new waveforms may easily be built to stress some aspect of the system under test The next signal is a pulse doublet which are two pulses placed very close in time When testing an elint system a doublet is used to verify the ability of the system to correctly identify two closely spaced pulses rather than a sin gle long pulse Often a series of doublets will be created with a different amount of sepa ration between each doublet Also an amplitude change will be introduced between the pulses to place additional stress on the system Generating a pulse doublet using Pulse m as a starting point is fairly straightforward Define three new variables pulse1 pulse2 and separation The variables pulse1 and pulse2 will contain the amplitude envelope of each pulse The amplitude of each pulse can be scaled independently of the other The variable separation will define the number of points and the time between the two pulses Finally concatenate the new pulses with separation between them The following block contains a subset of the code in Doublet m r separation zeros 1 128 separation between the pulses define arrays which contain the pulse envelope for each pulse pulsel rise on fall pulse2 5 rise on fall concatenate and scale the pulses i 707 pulsel separation pulse2 off PA Agilent 89600 Yector Signal Analyzer Ete Edit Control Source Input MeasSetup Display Trace Marke
25. ff The on and off sections of the pulse are built using the ones 1 10 and zeros 1 70 functions In this case the ones command creates a 1 by 10 array and fills it with 1s Likewise the zeros command creates a 1 by 70 element array and fills it with 0s This method provides a simple way to establish the on time and off time of the pulse The rising and falling edges of the pulse are shaped using a raised cosine function To build the two cosine waveforms the program starts by building a linear ramp from 1 to almost 1 using the function ramp 1 2 n 1 2 n For the ramp function if the linear ramp were to continue the point following the last point in the array would be exactly 1 Ramp functions are often multiplied by some multiple of 7 represented in MATLAB by the variable pi as part of a function to build sine waves Given that r and 7 represent the exact same point on the unit circle when the ramp is multiplied by 7 and the sine or cosine taken of the array a perfect sinusoidal waveform is produced This idea will be used in several of the example programs In the case of the rising edge of the pulse multiply the ramp with 7 2 then take the sine of the result This will produce the center of the sine wave with a first point of 1 and a final point of almost 1 Adding one to the result and dividing by two produces the desired waveform The final equation takes the form rise 1 sin ramp pi 2 2 The falling edge is simply
26. hape off time characteristics envelope 25 26 Appendix E Pulse with barker code continued pm pi 2 0 0 0 rise pos SBit 1 high pos_pos pos SBit 2 high pos_pos pos SBit 3 high pos_neg neg SBit 4 low neg_neg neg SBit 5 low neg_pos pos SBit 6 high pos_neg neg SBit 7 low rise 1 0 0 off plot the pm samples and scale the plot plot pm axis 0 length pm 2 2 convert am and pm to i and q i am cos pm q am sin pm define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant IQData i j q o define a marker matrix and activate a marker to indicate the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1 set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 verify that communication with the PSG has been established status status_description query_result agt_query io idn if status lt 0 return end preset the instrument status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Download Assistant tatus status_description agt_sendcommand io SOURce FREQuency 1e9 tatus status_description agt_sendcommand io POWer 0 put the ALC into manual control and set t
27. he IQ real time scaling tatus status_description agt_sendcommand io POWer ALC STATe OFF tatus status_description agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData barker sampclk play no_normscale Markers Turn on modulation status status_description agt_sendcommand io OUTPut MODulation STATe ON Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON Appendix F Pulse with linear fm chirp Script file LFM_Chirp m Purpose To calculate and download an arbitrary waveform file that simulates a pulsed signal with a linear fm chirp to the PSG vector signal generator Record of revisions Date Programmer Description of change 4 15 2002 Randal Burnette Initial version for 2002 AD Symposium 8 14 2002 John Hutmacher Added comments and Download Assistant 9 4 2002 Randal Burnette Added Preset turned ALC off and IQ Scaling and corrected fm to pm integration calc 6 26 2003 Randal Burnette Added Modulation ON Define variables dP dP dP P AP DP AP dP BO dP BP AP BP AP DP ADP AP ADP ADP BP AP BO dP BP GP BP DP DP ADP DP BP AP BO oP n counting variable no units ramp ramp from 1 to almost 1 used to build sine waves rise raised cosine pulse rise time definition samples on pulse on time definiti
28. m convert am and pm to i and q and scale amplitude i 707 am cos pm g 707 am sin pm Appendix A Simple pulse Script file Pulse m Purpose To calculate and download an arbitrary waveform file to generate a simple pulsed signal with the PSG vector signal generator Record of revisions Date Programmer Description of change 4 15 2002 Randal Burnette Version for 2002 AD Symposium in MatLab VEE 8 14 2002 John Hutmacher Added comments and Download Assistant 9 4 2002 Randal Burnette Added Preset turned ALC off and IQ Scaling 6 26 2003 Randal Burnette Added Modulation ON Define variables dP dP dP dP AP P AP dP BO dP BP DP BP BP DP AP DP ADP DP ADP AP BP oP BO DP BP CP cP n counting variable no units ramp ramp from 1 to almost 1 used to build sine waves rise raised cosine pulse rise time definition samples on pulse on time definition samples fall raised cosine pulse fall time definition samples off pulse off time definition samples inphase in phase modulation signal samples quadrature quadrature modulation signal samples TQData complex array containing both i and q waveform samples Markers array containing markers for Event Markers 1 and 2 sampclk clock freq for the D A converters in the IQ modulator oe sampclk 100e6 ARB Sample Clock for playback oe number of points in the rise amp fall time ramp from 1 to almost 1 ove
29. nload Assistant The program enables users to easily download their IQ waveforms into the arbitrary waveform generator s memory In addition it allows the user to send any standard commands for programmable instruments SCPI command to the signal generator to control the instrument state Download Assistant adds keywords to MATLAB to format and download arrays of data through common GPIB interface cards or a LAN interface into the signal generator The examples used in this paper demonstrate how to use Download Assistant with MATLAB 6 5 or later revision to create download and generate radar signals Download Assistant and the programming examples used in this paper can be obtained for free at the Agilent web site http www agilent com find psg Performance spectrum analyzer To capture and demodulate signals the E4440A PSA Series spectrum analyzer is used with the 89601A vector signal analysis VSA software This configuration provides frequency coverage of 26 5 GHz with up to 36 MHz of analysis bandwidth Wide bandwidth configurations are also available refer to http www agilent com find 89600 for more information To adequately test elint receiver performance a wide variety of test signals are needed The user may need to simulate various types of radar emitters or to simulate the multiple modes of operation for a single type of radar This requires the test engineer to control the basic pulse parameters center frequency power pulse
30. o pm pm 2 pi sampclk cumsum fm 27 28 Appendix F Puls o plot axis oe Q de e with linear fm chirp continued plot the fm samples and scale the plot fm I0 length fm 10e6 10e6 convert am and pm to i and q and scale amplitude am cos pm am sin pm fine a composite iq matrix for download to the PSG using the PSG ESG Download Assistant IQData i j q l define a marker matrix and activate a marker to indicate the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1 set Marker to first ten points of playback sta LES f o Turn on RF output power status status_description agt_sendcommand io OUTPut STATe ON ke a new connection to the PSG over the GPIB interface agt_newconnection gpib 0 19 verify that communication with the PSG has been established tus status_description query_result agt_query io idn status lt 0 return end preset the instrument status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Download Assistant status status_description agt_sendcommand io SOURce FREQuency 1e9 status status_description agt_sendcommand io POWer 0 put the ALC into manual control and set the IQ real time scaling status status_desc
31. o translate from fm to pm pm 2 pi sampclk cumsum fm convert am and pm to i and q and scale amplitude i 707 am cos pm q 707 am sin pm Generating a Non Linear The final example will demonstrate how to add a known amount of non linear distortion 2 i to the fm chirp waveform The non linear distortion will be produced by the single cycle of FM Chirp N LFM_Chirp m a sine wave scaled to fit within the on time of the pulse The amount of non linearity is set by scaling the amplitude of the sine wave as some percentage of the total deviation Because the value of the sine wave is zero at its end points the maximum deviation of the chirp will not change The resulting S shape of the waveform is typical of the distortion seen in non synthesized chirped signals Bi Agilent 89600 Vector Signal Analyzer gt oj x LogMag Stop Trig Ch Delay 0 Sec Range Measurement paused INTREF f 2 Figure 10 Non linear fm chirp The following block contains a subset of the code in NLFM_Chirp m o chirp_dev 10e6 defines the total chirp deviation in Hz create some non linear distortion to add to the chirp nonlinear 2 sin pi 1 2 length on 1 1 add the nonlinearity to the chirp and concatenate the sections fm chirp_dev 2 ones 1 n nonlinear 1 2 length on 1 1 ones 1 n ones 1 length off use an integral to translate from fm to pm pm 2 pi sampclk cumsum f
32. occurs at maximum input power for the IQ modulator specifying a value below 100 percent may reduce the non linear dis tortion produced by the IQ modulator A value of 70 percent will reduce the output power by 3 dB The command in MATLAB which uses Agilent Download Assistant to set the real time scaling value is status status_description agt_sendcommand io RADio ARB RSCaling100 Calibration The final issue to deal with is user calibration This is a feature that allows the user to compensate for frequency dependent loss between the signal generator and the device under test DUT The automatic calibration process within the signal generator uses a GPIB power meter to measure the power at the DUT input to generate the user calibration array When the signal generator is set to a new frequency the processor within the PSG will correct for the losses and provide the displayed power at the DUT input For detailed information about using this feature refer to the E8267 s User s Manual Running Pulse m The file Pulse m is a complete MATLAB program used to generate and download a simple pulse into the PSG A printout of the program can be found in Appendix A Note that the pulse parameters were modified from the simple pulse example illustrated above to produce a more realistic signal The pulse is 1 ms wide with a pulse repetition interval of 10 ms The reference level for the signal generator is set to 0 dBm but the peak pulse amplitude
33. of the waveform is set to 0 707 producing an output power of 3 dBm Figure 3 illustrates the signal YX Agilent 89600 Vector Signal Analyzer ar Oj x Ete Edit Control Source Input MeasSetup Display Trace Markers Utilities Help gt u IG olo Quad 4 ID io lil Fl l x 50 Color Normal v 4 Chi Spectrum 316 2 my LinMag 31 62 mv div Start 0 Sec Trig Ch1 Delay 0 Sec D Chi Main Time Range 316 2278 mV 180 ri deg Measurement paused INTREF CAL OK Figure 3 Screen capture from the VSA signal The user should be able to justify the displayed results on the analyzer with the MATLAB program Pulse m The upper left hand plot shows the frequency spectrum of the signal The upper right hand plot shows the linear amplitude time domain waveform The lower left hand plot shows the IQ vector for the signal The lower right hand plot displays the phase of the signal versus time Observe the linear amplitude plot and note that the ampli tude of the signal is constant within a single pulse and between pulses From the phase plot versus time note that the phase of the pulse is constant within a single pulse and between pulses This infers that the PSG vector signal generator is coherent in frequency and phase with the vector signal analyzer Generating a Pulse Doublet Doublet m Having done the hard work of building a pulsed waveform and describing how each part of the program operat
34. on samples fall raised cosine pulse fall time definition samples off pulse off time definition samples ontime total number of points in the rise on fall i in phase modulation signal samples q quadrature modulation signal samples IQData complex array containing both i and q waveform samples Markers array containing markers for Event Markers 1 and 2 am amplitude envelope for the pulse linear units pm phase of the pulse vs time in rads fm offset frequency from carrier vs time in Hz sampclk clock freq for the D A converters in the IQ modulator chirp_dev total chirp frequency deviation in Hz sampclk 100e6 defines the ARB Sample Clock for playback chirp_dev 10e6 defines the total chirp deviation in Hz oe defines the number of points in the rise time amp fall time ramp from 1 to almost 1 over n points defines the raised cos rise time shape defines the on time characteristics defines the raised cos fall time shape defines the off time sample points n 4 ramp 1 2 n 1 2 n rise 1 sin ramp pi 2 2 on ones 1 92 fall 1 sin ramp pi 2 2 off zeros 1 900 dP dP dP oe concatenate the parts of the amplitude of the pulse into a single array am rise on fall off define an array which contains the the chirp waveform fm chirp_dev 2 ones 1 n 1 2 length on 1 1 ones 1 n ones 1 length off use an integral to translate from fm t
35. r n points defines the raised cos rise time shape defines the on time characteristics defines the raised cos fall time shape defines the off time characteristics n 4 ramp 1 2 n 1 2 n rise 1 sin ramp pi 2 2 on ones 1 92 fall 1 sin ramp pi 2 2 off zeros 1 900 af dP dP dP oe build the pulse envelop inphase rise on fall off plot the i samples and scale the plot plot inphase axis 0 length inphase 2 2 set the q samples to all zeroes quadrature zeros 1 length inphase define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant TQData inphase j quadrature Appendix A Simple pulse continued define a matrix and activate a marker for the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1 set Marker to first ten points of playback make a new connection to the PSG over the GPIB interface io agt_newconnection gpib 0 19 Sverify that communication with the PSG has been established status status_description query_result agt_query io idn if status lt 0 return end preset the instrument status status_description agt_sendcommand io STATus PRESet set carrier frequency and power on the PSG using the PSG Download Assistant status status_description agt_sendcommand io SOURce FREQuency 1e9 status status_description agt
36. ription agt_sendcommand io POWer ALC STATe OFF status status_description agt_sendcommand io RADio ARB RSCaling 70 7 download the iq waveform the PSG baseband generator for playback status status_description agt_waveformload io IQData lfm sampclk play no_normscale Markers Turn on modulation status status_description agt_sendcommand io OUTPut MODulation STATe ON Appendix G Pulse with non linear fm chirp Script file NLFM_Chirp m Purpose Record of revisions Date Programmer 4 15 2002 Randal Burnette 8 14 2002 John Hutmacher 9 4 2002 Randal Burnette 6 26 2003 Randal Burnette Define variables AP dP dP dP DP AP DP dP dP AP BP DP dP DP AP GDP dP DP ADP AP DP dP DP AP GDP dP dP DP AP PO To calculate and download an arbitrary waveform file that simulates a pulsed signal with a non linear fm chirp to the PSG vector signal generator Description of change Initial version for 2002 AD Symposium Added comments and Download Assistant Added Preset turned ALC off and IQ Scaling Added Modulation ON n counting variable no units ramp ramp from 1 to almost 1 used to build sine waves rise raised cosine pulse rise time definition samples on pulse on time definition samples fall raised cosine pulse fall time definition samples off pulse off time definition samples ontime total number of points in the rise on fall i in phase mod
37. rmance of the elint system Pulse compression Frequency chirp Overlapping returns can be separated on ff Generating a Barker Coded Pulse Barker m Barker coded signals are typical in pulse compression radar systems Barker codes are binary numbers containing between 2 and 13 bits that have unique auto correlation func tions The points adjacent to the peak of the correlation function equal zero This is very useful in a radar system since any spurious response can be misinterpreted as a target A Barker coded pulse typically uses binary phase modulation The chip rate is the dwell time for each bit within the pulse In this example we will build a 7 bit Barker coded waveform The 7 bit Barker code contains the bits 1 1 1 1 1 1 1 To build the phase waveform the seven bits of information must correctly encode into a binary phase shift keyed waveform and deal with the speed of the phase transitions The transition time between phase states will at least in part determine the occupied band width of the signal Within the program first define the possible phase states and transitions as individual arrays and then concatenate them into the final waveform The two possible states the waveform can occupy are positive and negative or 1 and 1 There are four possible transitions negative to positive positive to negative negative to negative and positive to positive The states are built with a constant
38. rs Utilities Help gt Tule Ofo ews IDE E e 068m C Chl Main Time 50 Color Normal z Trig Lv 2 V D Chi Main Time f 316 2278 mV Measurement paused INT REF Figure 4 Screen capture of pulse doublet signal Generating Phase Shift The next example will add a 7 2 phase shift 90 between the two pulses Note that in the previous examples the amplitude envelope was placed in the real array and zeros Between Pulses were placed in the imaginary array For signals that require no phase or frequency modu PM Doublet m lation that technique works fine and simplifies the math For this example the signals will be specified in terms of an am and pm array and converted into IQ The array for pm contains a constant but different phase during the on time of each pulse Pulse1 is set to 0 and pulse2 is set to 1 2 Multiplying the am waveform times the sine or cosine of the pm waveform performs the IQ conversion The period following the variable am instructs MATLAB to multiply the arrays on an element by element basis Note that in Figure 5 the 7 2 phase shift between pulse1 and pulse2 shown in both the IQ plot and the phase versus time plot i Agilent 89600 Vector Signal Analyzer a 5 x File Edit Control Source Input MeasSetup Display Trace Markers Utilities Help 7 J gt fule IG O O ww Ro liM ll 50 Colrnormal 316 2 mv LinMag 31 62 mv jdi 6 Start 0 Sec Stop 12 717 uSe
39. s counting variable pulse on time definition To calculate and download an arbitrary waveform file that simulates a simple 7 bit barker RADAR signal to the PSG vector signal generator Description of change Initial version for 2002 AD Symposium First draft Added Preset turned ALC off and IQ Scaling Added Modulation ON no units ramp from 1 to almost 1 raised cosine pulse rise time definition samples used to build sine waves samples raised cosine pulse fall time definition samples pulse off time definition in phase modulation signal quadrature modulation signal samples phase modulation samples samples clock freq for the D A converters in the IQ modulator transition from low bit to high bit transition form high bit to low bit defines high bit defines low bit defines high bit defines low bit defines the ARB Sample Clock for playback n 4 ramp 1 2 n 1 2 n rise 1 sin ramp pi 2 2 defines on ones 1 120 defines fall 1 sin ramp pi 2 2 defines off zeros 1 896 defines am rise on fall off defines neg_pos 1 sin ramp pi 2 1 pos_neg 1 sin ramp pi 2 1 pos_pos ones 1 4 neg_neg ones 1 4 pos ones 1 13 neg ones 1 13 i the the the the the pulse pulse pulse pulse pulse defines the number of points in the rise time amp fall time number of points translated to time rise time shape on time characteristics fall time s
40. the pulse vs time in rads sampclk 100e6 defines the ARB Sample Clock for playback defines the number of points in the rise time amp fall oe n 4 time ramp 1 2 n 1 2 n oe ramp from 1 to almost 1 over n points rise 1 sin ramp pi 2 2 defines the raised cos rise time shape on ones 1 120 defines the on time characteristics fall 1 sin ramp pi 2 2 defines the raised cos fall time shape off zeros 1 640 separation zeros 1 128 oe defines the off time sample points fines the separation between the pulses oe Q oO o define arrays which contain the pulse envelope for each pulse pulsel rise on fall pulse2 5 rise on fall concatenate and scale the pulses am pulsel separation pulse2 off set the phase of the first pulse to 0 rad and the second to pi 2 rad pm 0 ones 1 length pulsel separation pi 2 ones 1 length pulsel off 21 22 Appendix C Pulse doublet with phase offset continued plot the amplitude envelope and scale the plot plot am axis 0 length am 2 2 convert am and pm to i and q i am cos pm q am sin pm define a composite iq matrix for download to the PSG using the PSG ESG Download Assistant IQData i j q define a marker matrix and activate a marker to indicate the beginning of the waveform Markers zeros 2 length IQData fill Marker array with zero ie no markers set Markers 1 1 10 1
41. to hold the output power at a known level For pulsed signals generated by the IQ modulator the ALC will tend to drive the average power of the signal to equal the refer ence power driving the peak power well above the reference power This becomes a real problem when the signal becomes more complex It is good practice to turn off the ALC by putting the calibration process into manual mode This can be done from the front panel of the instrument or from MATLAB The command in MATLAB which uses Download Assistant to turn off ALC is status status_description agt_sendcommand io POWer ALC STATe OFF Note that the ALC is part of the signal generator calibration process Even when the ALC is turned off the value for the output gain correction is held but not updated in a digital to analog converter and applied to the output If the ALC is turned off for an extended period of time the output calibration may drift About once per day in laboratory condi tions it is a good practice to turn off the 10 modulation and press the Manual Calibration softkey under the Power hardkey to update the calibration Scaling factor The second issue to deal with is real time IQ scaling which is expressed as a linear per centage of the reference level This scaling factor is applied to all IQ waveforms to easily enable users to specify a known back off for the arbitrary waveform generator drive level into the IQ modulator Since the worst case compression
42. ulation signal samples q quadrature modulation signal samples TQData complex array containing both i and q waveform samples Markers array containing markers for Event Markers 1 and 2 am amplitude envelope for the pulse linear units pm phase of the pulse vs time in rads fm offset frequency from carrier vs time in Hz sampclk clock freq for the D A converters in the IQ modulator chirp_dev total chirp frequency deviation in Hz sampclk 100e6 defines the ARB Sample Clock for playback chirp_dev 10e6 defines the total chirp deviation in Hz n 4 defines the number of points in the rise time amp fall time oe ramp 1 2 n 1 2 n ramp from rise 1 sin ramp pi 2 2 defines t on ones 1 92 defines t fall 1 sin ramp pi 2 2 defines t off zeros 1 900 defines t concatenate the parts of the ampli am rise on fall off a oP oe chirp nonlinear 2 sin pi 1 2 length on 1 1 to almost 1 over n points he raised cos rise time shape he on time characteristics he raised cos fall time shape he off time sample points tude of the pulse into a single array define an array which contains the the non linearity of the chirp waveform the non linearity is in the form of one cycle of a sine wave across the fy 29 30 Appendix G Pulse with non linear fm chirp continued o add the nonlinearity to the chirp and concatenate the other sections fm
43. value over the chip period The transitions are built using raised cosine functions Note that the array rise was built as part of the am array but it is used here as a 0 to 1 phase transition At the end of the code sequence the function rise 1 is used to provide a 1 to 0 transition Having constructed the array with 1 and 1 states multiply the waveform by 7 2 to provide the appropriate phase deviation The resulting waveform is converted to IQ and downloaded into the signal generator The following block contains a subset of the code in Barker m neg_pos 1 sin ramp pi 2 1 pos_neg 1 sin ramp pi 2 1 pos_pos ones 1 4 neg_neg ones 1 4 pos ones 1 13 neg ones 1 13 pm pi 2 0 0 0 rise pos SBit 1 high pos_pos pos SBit 2 high pos_pos pos SBit 3 high pos_neg neg SBit 4 low neg_neg neg SBit 5 low neg_pos pos SBit 6 high pos_neg neg SBit 7 low rise 1 0 0 off i 707 am cos pm q 707 am sin pm Generating a Linear FM Chirp LFM_Chirp m Figure 8 shows the demodulated signal The lower right hand plot displays the demodu lated phase versus time Note that during the on time of the pulse the seven bits of the code are clearly visible Markers may be used to verify the phase state accuracy and tim ing The noise in phase between the pulses is due to the fact that during the off time of the pulse the phase of the signal is undefined W Agilent 89600
44. width PW and pulse repeti tion interval PRI Doing a reasonable simulation of a simple emitter also requires control of the rise time and fall time of the pulse Shaping the rising and falling edge of the pulse enables the user to control the frequency spectrum of the waveform Generating a signal To generate the signal we will build an array in MATLAB that describes the in phase and quadrature time domain waveforms and download the arrays into the signal generator Figure 1 shows a plot of a typical pulsed waveform Figure No 1 Eile Edit Tools Window Help JoeaeSlKaAAs E2 15 x 0 10 20 30 40 50 60 70 80 g0 100 Figure 1 Typical pulsed waveform plot The following block contains a subset of the code in Pulse m sampclk 100e6 ARB Sample Clock for playback D n 10 number of pts in the rise amp fall time ramp 1 2 n 1 2 n ramp from 1 to almost 1 over n pts rise 1 sin ramp pi 2 2 raised cos rise time shape on oneon ones 1 10 on time characteristics fall 1 sin ramp pi 2 2 raised cos fall time shape off zeros 1 70 defines the off time characteristics build the pulse envelop i rise on fall off plot the i samples and scale the plot plot i axis 0 length i 2 2 set the q samples to all zeroes q zeros 1 length i IQData i j q Mo In the program to build the waveform the pulse is broken down into four parts rise on fall and o
45. y a 100 KHz doppler shift over 1 ms should be 100 KHz 360 cycle 1e 6 sec 36 Note that the displays show 36 of phase shift during the on time of the pulse In Figure 7 the vector signal analyzer has been tuned to the doppler offset frequency Note that the phase of the pulse is constant and stable over at least two pulses This infers that the signal generator and arbitrary waveform generator are coherent with the vector signal analyzer This also provides confirmation that the math used to calculate the doppler waveform is correct W Agilent 89600 Vector Signal Analyzer t 7 Oj x Ete Edit Control Source Input MeasSetup Display Trace Markers Utilities Help gt u ileo Quad4 hk ii o IiI FI l x 50 Color Normal X 1 316 Start 0 Sec Stop 12 717 uSec Trig Ch Delay 0 Sec Trig Lvl 2 V D Chi Main Time deg Wr Phs P 36 deg div Delay 0 Sec INTREF CAL OK A Figure 6 Doppler signal when VSA is tuned to center frequency of the signal generator Measurement paused AI Agilent 89600 Vector Signal Analyzer p oj x Ete Edit Control Source Input MeasSetup Display Trace Markers Utilities Help gt u IHG Quad 4 ES ia o i Fl l 50 Color Normal X m 316 2 LinMag 31 62 mV D Chi Main Time 180 Measurement paused INTREF CAL OK Figure 7 Doppler signal when VSA tuned to dopper offset frequency 11
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