examining dynamic range

8/3/2019 Examining Dynamic Range

1/9www.SandV.com12 SOUND AND VIBRATION/AUGUST 2007

Examining the Dynamic Rangeo Your Vibration ControllerPhilip Van Baren , Vibration Research Corp., Jenison, MichiganGeorge Fox Lang, Independent Consultant

Dynamic range is one o the undamental metrics describing thecapability o a shaker controller. We all know that dynamic range

describes the span o small-to-large acceleration amplitude thatcan be properly controlled during a test. Since modern control-lers are digital instruments, we also know the dynamic range to

be six times the number o bits in the analog/digital converter.But what do we really know? Lets examine the dynamic range o a vibration controller more scientifcally.

A controller orms a loop around the shaker and device undertest (DUT) by providing an analog signal to the power ampli erdriving the shakers armature (or control valve) voice coil (seeFigure 1). This signal is called the drive, and the controller ormsit by comparing the (analog) control acceleration measured on theshaker table (or on the DUT) with a desired demand re erence. Thecontrol algorithms seek to systematically minimize the di erence

between the control and demand signals by adjusting the shapeand amplitude o the drive signal.

Figure 1 shows clearly that the available dynamic range o atest is limited not only by the controller dynamic range, but also

by the characteristics o the power ampli ier, shaker, control-point accelerometer, test object and all the mounting hardware,and methods employed. It is also clear that the controllers roleinvolves measuring the control signal, per orming calculations andprocesses upon this measurement, and generating the drive signal.The amplitude-depth o each o these three processes a ects theavailable test dynamic range.

The shaker and its ampli er must be power ul enough to drivethe DUT and xturing to the required orce and motion levels o the test. The shakers suspension must be su ciently linear toaccurately reproduce the low amplitude details o the demand, and the ampli ers noise foor must be low enough not to maskthese eatures. The accelerometer and its signal conditioning musthave adequate dynamic range to ollow the control motion withdelity, and this range must be properly matched to the accelera-tion span o the test. When all o these conditions are met, thecontroller becomes the limiting actor in the loops per ormance.So it is important to have a controller with as much dynamicrange as possible.

You can never have too much dynamic range in any piece o testequipment. Physical realities o a test always stack up un avor-ably to consume every ounce o available dynamic range a systemcan muster. It is also important that you understand the dynamicrange o your equipment, so that you can accurately predict test

system per ormance analytically. This avoids employing time andlaboratory assets on a wing-and-a-prayer basis, always a costlyoperating philosophy.

dB(SNR) What Dynamic Range Really SaysDynamic range is the ratio o the largest and smallest signals

that can be simultaneously properly processed by an instrumentor system. This ratio is normally expressed in decibels (dB) tocompact the range o numbers we need to think about. The largestsignal is the ull-scale input or output, while the smallest is thenoise foor or resolution limit o the process. Thus, the dynamicrange is really a signal-to-noise ratio (SNR) expressed in dB. Quiteo ten, physics demands that the ull-scale and noise-foor speci ca-tions be presented in a dimensionally inconsistent manner. It iscommon to know the ull scale as a peak value and the noise fooras a root-mean-square (RMS) value. Consider the accelerometerspeci cations shown in Figure 2 as an example.

This 100 mV/g sensor has a measurement range or ull scaleo 50 g and an equivalent noise or noise foor o 0.0001 g RMS.The ull scale refects the largest peak acceleration that can bemeasured without clipping, or limiting the output (voltage) signal.

In contrast, the sensors noise foor has a continuous broadbandspectrum, so the minimum resolvable signal is expressed as anRMS value over a speci ed bandwidth (1 Hz to 10 kHz in this case).Note that this noise foor likely changes height with requency; i it were fat, it could be expressed as a constant (spectraldensity ) or g2/Hz (power spectral density ).

Dynamic range is always expressed as a ratio o consistentnumbers. So we will assume the 50 g ull-scale signal to be asine wave and use its RMS value (0.707 50 gpeak = 35.4 g RMS) inthe dynamic range calculation. This gives us a ull-scale to noise-foor ratio o 35.4 divided by 0.0001, or 353,500. Converting thisnumber to decibels yields 111 dB (= 20 log10[353,500]). Notethat a sine wave is always used or such peak-to-RMS conversion

by industry convention. Also note that the 111-dB dynamic rangeis or the requency span 1 Hz to 10 kHz. I the sensors input iscon ned to a narrower bandwidth, the dynamic range will actu-ally increase, refecting integration o the noise foor over a smaller

Figure 1. Vibration controller generates drive signal that causes measured control acceleration to closely match prescribed demand.

Figure 2. Typical specifcations o a modern accelerometer ( courtesy DytranInstruments ).

g/ Hz


2/9www.SandV.com DYNAMIC TESTING REFERENCE ISSUE 13

requency interval. The same characteristic is ound in vibrationcontrollers.

Testing Your ControllerTo test the dynamic range o a device, it is necessary to use a

care ully constructed signal that has a peak value just below themaximum level that the device can measure and also has a smallsignal that is just above the noise foor. These two signal levelscould be at the same requency and applied sequentially or could

be two simultaneous signals applied at di erent requencies. Thedynamic range measurement is the ratio between the largest signal

that can be measured and the smallest that can be measured.No single test can ully tax and capture all aspects o a controllersdynamic range. However, the ollowing group o tests collectivelydocument a particular instruments capabilities. Each test hasstrengths and weaknesses that are discussed. Some o these testsrequire external equipment; such tests must be approached withsome trepidation. It is all too easy to ignore the railty o an in-experienced operator or an external instrument on the controllerunder examination. Digital storage oscilloscopes typically have8-bit resolution, and unction generators rarely are harmonicallypure to 100 dB. Modern vibration controllers are as accurate asmost digital signal analyzers and o ten will be the most accurateunction generator and signal analyzer in your lab.

We will use tests that ocus on three aspects o the controller

input channels, output channels and control algorithms. Thesethree aspects will be interdependent, especially the control al-gorithm tests, which depend on the signals rom the input andoutput channels and there ore can be no better than either o those.In many cases, both the controller input and output will be usedsimultaneously.

We will look at two di erent tests o an input channel, wherecare ully produced external analog signals are applied to the control input, and the controller is used to capture the signal ordigital analysis. Then we will examine the dynamic range o thedrive output by having the controller generate a ull-scale, xed-requency sine wave and measure this with an external signal ana-lyzer. Next we will use a severe demand spectrum in a bare-wireor loop-back test to examine both the drive and control signalssimultaneously. Two additional loop-back tests will be discussed,one using swept sine and the other narrow bands o random noise.Finally, we will examine controlling a high-Q active lter actingas a simulation o a structure on a shaker.

Two-Tone Input TestThe two-tone dynamic range o a control input channel is bor-

rowed rom the IEEE recommended practice or testing a time-

compression or FFT spectrum analyzer. As shown in Figure 3,an analog signal with two sine wave components is applied. Onecomponent is adjusted to be a ull-scale input. The second sine,at a di erent requency, is attenuated until it is just lost in the

baseline o a spectrum computed rom the sum. The ratio o thesecomponents is determined by the setting o a precision attenuator,and this setting is recorded as the dynamic range when the smallersignal is just indistinguishable rom the spectral foor.

The test signal required or this test may be generated by ahigh-per ormance arbitrary unction generator. Alternatively, twohigh-quality oscillators or sine synthesizers, a precise attenuatorand a precision summing circuit may be used to build the signal.The analog sine sources need to provide an output greater than theull scale o the controller input channel to allow use o a passive summing circuit. Using an active summer introduces an externalnoise foor to the equation and also introduces possible signalarti acts, including intermodulation products.

The results o this test depend strongly on the block length usedor the FFT and the type o window unction used. The quantizationnoise o the primary tone acts as a dither signal and this allowsmeasurement o low-amplitude signals that could not be measuredindependently. For example, with a 65,536-sample block lengthand a Hanning window unction, an ideal 14-bit system wouldshow 120 dB with this test. Obviously this is much greater thanthe 84-dB SNR one would normally expect rom a 14-bit input. Forthis reason, this test is not a good measure o dynamic range.

Also, note that the requency peaks due to harmonic distortionwill, in all likelihood, be higher than the lower o the two summedsignals. I the two signals being measured are harmonics o eachother, then the level o harmonic distortion will be the limitingactor. This is evident in Figure 4, where the harmonics o theprimary tone are more prominent than the low-level tone. So,while the noise foor allows or distinguishing some signals 120dB apart, this test may be more use ul as a measure o the amount

o harmonic distortion present. What cannot be determined romthis test is whether the harmonic distortion is due to the arbitraryunction generator or the controller input electronics.

E ective Bits Input TestThis is a more recent test method sanctioned by the IEEE or

digital recording devices. As shown in Figure 5, a single sine waveis applied to the control input channel. An untriggered digitalrecording o the signal is made by the controller input hardwareand these data are curve- tted to yield the our parameters ( , A,B and C ) o a model o the orm: y (t ) = A cos(2 p n Dt ) + B sin(2 p n Dt ) +C , where Dt is the known intersample interval and n is thesample count. This parameter identi cation allows the signalto be separated rom the noise, permitting calculation o a SNR.The result is then expressed in terms o e ective-bits, ratherthan in dB.

To understand the conversion rom a dB(SNR) to e ective-bits,

Figure 4. Two-tone test o VR 8500 controller indicates 120 dB between ull-scale and small tone.

Figure 3. Testing dynamic range o control input using the two-tonemethod.

Figure 5. Testing the dynamic range o a control input using the IEEE e - ective-bits method.

. . . comparing controllers using dynamic rangenumbers is di cult at best. For unbiased com-parisons, it is better to compare the maximumsignal level, the noise foor and the harmonic

distortion characteristics o the systems.



consider the per ect n-bit converter. A per ect n-bit converterexhibits 2 n unique output codes uni ormly spanning its V FS in-put voltage range. Each least-signi cant bit (LSB) change in theoutput code refects a change in input voltage by an amount, V q,termed the quantization voltage , where V q = V FS /2

n -1. Note thatthe code representation is exactly correct at only 2 n speci c volt-ages; in all other cases, it is in error by as much as V q/2. Thus,the converter is said to be precise to LSB. As a result, the idealconverter has an RMS noise foor o . When a sine signalo V FS peak is applied to the converter, the (RMS) signal/noiseratio is given by:

This result is plotted in Figure 6, and we now have a better un-derstanding o the long-accepted 6 dB-per-bit truism! E ective

bits compress a large range o numbers into a more comprehensiblespan, as does a dB calculation. For example, the accelerometer pre-viously discussed has a claimed SNR o 111 dB. Use this numberto enter the vertical axis o Figure 6; read the equivalent numbero bits (slightly more than 18) rom the horizontal axis. Clearly,this sensor would have no problem in eeding a 16-bit ADC to ulldynamic range capability. It would be a clear choke-point in a24-bit system.

The major advantage o an e ective-bits test is that it requiresno comparative measurements. The requency o the test sine must

be within the selected bandwidth o the controller. Its amplitudemust be less than the F s voltage o the input. However, neither therequency nor the amplitude o the test signal need be measured orknown. The sine must be stable in requency and amplitude andpure in wave orm. For this reason, the analog- ltered output o a digital synthesizer is the pre erred signal source. However, thecontroller must provide access to the raw wave orm data, and a digi-tal curve- tting algorithm is required to accomplish the test. TheIEEE particularly warns against using an FFT as the curve- ttingprocess and recommends the direct application o least-squaresminimization between the model and the acquired samples.

This test was run on a Vibration Research 8500 controller, usingthe controller output as a high-quality sine wave synthesizer andusing the RecorderVIEW eature to record the raw input wave ormsto disk. These wave orms were then loaded into M atlab andprocessed with a curve- tting algorithm. Typical test results orthe VR-8500 are shown in Figure 7. The our test bandwidths o 20Hz and less correspond to selected sine tracking lter bandwidths.The six higher bandwidths show typical broadband results; theseinclude the 200-Hz ASTM transportation test bandwidth, the2000-Hz NAVMAT test bandwidth and the 8500s maximum band-width. The corresponding dynamic ranges or these bandwidthsare shown in Figure 8.

Single-Tone Output TestThe test shown in Figure 9 looks at the the spectrum o a xed-

requency, ull-scale sine wave produced by the controller. Outputdynamic range is recorded as the dB di erence between the sinepeak and the spectrums noise foor. Clearly, the results can be no

better than the two-tone dynamic range o the spectrum analyzeremployed, so this test is typically limited by the capabilities o theanalyzer rather than the controller. As with the two-tone input test,this test is also strongly infuenced by the block length o the FFTused in the analyzer, and there ore will not correlate well with thetrue dynamic range o the controller.

Figure 10 shows the spectrum o a 1000-Hz (2 V) sine wavegenerated by a VR-8500 controller output and analyzed using anexternal FFT analyzer. The background noise is more than 120 dB

below the signal, with the highest harmonic peak about 100 dB below the signal.

Loop-Back TestsThe drawback o the preceding tests is the requirement or ex-

ternal equipment and/or external mathematical analysis. However,vibration controllers have the ability both to produce output andanalyze the input, and both o these unctions are used simultane-ously while in operation. There ore, it is desirable to apply a testthat uses the controllers output and input so that both are testedsimultaneously and no additional equipment is required. Theresults o the test will then refect the combined dynamic rangeo both the output and input. It is also possible to do these same

tests with only the output, using an external signal analyzer or onlythe input using an external signal synthesizer. This would allowseparate results to be stated or both the output and the input atthe expense o requiring additional equipment.

Sine Loop-Back TestIn this test, the drive is looped back to the control input as shown

in Figure 11. A swept-sine test is run, with the test speci ying axed- requency sine with an exponential decrease in amplitudeover the duration o the test. The amplitude starts at the ull-scalelevel and then decreases to a level below the anticipated dynamicrange o the controller. The drive and control are viewed as RMS-versus-time plots with a log-amplitude axis. The transmissibility(RMS-to-RMS ratio) o the control with respect to the drive is alsodisplayed.

As shown in Figure 12, both o these traces are clean straightlines within the dynamic range o the controller. The amplitude

4 8 12 16 20 24Number of Bits in ADC or DAC

24

36

48

60

72

84

96

108

120

132

144

S N R

, d B

Figure 6. Relationship between e ective bits and dynamic range or SNR.

1 10 100 1000 10000 100000Bandwidth (Hz)

17

18

19

20

21

22

23

E f f e c t i v e - B

i t s

Figure 7. Measured e ective bits o the VR 8500 control input channel at various bandwidths.

1 10 100 1000 10000 100000Bandwidth (Hz)

105

110

115

120

125

130

135

140

S N R

, d B

Figure 8. Dynamic range o the VR 8500 controller at various bandwidths.

(1)dB(SNR) SNR

= =

=20 2022

12

10 10log ( ) logV

V

FS

q

20 2 6 6 02 1 76101 ( )= +-log . .n n

V q / 12



is at the controllers ull-scale at the le t side o the display andsweeps down into the noise on the right. In this region, thetransmissibility is exactly 1.0 ( or 1000 mV/g). At the (right) edgeo the dynamic range, where the envelope o the transmissibilityspans 0.707 to 1.41, the signal and noise values are at the sameamplitude. The drive voltage RMS at this point in the test is equalto the instruments RMS noise foor within the requency bandpassed by the tracking lter. The amplitude o the drive voltage atthis point is there ore a measure o the noise foor. The dynamicrange o the output and input is the ratio o the maximum voltage( ull-scale voltage) to this noise-foor measurement.

It is important to note here that the RMS noise foor in this test isthe amount o noise measured a ter the tracking flter . The narrowerthe tracking lter, the less noise it will pass through. There ore thesine tracking lter bandwidth is an important parameter in thistest, and when using results o this test to compare controllers, it is

Figure 9. Testing dynamic range o drive output.

Figure 11. Ramped-sine, loop-back test setup.

Figure 10. Single-tone test o VR 8500 drive output shows more than 100dB dynamic range.

Figure 12. Ramped-sine test o VR 8500 controller indicates about 120 dBinput/output dynamic range.

Figure 14. Random test indicates 100 dB o clean dynamic range or VR8500.

Figure 13. Narrow-band random loop-back test setup.

important to use the same bandwidth or each controller. Figure 12illustrates that the VR-8500 controller, with a 10-Hz tracking lter

bandwidth, shows a dynamic range o more than 120 dB.

Random Loop-Back TestThe controller can be tested in a similar manner using a random

test employing a sequence o stepped demand levels ranging rom below the noise foor to the ull-scale spectral density (see Figure13). To determine the lower limit, the coherence between the drive and control is computed. The lower limit is the level prior to thepoint where the coherence drops below 0.5. The dynamic rangemeasurement is then the ratio o the ull-scale density over thislower limit.

The ull-scale density or this test is determined by the levelwhere the RMS o the highest band nearly makes the signal peaksreach the ull-scale voltage. This will happen when (Density max Bandwidth) 1/2 = V FS/6, where V FS is the ull-scale voltage level,and bandwidth is the requency width o the steps used. The im-plication o this is the ull-scale spectral density will depend onthe bandwidth used in this test; there ore, the resulting dynamicrange measurement will depend on the bandwidth used in thetest. The narrower the bandwidth used in the test, the higher themaximum density level achieved, and there ore, the wider thedynamic range value reported. Because o this and when compar-

ing controllers using this test, one must be care ul to use the sameparameters on both controllers.

Figure 14 shows a loop-back random test being run on a VR-8500controller. As shown, 24 demand PSD steps, each 50 Hz wide, span115 dB. Control appears to be tight rom 3.16 10 -1 V2/Hz downto 1 10 -12 V2/Hz, a span o 105 dB.

However, the accompanying coherence and transmissibilityplots indicate that the noise foor is closer to 3.16 1012 V2/Hzor a conservative random dynamic range o 100 dB. Note that theCoherence is greater than 0.9 all the way down to 100 dB. It isstill about 0.8 at 105 dB, where transmissibility departs sharplyrom 1.0.

Note that this test is run with a demand PSD that has increas-ing amplitude steps with requency. This assures that the lowestamplitude steps in the control signal refect the instruments noisefoor rather than harmonic distortion. That is, no step o this s ignalintroduces signi cant harmonics o itsel in other steps.



Input/Output Test Using a Severe DemandAn interesting alternative to the previous tests was developed by

the Chinese government around 1988. This test (see Figure 15) ismeritorious in that it requires no external equipment; it taxes boththe control input and drive output simultaneously. It requires thetester to understand nothing beyond the operation o the control-ler and does not involve curve- tting or advanced mathematics.In short, it is absolutely elegant in its simplicity.

The key to this e cient evaluation is the requency span between350 and 500 Hz, shown in Figure 16. The demand spectrum in thisregion is successively programmed to lower g 2/Hz power spectral

density levels until the controller ails to conduct the test. Thelowest notch level at which control can be achieved determinesthe control system dynamic range.

As shown in Figure 16, the VR 8500 success ully controlled thenotch down to a depth o 90 dB with respect to the highest PSDlevel. It could not ollow the 100-dB demand o the lowest gure.Figure 17 shows the 90-dB test in more detail, including the limitsand the drive signal.

Note that the JJG 529-88 test pro le is speci ed in g 2/Hz units.Also recall that to test dynamic range, the signals used must becare ully cra ted so that the peak levels are just below the maxi-mum value the system is capable o measuring. There ore, theoperator must select the mV/g sensitivity o the (nonexistent)accelerometer so that the peak levels o the 10-g RMS signal are just

below the maximum input voltage o the system or the input range being tested. This allows this test to be independent o the inputrange used. For a system with 10 V control and drive ull scales,this optimum is about 100 mV/g, which results in voltage levelso 1 V RMS, and 6 V peak At this point, the achievable depth o thenotch will measure the range between the ull-scale signal and thenoise foor. I the sensitivity is increased above 200 mV/G, thenthe wave orm peaks will begin to saturate. This will be evident asa sudden increase in the measured g 2/Hz level in the 350-500 Hznotch and will severely impact the test results.

I we actor out the sensitivity scale actor and consider the re-lationship between the maximum V 2/Hz level and ull-scale inputvoltage and also the relationship between the minimum V 2/Hz leveland the noise foor, we gain more insight into this test. For the givenspectrum, the maximum PSD level is 10 3 times the square o theRMS voltage, V

RMS. Assuming a crest actor o 5, the maximum

achievable V RMS level will be V FS/5. The minimum achievableV2/Hz level, assuming a fat noise spectrum, will be ( V noise

2)/(2000Hz), where V noise is the RMS noise foor. The expected randomdynamic range (RDR) o the JJG 529-88 test will then be the dBratio o these two power spectral densities.

This result can be recast in terms o the SNR measured in ane ective-bits test. V noise can be recognized as including the quanti-

zation noise o an ideal converter and the noise o the supportingsignal conditioning. There ore the RDR can be restated in termso SNR as:

This is a very interesting result, because it tells us that the bestresults one could expect rom this test will be 8 dB less than thedB(SNR) as measured using a sine tone. This is to be expected,

because the peaks in a random signal are higher than or a sinesignal, so the random ull-scale RMS will be lower than the sineull-scale RMS.

Figure 15. Testing both drive and control dynamic range using a severedemand.

Figure 16. VR 8500 per orming Chinese JJG 529-88 challenge test at 60, 70,80, 90 and 100 dB.

(2)

dB(RDR) RMSnoise

RMS=

= -

10 102000

10 2103 2

2 10

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V nnoise

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=20 25

20 0 4

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log

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V V

V

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iisedB(SNR)

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To apply these results practically, we re er to Figure 8 and notethat or the VR-8500 with a 2000 Hz bandwidth, the SNR is 114dB, so we could reasonably expect a 106 dB result rom the the JJ529-88 test. But we only ound a result o 90 dB. What accounts orthis di erence? The answer lies in the high band rom 80 to 300Hz. The notch rom 350 to 500 Hz corresponds to the harmonicso the 80 to 300 Hz band. Any harmonic distortion o the 80 to300-Hz band will show up as an increased noise level in the 350to 500-Hz notch. There ore, this test measures dynamic range upto a point (typically to 16 e ective bits), but beyond that point,the results are limited by harmonic distortion. Since most currentcontrollers have more than 16 bits o resolution, their results usingthis test will be limited by the harmonic distortion o the systemand not the dynamic range.

Random Algorithm/Output TestThere is one valid criticism that can be directed at the JJ 529-88

test: it does not demonstrate control over any sharp resonance peaksand notches that may exist in a structure. Our next test addressesthis issue. At least two controller manu acturers have built activechallenge lters and issued them to their sales sta or elddemonstrations. These two designs are remarkably similar; bothmanu acturers selected similar peak and notch requencies andamplitudes. The VR 8500 was recently tested against the newer

o these two challenge lters.In this test, the lter is driven by the drive signal, and its out-

put is applied to the control channel, as shown in Figure 18. Thetest demand is a fat spectrum spanning 20 to 2000 Hz. Whenully-controlled, there ore, all signi cant signal dynamics will berefected by the drive signal. The implication o this is that the testexercises the control algorithm and the output signal, but since there erence spectrum is fat, the input dynamic range is essentiallyuntaxed by this test.

Testing these lters is a challenge until a couple o things areunderstood. First, the lter uses active electronics with a limitedvoltage range; the lter becomes wildly nonlinear when it is over-loaded. Neither design incorporates any orm o overload indica-tion, so the experimenter needs to determine the maximum whitenoise drive signal (equal energy/unit requency) that can be appliedwithout causing the lter to grossly misbehave.

Second, the lters DC gain o 10 (20 dB) is a bit deceptive. As it



Figure 17. Details o JJG 529-88 operation at 90 dB showing control withlimits and drive signal.

Figure 18. Testing dynamic range by closing loop around simulation flter.

would suggest, the RMS output o the lter is greater than the RMSinput, when the input requency is below the requency o the rstpeak. However, when a white noise input is applied to the lter,the output RMS is about 36 dB greater than the input RMS. Then,when the input is properly shaped to produce a white noise lteroutput, the output RMS is about 23 dB less than the input RMS.(See RMS Gain sidebar or the explanation.)

All o this means that the test must be conducted with a properlychosen RMS demand level. The 20-dB DC gain might lead one tothink the re erence spectrum should be chosen to give 1 V RMS. Butonce the drive signal is properly shaped to make the lter outputwhite, the lter input would be 23 dB higher than 1 V RMS, or 14.6VRMS. Clearly this would overdrive the lter input! The properchoice o the demand level is ound by determining the input levelthat overloads the lter and then setting the re erence spectrum to

be 23 dB lower than this level. Typically, such a lter will workproperly up to a 1 V RMS input, so setting the re erence spectrumto give 68 mV RMS would yield the best results.

Figure 19 illustrates success ul control lock on a challenge lterusing a VR 8500 with 800 lines o control, with all control lineswithin 3 dB o the demand line. From this gure, one could

believe that the controller has passed this test. However, the chal-lenge lter has a notch at 380 Hz with a bandwidth o only 0.35Hz. The control bandwidth o 2000 Hz divided by 800 lines o control gives a controller line resolution o 2.5 Hz. Knowing this,we recognize it is impossible or any controller to properly controlthis lter with only 800 lines!

Adding an external analyzer to monitor the drive and controlsignals is probably prudent or independent validation o any loop-

back test. In this particular case, however, we see that dependingentirely on an instrument to analyze its own worth is a seriouserror in judgement. In lieu o a stand-alone analyzer, you mightsubstitute the use o a digital recorder (or recording so tware us-ing the controllers hardware) and o -line analysis using so twaresuch as M atlab .

Figure 19. Closing loop around challenge flter with VR 8500 using 800lines o resolution.

Figure 20. An 800-line control signal spectrum-analyzed by an external analyzer with more resolution.

Figure 20 shows the control signal as analyzed independentlyusing a high-resolution FFT with a line resolution o 0.08 Hz. Whenanalyzed independently, we can see that the control signal actuallyhas more than 20 dB o error around the notch, ar beyond the 3dB the controller display reveals. From this we can see that anychallenge lter test must be veri ed using an independent analyzer.Simply relying on the controllers display allows the controllerimper ections to hide the true errors present in the signal.

To properly control this test, we need a line resolution o 0.35 Hzor better. This can be achieved by increasing the number o lineso resolution employed by the controller. Figure 21 illustrates asuccess ul control lock on a challenge lter using a VR 8500 with13,000 lines o control, with all control lines within 3 dB o thedemand line. Figure 22 shows the independent analysis o thistest, demonstrating proper control o this lter using 13,000 lines,with a maximum error o less than 2 dB.

Figure 23 presents a summary o worst-case loop error as a unc-

tion o control resolution. In all cases, the worst error occurredat the 380-Hz lter notch. This investigation disclosed that atleast 8,000 lines o controller resolution are required to controlthis challenge lter within 3 dB over the 20-2000 Hz NAVMAT

bandwidth.Figure 24 presents the trans er and coherence unctions o the

lter rom the test o Figure 21. The dynamic range o the test isread rom the amplitude extremes o the trans er unction. Thehigh coherence values at each trans er unction peak and valleyindicate clean control and linear lter behavior.

Proponents o this test claim the dynamic range o the controllercan be determined by taking the ratio o maximum drive output tothe minimum drive output. In this test, we see the VR 8500 dem-onstrates greater than 105 dB, which corresponds to the dynamicrange o the challenge lter. However, this test isnt truly testingdynamic range.

In act, a 16-bit controller with 13,000 lines can also success ully



Two controller manu acturers have produced extremelysimilar challenge lters, each based on two, cascaded, our-ampli er. state-variable lter sections. Each section sums ahigh-pass and low-pass component in the manner normallyused to orm a notch lter. However, the summing gains o thenal stage are deliberately unequal. This produces a high peakat the tuned requency, n, and a deep notch (a zero) at a secondrequency determined by the nal gain ratio.

The trans er unction o the lter section is shown in the up-per gure with certain key eatures noted. The circuit producingthis Trans er Function and the tuning equations are shown inthe lower gure. Five component values ( C , R , RQ, RA and RB)must be chosen to tune this circuit.

Simplifed schematic o a flter section; challenge flter is comprised o two di erently tuned sections in series.

Gain characteristics o each section o challenge flter.

demonstrate greater than 100 dB o dynamic range using this test,even though the true dynamic range o a per ect 16-bit converteris only 96 dB. To understand how this can be, consider that whenrunning the challenge lter test the drive output rom the controllermust be the inverse o the lter trans er unction to get a fat spec-trum output rom the lter. The notch in the lter trans er unctionwill correspond to a very narrow peak in the required drive output.The maximum value o that peak is measured in V 2/Hz, where theHz portion is determined by the bandwidth o the peak. It ollowsthat the maximum V 2/Hz value can be increased without increasingthe signal level simply by reducing the bandwidth.

In the sample case examined here, the highest peak has a 2.5-Hz

bandwidth. I we assume a 1 V RMS signal, with hal o the totalsignal concentrated in this peak, then we would expect the V 2/Hzlevel to be (0.5 V) 2/(2.5 Hz) = 0.1 V 2/Hz. Indeed, when scaled toa 1 V RMS level, we nd the drive spectrum has a peak o 1 10-1 V2/Hz. On the lower end, a 16-bit converter with 10V range hasa quantization noise foor o 8.8 105 VRMS, or 3.1 1012 V2/Hz.Taking the ratio o these two numbers, we see a 105-dB range can beshown with this test on a 16-bit system that we already know cannotexceed 96 dB o true dynamic range. For this reason, the challengelter test, while use ul to exercise the control loop and line resolu-tion, should not be used as a measure o dynamic range.

Sine Algorithm /Output TestThe challenge lter may also be used in the setup in Figure 18 to

measure dynamic range with a swept-sine test. For this test, a fatdemand amplitude is set, and the sine requency is swept throughthe peaks and notches o the challenge lter. The implication o this

Challenge Filter

is only that the dynamic range o the control loop and the control-ler output signal are tested. Since the controller input is speci edto maintain one amplitude level or the duration o the test, thedynamic range o the controller input remains untested. This testmeasures the relative values o the largest achievable output, whichis required at the lowest notch in the lter trans er unction, tothe smallest achievable output (just above the noise foor) at therequency o the highest peak in the lter trans er unction.

Recall that to measure the dynamic range, the test signals must be care ully cra ted so that the highest output corresponds to themaximum range o the system. To success ully run this test, the

Figure 21. Closing loop around challenge flter with 13,000 lines o resolu-tion.

Figure 22. A 13,000-line control signal spectrum-analyzed by an external analyzer.

0

5

10

15

20

25

30

100 1000 10000 100000

Lines of Resolution

M a x i m u m

C o n

t r o

l E r r o r

( d B )

Figure 23. Maximum loop-error versus random control resolution shows at least 8,000 lines o resolution required to hold challenge flter in control within 3 dB over the NAVMAT band.



I the lter is excited by white noise o constant power spectraldensity, d (V2/Hz), it has an input RMS value o :

The corresponding output RMS value is:

This allows the ratio o RMS values to be stated:

For the challenge lter examined, the ratio o Equation 8 evaluatesto 62.9 (or 36 dB). There ore, the output is considerably greaterthan the input at the initiation o control equalization.

Once the control signal has been orced to match the requiredfat spectrum, the situation changes. With a fat lter output(control ) spectrum, we can evaluate the output/input RMS ratio

by computing H AB 1( ) and substituting it into equation (9). This

results in a nal control/drive ratio o 0.0679 or 23 dB. That is,the control RMS is considerably less than the drive signal, oncecontrol to a white spectrum is achieved.

It is interesting to observe the RMS values o the drive andcontrol signals during the controllers pretest equalization in-terval. As shown below, the drive RMS (black) makes a gradualmonotonic increase as the controller converges on the properH AB

1 ( ) to equalize the challenge lters trans er unction, H AB( ).The control RMS (red) increases rapidly at the start and thensoon levels out.

The ratio o these two RMS values (blue) is particularly inter-

esting. Note that the lters output RMS ( control ) is considerablylarger than the lters input RMS ( drive ) when the equalizationprocess starts. At this time, the drive is essentially a white noise,refecting the constant-amplitude re erence entered or the chal-lenge. The early control spectrum shape looks like the lters gaincharacteristic, | H AB( )|. At this time, the lters output RMS isa large multiple o the input RMS.

A ter the drive and control signals have converged on theirstable run values, the control spectrum is fat, while the drive spectrum looks like the reciprocal o the lters trans er unctiongain, | H AB

1 ( )|. At this time, the lters output RMS is only asmall raction o the input RMS.

This e ect is entirely normal and is predictable rom the lterstrans er unction, H AB( ). The ollowing gure shows H AB( ) in

black and its inverse, H AB 1( ) in red.

We know that the magnitude o a trans er unction, | H AB( )|,relates its input power spectral density, G AA( ), and its outputpower spectral density (PSD), G BB( ), in accordance with:

The RMS value (over a bandwidth rom 1 to 2) o a signalrelates to the PSD, speci cally:

(4)G H G BB AB AA( ) ( ) ( )= 2

(5)RMS G d x xx

= ( ) 1

2

(6)RMS G d d A AA

= ( ) = = - 1

2

1

2

12d d ( )

(7)RMS G d H G d B BB

AB AA

= ( ) = = 12

1

2

2( ) ( )

d H d AB

( )21

2

(8)RMSRMS

H d

B

A

AB

= - ( )

( )1

22

2 1

(9)RMSRMS

H d

B

AAB

= -

- ( )

( )

2 1

12

1

2

0 50 100 150

Time, Seconds

0.1

1

10

0.001

0.01

100

F i l t e r

I n p u

t a n

d O u

t p u

t , V o

l t R M S

Input - Drive Output - Control ratio

1

0 1000 2000

Frequency (Hz)

0.0001

0.001

0.01

0.1

10

100

1000

10000

F i l t e r

G a

i n a n

d i t s

I n v e r s e ,

d B

RMS Gain

loss at the lowest notch must be known in advance. For the samplecase here, the lter trans er unction has a 50-dB loss at the lowestnotch, so the demand level must be at least 50 dB lower than themaximum achievable output voltage. For a controller with a 10V maximum, we choose a demand level o 0.01 V peak , or 60 dB

below the maximum.Figure 25 illustrates a swept-sine test using a constant-amplitude

0.01 Vpeak demand . Note that drive signal swings o 119 dB areclearly evident.

ConclusionsEight tests o various aspects o controller dynamic range have

been demonstrated and discussed. The two-tone input and single-tone output tests, while use ul or measuring harmonic distortion,

were demonstrated to be poor measures o dynamic range. Theirresults depend more on the length o the FFT used or analysisthan on the actual dynamic range o the device. The e ective-bitstest was also presented. While di cult to per orm, this test doesgive a good measure o the systems signal-to-noise ratio.

The use o a closed-loop, random-control challenge lter thatsimulates a lightly-damped system was also discussed. This testwas shown to be prone to incorrect evaluation unless the resultsare veri ed independent o the controllers display. It also providesan inaccurate and infated measure o the dynamic range o the sys-tem. This test is use ul or exercising the control loop in a realisticmanner and is a good test o the line resolution o the controller.However, the dynamic range numbers given by this test can be morethan 10 dB greater than the true dynamic range o the system, so


9/920

Figure 25. VR 8500 control and drive signals during a swept-sine test.

Figure 24. A 13,000-line trans er unction o challenge flter shows morethan 105 dB o dynamic range; corresponding coherence unction indicatesan extremely clean measurement.

this test should not be used as a measure o dynamic range.Three loop-back tests were discussed; these test controller input

and output simultaneously without requiring any external equip-ment. These three tests are simple to per orm, and they combine togive good insight into the true capabilities o the controller.

Importantly, the limits o a controller are determined by themaximum signal level, the noise foor, and the harmonic distortioncharacteristics o the system. The various measures o dynamicrange will depend on these characteristics, but as shown here,dynamic range measurements can vary widely depending on howit is measured, and who is doing the measurement. Because o this, comparing controllers using dynamic range numbers is di -

cult at best. For unbiased comparisons, it is better to compare themaximum signal level, the noise foor, and the harmonic distortioncharacteristics o the systems.

BibliographyIEEE Std. 1057-1994 (R2001), IEEE Standard or Digitizing Wave orm

Recorders, January 30, 2001.IEST-RP-DTE009.1, Vibration Shaker System Selection, October 1997.Lang, G. F., Understanding E ective Bits, Catalog 1990 , pp. IV-59 to 63,

LeCroy Corporation, 1990.Lang, G. F., Quantization Noise in A/D Converters and National Elections,

Sound and Vibration , November 2000.E ective-Bits Testing Evaluates Dynamic Per ormance o Digitizing Instru-

ments, Tektronix, 2006.Keller, A. C., A straight orward Way to Measure Control System Dynamic

Range, Spectral Dynamics Corporation, 2004.TN 002: Control Dynamic Range, LDS-Dactron, 2005.

The author may be reached at: [email protected] ; [email protected] .

The Vibration Research 8500 is a modern, cost-e ective,shaker controller providing superior dynamic range. It mates 24-

bit A/D and D/A converters with a foating-point digital signalprocessor (DSP). All input channels are ICP-capable with 24-voltsensor compliance voltage. Each input can be selected to be sin-gle-ended or di erential; all inputs have galvanic isolation andare IEEE TEDS capable. The Ethernet inter ace is trans ormercoupled rom the host PC, breaking potential ground loops andcan unction through a low-cost USB converter, i required. Caregiven to important analog considerations including potentialsources o ground loops, power-supply ltering, power-planelayout, ground-plane protection and digital/analog cross-talksuppression is evident throughout this design.

The compact 8500 chassis provides our input channels,drive and COLA outputs (all o 10 V span). It also provideseight low- requency analog (10 V, 12-bit) rear-panel inputs(can be con gured to accept logic signals) and eight rear-panelprogrammable logic output signals. Units may be stacked, andup to eight can be integrated into a single 32-channel system.Sine and random control to 20,000 Hz are supported (restrictedto 4 kHz or license- ree export) and up to 13,000 lines o ran-dom-control resolution are provided.

The so tware is modular, acilitating simple eld upgrades.Sine, Random or Shock control are included at initial purchase.Add exclusive Kurtosion TM to per orm random tests with morerealistically damaging (non-Gaussian) amplitude distributions.Update with Sine-on-Random and/or Random-on-Random con-trol or more sophisticated pro les and simulations. Chose theVR, industry-standard, Field Data Replication to shake in thelab with eld-recorded responses. Add the Wave orm Recordermodule and use the 8500 and a laptop as an instrument-gradedigital recorder in the eld. Augment your so tware with thenew MEscopeVES TM inter ace and use the 8500 or modal test-

ing and related activities.The user inter ace is intuitive, with a real shaker-lab workunderstood here mind-set. It provides productivity eatures thatlet the new user get right to work. These include a linked libraryproviding all required shaker parameters, a generous collectiono classic test pro les with all controller settings optimizedand on-line help with context-sensitive entry. Experienced userswill use the web inter ace to access and/or store libraries o testreports and data, or to operate the controller rom a remote loca-tion. The 8500 can send you an e-mail when a running test doessomething you need to know about. You can let the controllerautomatically generate a complete report at each test end usingyour company-designed report template. Keep it simple, or letit expand to the extreme limits o your companys in ormationin rastructure. This is a tool that will grow with you, but it willlet you set the pace.

A Multi-Function Shaker Controller/Analyzer

examining dynamic range

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