Medición de distorsión

8/2/2019 Medicin de distorsin

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SECTION 8

DISTORTION MEASUREMENTS

High Speed Op Amp Distortion

High Frequency Two-Tone Generation

Using Spectrum Analyzers in High FrequencyLow Distortion Measurements

Measuring ADC Distortion using FFTs

FFT Testing

Troubleshooting the FFT Output

Analyzing the FFT Output


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SECTION 8

DISTORTION MEASURE MENTS

H I GH S P E E D O P A MP D I S TO RT I O NWa l t K e s t er

Dynam ic ra nge of an op amp m ay be defined in several wa ys. The most comm onways a re t o specify Ha rm onic Distort ion, Total H ar monic Distortion (THD), or Tota lHa rm onic Distortion Plus Noise (THD + N).

Ha rm onic distortion is measu red by applying a spectr ally pure sinewave to an opamp in a defined circuit configuration and observing the output spectrum. Theam oun t of distortion presen t in th e out put is usua lly a function of severalpar amet ers: the small- and large-signal nonlinear ity of the am plifier being tested,the amplitude a nd frequency of the input signal, th e load a pplied to the outpu t of theam plifier, th e am plifier's power su pply volta ge, printed circuit board la yout ,grounding, power supply decoupling, etc. Therefore, any distortion specification isrela tively mea ningless un less the exact t est conditions ar e specified.

Ha rmonic distortion ma y be measur ed by looking at the outpu t spectrum on aspectru m a na lyzer a nd observing th e values of th e second, third, four th , etc.,ha rmonics with r espect t o the am plitude of the fundamen ta l signa l. The value isusu ally expressed as a ra tio in %, ppm, dB, or dBc. For inst an ce, 0.0015% distortioncorr esponds to 15ppm, or 96.5dBc. The un it "dBc" simply mean s th at th eha rm onic's level is so man y dB below th e value of th e "car rier" frequency, i.e., thefundamental .

Ha rm onic distortion ma y be expressed individually for each component (usua lly onlyth e second a nd t hird ar e specified), or t hey all ma y be combined in a r oot-sum -squa re (RSS) fash ion t o give the Tota l Ha rm onic Distortion (THD). The distortioncomponent which mak es up Total Ha rm onic Distortion is usu ally calculated byta king th e root su m of th e squa res of th e first five or six ha rm onics of th efunda men ta l. In m an y practical situ at ions, however, th ere is negligible error if onlythe second and third ha rmonics a re included. This is because the RSS process causesth e higher -order ter ms t o have negligible effect on t he TH D, if th ey ar e 3 to 5 timessmaller tha n t he largest ha rmonic. For example,

010 2 00 3 2 00109 0104 01. . . . .+ = =


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DEFINITIONS OF THD AND THD + N

Figure 8.1

It is importa nt to note th at the THD m easur ement does not include noise terms,while THD + N does. The noise in the TH D + N measu rement must be integratedover the m easur ement bandwidth. In a udio applications, the bandwidth is norma llychosen t o be ar ound 100kHz. In n ar row-ban d applications, the level of th e noise maybe reduced by filtering. On t he other han d, har monics a nd int ermodulation productswhich fall within the mea surem ent ban dwidth cann ot be filtered, and t herefore ma ylimit t he system dynam ic ra nge. It should be evident t hat the THD+Nappr oximat ely equals THD if the r ms n oise over the m easur ement bandwidth issevera l times less th an the TH D, or even th e worst ha rmonic. It is worth noting thatif you k now only th e THD, you can calculat e th e THD+N fairly accur at ely using th eam plifier's voltage- an d cur ren t-noise specificat ions. (Therm al n oise ass ociat ed withth e sour ce resist an ce an d th e feedback network m ay also need to be computed). Butif th e rm s noise level is significan tly higher t ha n t he level of the h ar monics, an d youar e only given t he TH D+N specification, you can not compu te t he TH D.

Special equipmen t is often used in au dio applications for a m ore sensitivemea sur emen t of th e noise an d distortion. This is done by first u sing a ban dstop filterto remove th e fun dam ent al signal (this is to prevent overdr ive distortion in themeasu ring instr umen t). The total rm s value of all the other frequency components(ha rmonics an d noise) is then m easur ed over an appr opriate ba ndwidth. The ra tio tothe fundamental is the THD+N specification.

Audio frequency am plifiers (such a s t he OP-275) ar e optimized for low n oise an d lowdistortion within t he au dio ban dwidth (20Hz to 20kHz). In a udio applicat ions, tota lha rm onic distortion plus noise (THD+N) is usu ally measu red with specializedequipment, such as the Audio Precision System One. The output signal amplitude ismea sur ed at a given frequen cy (e.g., 1kHz); th en th e fun dam ent al signal is removedwith a ban dstop filter, an d the system mea sures t he rm s value of the remainingfrequency component s, which cont ain both h ar monics an d noise. The n oise andha rmonics ar e measu red over a bandwidth t ha t will include the h ighest h ar monics,


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usua lly about 100kHz. The measu rement is swept over t he frequency range forvar ious conditions.

THD+N r esults for t he OP -275 ar e plott ed in Figur e 8.2 as a function of frequency.The signa l level is 3V rm s, an d th e am plifier is conn ected as a un ity-gain follower.The da ta is shown for t hr ee load conditions: 600ohm , 2kohm , and 10kohm. Noticeth at a TH D+N value of 0.0008% corresponds t o 8ppm, or 102dBc. The inpu t voltagenoise of the OP -275 is typically 6nV/rt Hz @ 1kHz, a nd integra ted over a n 80kH znoise bandwidth , yields an rm s n oise level of 1.7V rms. F or a 3V rm s signal level,th e corr esponding signal-to-noise ra tio is 125dB. Becau se th e THD is consider ablygreater tha n t he n oise level, the THD component is th e primar y contr ibutor.Multiple plots with variable bandwidths can be u sed to help separat e noise an ddistortion.

THD + N FOR THE OP -275 OVER 100kHz BANDWIDTHIS DOMINATED BY DISTORTION

Figure 8.2

Now, consider th e AD797, a low noise am plifier (1nV/rt Hz) where m easu rem entequipment distortion, an d not t he a mplifier distortion, limits the measu rement . TheTHD sp ecificat ion for th e AD797 is 120dBc @ 20kH z, an d a plot is sh own in Figu re8.3. The distortion is at the limits of measurement of available equipment, and theactu al am plifier noise is even lower by 20dB. The measu rem ent wa s ma de with aspectr um ana lyzer by first filtering out the funda ment al sinewave frequency aheadof th e ana lyzer. This is to prevent overdr ive distortion in the spectr um an alyzer. Thefirst five ha rmonics were th en mea sured and combined in an RSS fashion t o get t heTHD figure. The legend on the graph indicat es tha t th e measur ement equipment"floor" is about 120dBc; hence at frequencies below 10kHz, the THD may be evenless.


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THD OF THE AD797 OP AMP SHOWS MEASUREMENT LIMITAT -120dBc, WHILE AMPLIFIER NOISE FLOOR IS AT -140dBc

(1nV/ Hz INTEGRATED OVER 100kHz BANDWIDTH)

Figure 8.3

To calculate th e AD797 noise, mu ltiply the volta ge noise spectra l density (1nV/rt Hz)

by the squa re r oot of th e measu rem ent ba ndwidth to yield th e device's rms noisefloor. For a 100kHz ban dwidth, t he n oise floor is 316nV rm s, corr esponding to asignal-to-noise ra tio of about 140dB for a 3V rm s outpu t s ignal.

Rath er t han simply examining the THD pr oduced by a single tone sinewave input , itis often useful to look a t t he dist ortion p roducts pr oduced by two tones. As sh own inFigur e 8.4, two tones will produce second an d th ird order int erm odula tion products.The examp le shows the second a nd t hird order pr oducts pr oduced by app lying twofrequencies, f 1 and f 2 , to a nonlinear device. The second order products locat ed at f 2+ f 1 and f 2 f 1 ar e located far a way from th e two tones, an d ma y be rem oved byfilterin g. The th ird order pr oducts located a t 2f 1 + f 2 and 2f 2 + f 1 ma y likewise befiltered. The th ird order pr oducts located at 2f 1 f 2 and 2f 2 f 1, however, are close

to the original tones, an d filterin g them is difficult. Third order IMD pr oducts a reespecially troublesome in multi-channel communications systems where the channelsepara tion is consta nt across th e frequency band.


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SECOND AND THIRD-ORDER INTERMODULATIONPRODUCTS FOR f 1 = 5MHz and f 2 = 6MHz

Figure 8.4

Inter modulat ion distortion pr oducts are of special interest in t he RF a rea, an d ama jor concern in th e design of radio receivers. Third-order IMD products can ma sk out sm all signals in t he pr esence of lar ger ones. Third order IMD is often specified interm s of the th ird order intercept point as sh own in F igure 8.5. Two spectra lly pur etones ar e applied to th e system. The out put signal power in a sin gle tone (in dBm) aswell as t he r elative amplitu de of th e thir d-order products (referen ced to a singletone) is plott ed as a fun ction of inpu t signa l power. If the syst em n on-linear ity isapp roxima ted by a power ser ies expan sion, th e second-order IMD amp litudesincrease 2dB for every 1dB of signal increase. Similar ly, th e th ird-order IMDam plitudes in crease 3dB for every 1dB of signal in crease. With a low level two-toneinput signal, and two data points, draw th e second an d third order IMD lines as a reshown in Figur e 8.5, becau se one point a nd a slope deter mine ea ch stra ight line.

Once the inpu t r eaches a cert ain level, however, th e out put signal begins t o soft-limit, or compr ess. But th e second a nd t hird -order inter cept lines ma y be extendedto inters ect t he extens ion of th e out put signal line. These inter sections a re called thesecond- a nd third order intercept points , respectively. The values a re u sua llyreferen ced to the outpu t power of th e device expressed in dBm. Another par am eterwhich may be of inter est is th e 1dB com pression point . This is th e point a t which theoutput signal is compressed by 1dB from the ideal input/output transfer function.This point is also shown in F igure 8.5.

I


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NTERCEPT POINTS, GAIN COMPRESSION, AND IMD

Figure 8.5

Knowing th e th ird order int ercept point allows calculation of th e appr oximat e levelof th e th ird-order IMD products a s a fun ction of outpu t signa l level. Figur e 8.6shows the t hird order inter cept value as a function of frequency for t he AD9622volta ge feedback a mplifier.


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AD9622 THIRD ORDER IMD INTERCEPTVERSUS FREQUENCY

Figure 8.6

Assume th e op am p out put signal is 5MHz and 2V peak-to-peak into a 100ohm load(50ohm source and load t erm inat ion). The voltage int o the 50ohm load is t her efore

1V peak -to-peak, corresponding to +4dBm. The value of th e th ird order int ercept a t5MHz is 36dBm. The differen ce between +36dBm an d +4dBm is 32dB. This value isth en m ultiplied by 2 to yield 64dB (th e value of th e th ird-order inter modulat ionproducts r eferen ced to th e power in a single tone). Ther efore, the int erm odula tionproducts s hould be 64dBc (dB below carr ier frequen cy), or at a level of 60dBm.Figur e 8.7 shows the gra phical ana lysis for this examp le.


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USING THE THIRD ORDER INTERCEPT POINTTO CALCULATE IMD PRODUCT FOR THE AD9622 OP AMP

Figure 8.7

H I GH F R E Q U E N C Y T WO -T ONE G E N E R AT I O N

Generat ing test signals with th e spectr al pur ity required to make low distort ion h ighfrequency measurem ents is a challenging task. A test set up for genera ting a singletone is shown in F igure 8.8. The sinewave oscillat or should ha ve low pha se noise(e.g., Marconi 2382), especially if the device un der test is an ADC, where pha se n oiseincreases t he ADC noise floor. The out put of th e oscillat or is pa ssed th rough aban dpas s (or lowpass) filter which rem oves any ha rm onics present in th e oscillatoroutpu t. The distortion should be 6dB lower th an th e desired accur acy of th emeasu rement . The 6dB atten ua tor isolates th e DUT from the outpu t of the filter.The impedance at each interface should be maint ained at 50ohms for bestperforma nce (75ohm components can be u sed, but 50ohm at tenu at ors a nd filters ar egenera lly more rea dily available). The ter mina tion resistor, R T, is selected so tha tth e pa ra llel combina tion of R T an d th e input impedance of the DUT is 50ohms.

LOW DISTORTION SINGLE-TONE GENERATOR

Figure 8.8


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Before performing the actual distortion measurement, the oscillator output shouldbe set to the corr ect frequency and am plitude. Measur e the distortion a t t he outputof the a tten uat or with th e DUT replaced by a 50ohm ter minat ion r esistor (genera llythe 50ohm input of a spectru m a nalyzer. Next, replace th e 50ohm load with R T andthe DUT. Measur e th e distortion at the DUT input a second t ime. This allows non-linear DUT loads to be identified. Non-linear DUT loads (such a s flash ADCs withsignal-dependent inpu t capa cita nce, or switched-capacitor CMOS ADCs) canintroduce distort ion a t t he DUT input.

Gener at ing two tones suita ble for I MD meas ur emen ts is even m ore difficult. A low-distortion two-tone gener at or is shown in Figur e 8.9. Two ban dpass (or lowpass)filters are required as shown. Harmonic suppression of each filter must be bettertha n th e desired measurem ent accura cy by at least 6dB. A 6dB attenu at or at theoutpu t of each filter ser ves to isolate t he filter outpu ts from each oth er a nd pr eventpossible cross-modulat ion. The outpu ts of th e att enu at ors ar e combined in a pa ssive50ohm combining net work , and t he combiner drives th e DUT. The oscillator outpu tsar e set t o th e requ ired level, and t he IMD of th e fina l out put of th e combiner is

measu red. The measur ement sh ould be made with a single term ination r esistor, andaga in with t he DUT conn ected to ident ify non-linear loads.

LOW DISTORTION TOW TONE GENERATOR

Figure 8.9

U SING S P E C T R U M A NALYZER S IN H I GH F R E Q U E N C YL OW D I S TO RT I O N M E A S U R E M E N T S

Analog spectrum analyzers are most often used to measure amplifier distortion.Most h ave 50ohm in put s, ther efore an isolat ion r esistor between th e device un der

test (DUT) and th e ana lyzer is required to simulat e DUT loads great er th an 50ohms.After adjusting the spectru m a na lyzer for ba ndwidth, sweep rat e, and sen sitivity,check it car efully for in put overdr ive. The simplest met hod is to use th e varia bleat tenu at or to introduce 10dB of at tenu at ion in th e ana lyzer input pat h. Both t hesignal an d an y har monics should be att enu at ed by a fixed am oun t (10dB, forinstan ce) as observed on th e screen of the spectr um an alyzer. If the ha rm onics ar eat tenu at ed by more tha n 10dB, then th e input a mplifier of the ana lyzer isintroducing distortion, and the sensitivity should be reduced. Many analyzers have a


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butt on on th e front pa nel for int roducing a kn own a mount of at tenu at ion whenchecking for overd rive.

MEASURING AMPLIFIER DISTORTION REQUIRESCARE TO PREVENT ANALYZER OVERDRIVE

Figure 8.10

Anoth er m eth od to minimize sensitivity to overdrive is shown in F igure 8.11. Theam plitude of the fundam enta l signa l is first m easur ed with th e notch filter switchedout. The har monics ar e measu red with the notch filter switched in. The insertionloss of th e notch filter, XdB, mu st be a dded to th e mea sur ed level of the h ar monics.


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NOTCH FILTER REMOVES THE FUNDAMENTALSIGNAL TO MINIMIZE ANALYZER OVERDRIVE

Figure 8.11

M EASURING ADC D I S TO RT I O N U SING F F T S

The speed of persona l computer s an d th e availability of suitable softwa re n ow ma kesDSP bench t esting of high s peed ADCs relatively easy. A block diagra m of a typicalDSP P C-based t est system is sh own in Figur e 8.12. In order t o perform a ny DSP

test ing, th e first r equirem ent is a h igh speed buffer memory of sufficient width an ddepth. H igh speed logic ana lyzers ma ke a convenient m emory a nd eliminat e th eneed for designing special h ar dwar e. The H P1663A is a 100MHz logic an alyzerwhich h as a simple IEE E-488 outpu t port for ea sy interfacing to a personalcompu ter . The an alyzer can be configur ed as eit her a 16-bit wide by 8k deep, or a 32-bit wide by 4k deep mem ory. This is more tha n su fficient t o test a h igh speed ADC atsample ra tes u p to 100MHz. For higher sa mple rat es, faster logic analyzers a reava ilable, but ar e fairly costly. An a ltern at ive to using a high speed logic an alyzer isto opera te th e ADC at t he desired sa mple ra te, but only clock the fina l out putregister at an even sub-mu ltiple of the sa mple clock frequen cy. This is somet imescalled decimation and is useful for relaxing memory requirements. If an FFT isperformed on the decimated output da ta, th e funda ment al input signal and its

associated harmonics will be present, but translated in frequency. Simple algorithmscan be used t o find t he locations of the signal an d its ha rm onics provided th eoriginal signal frequ ency is known.


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A SIMPLE PC-BASED TEST SYSTEM

Figure 8.12

F F T T ESTING

Easy to use mathematical software packages, such as Mathcad (available fromMat hSoft, In c., 201 Broadway, Cam bridge MA, 02139) are ava ilable to perform fastFF Ts on most 486-based P Cs. The use of a co-processor allows a 4096-point F FT t oru n in a few seconds on a 75MHz,486 PC. The entire system will run under theWindows environment and provide graphical displays of the FFT output spectrum.It can be progra mm ed to perform SNR, S/(N+D), THD, IMD, an d SFDR

computations. A simple QuickBasic program transfers the data stored in the logican alyzer int o a file in t he P C via th e IEE E-488 port (Referen ce 3, Section 16).

Pr operly understa nding of FFT fundam enta ls is necessary in order t o achievemean ingful results. The first step is t o determ ine the num ber of samples, M, in theFF T record length . In order for t he F FT to ru n pr operly, M mu st be a power of 2.The value of M determ ines th e frequ ency bin width , Delta f = f s /M. The lar ger M, th emore frequency resolution. Figure 8.13 shows the r elationship between t he aver agenoise floor of the F FT with respect t o the broadba nd qu an tizat ion n oise level. Eachtime M is doubled, th e avera ge noise in th e Delta f bandwidth decreases by 3dB.Lar ger values of M also ten d to give more repea ta ble resu lts from r un to run (seeFigur e 8.13).


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RELATIONSHIP BETWEEN AVERAGE NOISE IN FFT BINSAND BROADBAND RMS QUANTIZATION NOISE LEVEL

Figure 8.13

M va lues of 512 (for 8-bit ADCs), 2048 (for 10-bit ADCs), an d 4096 (for 12-bit ADCs)ha ve proven t o give good accur acy and repea ta bility. For extrem ely wide dyna micra nge app licat ions (such as s pectra l ana lysis) M=8192 may be desirable. It sh ould benoted tha t a veraging th e results of several F FTs will tend t o smooth out the noisefloor, but will not cha nge t he avera ge value of the floor.

In order to obtain spectrally pure r esults, the FF T data window must conta in anexact integr al n um ber of sinewave cycles as s hown in F igure 8.14. These frequen cyra tios must be precisely observed to prevent end-point discontinu ity. In a ddition, itis desirable tha t t he nu mber of sinewave cycles conta ined within t he da ta window bea pr ime number. This meth od of FF T testing is referred t o as coherent testingbecause two locked frequency synthesizers are used to insure the proper ratio(coherence) between t he sa mpling clock an d th e sinewave frequen cy. Therequirement s for coherent sampling are summ ar ized in Figure 8.15.


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FFT OF SINEWAVE HAVING INTEGRALNUMBER OF CYCLES IN WINDOW

Figure 8.14

REQUIREMENTS FOR COHERENT SAMPLING

fs = Sampling Rate

fin = Input Sinewave Frequency

M = Number of Samples in Record (Integer Power of 2)

Mc = Prime Integer Number of Cycles of Sinewave DuringRecord (Makes All Samples Unique)

Make f in / fs = Mc / M

Figure 8.15

Making the n umber of cycles within th e record a prime nu mber ensu res a unique setof sam ple points with in th e dat a window. An even num ber of cycles within t herecord length will cau se th e quan tizat ion noise energy to be concent ra ted in th e

ha rmonics of the fundamen tal (cau sing a decrease in SF DR) ra ther tha n beingra ndomly distr ibuted over t he Nyquist ba ndwidth . Figure 8.16 shows a 4096-pointFF T out put for a th eoret ically perfect 12-bit sinewa ve. The spectru m on th e left wa sma de with exactly 128 sam ples with in th e record lengt h, corr esponding to afrequency which is 1/32 tim es f s . The SFDR is 78dB. The spectr um on t he r ight wasma de with exactly 127 samples within the record, an d th e SFDR increases to 92dB.


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CHOOSING A PRIME NUMBE OF CYCLES WITHIN THEFFT RECORD LENGTH ENSURES RANDOMIZATION OF

THE QUANTIZATION NOISE (IDEAL 12-BIT ADC)

Figure 8.16

Coheren t F FT test ing ensures th at the funda ment al signal occupies one discrete linein th e outpu t spectrum . Any leakage or sm earing into adjacent bins is th e result of apert ur e jitter , phase jitter on t he sa mpling clock, or other unwa nted noise due t oimpr oper layout , grounding, or decoupling.

If the ra tio between t he sa mpling clock and th e sinewave frequ ency is such tha tther e is and endpoint discontinu ity in the data (shown in Figure 8.17), then spectra lleaka ge will occur . The discont inuit ies ar e equivalent to multiplying the sinewa veby a r ectan gular windowing pulse which ha s a sin(x)/x frequ ency response. Thediscontinu ities in t he t ime doma in result in leakage or smear ing in the frequencydomain, because many spectral terms are needed to fit the discontinuity. Because of th e endpoint discont inuity, th e FF T spectr al response shows the m ain lobe of th e

sinewave being smear ed, and a large nu mber of associat ed sidelobes which h ave th ebasic cha ra cteristics of the rectangular time pulse. This leakage mu st be m inimizedusin g a technique called windowing (or weighting ) in order to obta in usa ble resultsin non-coherent tests.


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FFT OF SINEWAVE HAVING NON-INTEGRALNUMBER OF CYCLES IN WINDOW

Figure 8.17

This situ at ion is exactly wha t occurs in r eal-world spectra l ana lysis applicationswhere t he exact frequencies being sa mpled are unk nown and uncontr ollable.Sidelobe leakage is reduced by choosing a windowing (or weighting ) function othertha n th e recta ngular window. The input time samples are m ultiplied by anapp ropriat e windowing fun ction which brings t he signa l to zero at t he edges of thewindow. The selection of an app ropriat e windowing fun ction is pr imar ily a t ra deoff between ma in-lobe spr eading an d s idelobe r olloff.

The t ime-doma in a nd frequen cy-doma in char acter istics of a simple windowingfunction (th e Ha nn ing Window) ar e shown in F igure 8.18. A compa rison of th efrequency response of the Hanning window and the more sophisticated Minimum 4-Term Blackman -Har ris window is given in F igures 8.19 and 8.20. For gener al ADCtest ing with non-coherent input frequencies, th e Ha nn ing window will givesat isfactory results . For critical spectr al an alysis or t wo-tone IMD test ing, theMinimum 4-Term Blackma n-Ha rr is window is th e better choice becau se of th eincrease in spectral resolution.


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TIME AND FREQUENCYREPRESENTATION OF THE HANNING WINDOW

Figure 8.18

FREQUENCY RESPONSE OF THE HANNING WINDOW

Figure 8.19


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FREQUENCY RESPONSE OF THEMINIMUM 4-TERM BLACKMAN-HARRIS WINDOW

Figure 8.20

The a ddition of a windowing function to th e FF T softwa re in volves first calculatin gth e proper coefficient for ea ch time sa mple within t he r ecord. These values ar e th enstored in a m emory file. Ea ch time sam ple is mu ltiplied by its app ropriat e weightin gcoefficient before perform ing th e actu al F FT. The softwa re r out ine is easy t oimplement in QuickBasic.

When an alyzing the FF T outpu t r esulting from windowing the input da ta samples,car e must be exercised in determining the energy in t he fundamen tal signal and t heener gy in t he var ious spu rious component s. For example, sidelobe energy from t hefunda ment al signa l should not be included in t he r ms n oise measur ement. Consider

th e case of th e Ha nn ing Window fun ction being us ed to test a 12-bit ADC with ath eoretical SNR of 74dB. The sidelobe att enu at ion of th e Ha nn ing Window is asfollows:

Bins Fr om SidelobeFundamen ta l At tenua t ion

2.5 32dB5.0 50dB10.0 68dB20.0 86dB

Ther efore, in calcula ting th e rms va lue of th e fun dam ent al signal, you should

include at least 20 samples on either side of the funda menta l as well as thefunda ment al itself.

If other weighting functions are used, their particular sidelobe characteristics mustbe known in order to accur at ely calculat e signal an d noise levels.


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A typical Math cad FFT outpu t plot is shown in F igure 8.21 for t he AD9022 12-bit,20MSPS ADC using th e Ha nn ing Window and a record lengt h of 4096.

MATHCAD 4096 POINT FFT OUTPUTS FORAD9022 12-BIT, 20 MSPS ADC (HANNING WEIGHTING)

Figure 8.21

The actua l QuickBasic routine for t ra nsferring the H P an alyzer's data to a DOS filein the PC a s well as the Math cad routin e ar e given in Referen ce 3, Section 16.

T ROUBLESHOOTING T H E F F T O U T P U T

Er roneous r esults are often obtained the first t ime an F FT test set up is put t ogether.The most comm on er ror is improper t iming of th e latch st robe to th e buffer m emory.The H P1663A logic an alyzer accepts pa ra llel dat a a nd a clock signal. It h as a ninter na l DAC which m ay be used t o examine a record of time sa mples. Largeglitches on the st ored waveform probably indicate t ha t th e timing of th e latch str obe

with respect to the dat a sh ould be cha nged .

After ensuring correct timing, the FFT routine should produce a reasonable spectraloutpu t. If ther e ar e large values of ha rmonics, the input signa l may be overdrivingth e ADC at one or both ends of th e ra nge. After brin ging the signal within th e ADCra nge (usu ally about 1dB below fullscale), excess h ar monic cont ent becomes moredifficult t o isolate .

Make sur e tha t t he sinewave input to the ADC is spectr ally pure. Ban dpass filtersar e usu ally required t o clean up t he outpu t of most high frequen cy oscillators,especially if wide dyna mic ra nge is expected.

After en suring th e spectr al purity of the ADC input , make sur e the da ta outpu t linesar e not coupling to either t he sa mpling clock or to the ADC ana log inpu t. Rememberthat the glitches produced on the digital lines are signal-dependent and willth erefore cont ribut e to ha rm onic distort ion if they couple int o either one of th ese twolines. As ha s been discussed pr eviously, noise or digita l modulation on th e sam plingclock can also produce ha rm onic distortion in th e FF T out put . The use of anevalua tion boar d with sepa ra te sa mpling clock and a na log inpu t conn ectors willusu ally prevent th is. The special ribbon cable used with th e logic an alyzer to capt ur e


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the ADC outpu t da ta has a cont rolled impedance an d should not cau se performa ncedegradation.

In a ddition to the a bove har dwar e checks, the F FT softwa re sh ould be verified byapplying a t heoretically perfect qua ntized sinewave to the FF T an d compar ing theresu lts t o theoretical SNR, et c. This is easy t o do using th e "roun doff" functionava ilable in m ost m at h pa ckages. The effects of windowing non-coherent input sshould also be examined before r un ning actu al ADC tests .

In performing calculations with t he FF T outpu t, the t erm a t dc and f s /2 sh ould beomitted from any calculations, as they can produce erroneous results. Inputfrequencies which a re int eger subm ultiples of th e sam pling clock can also producear tificially lar ge ha rm onics.

TROUBLESHOOTING THE FFT OUTPUT

Excess harmonic distortion:

Distortion on input signalSignal outside ADC input rangeDigital runs coupling into analog input or sampling clockPoor layout, decoupling, and groundingBuffer memory not clocked at correct timeAnalog input frequency locked to integer submultiple ofsampling clock

Excess noise floor:

Noise or phase jitter on input signalNoise or phase jitter on sampling clock

Poor layout, decoupling, and groundingEliminate dc and f s /2 FFT components from calculations

Figure 8.22

A NALYZING TH E F F T O U T P U T

Once the FF T out put is obtained, it can be a nalyzed in a num ber of ways, similar t otha t of the display on an an alog spectru m a na lyzer. The spurious free dynamicra nge (SFDR) is th e ra tio of the fundam enta l signa l to the worst frequency spur.Tota l har monic distortion (THD) is obta ined by tak ing the r at io of the signal to th erms value of the first several h ar monics (and t hen ta king the logar ithm of the ra tio).

Becau se of aliasin g, however, locating th e ha rm onics in th e frequ ency spectr um canbe difficult. For inst an ce, if a 3MH z signa l is sampled a t 10MSP S, th e secondha rmonic (6MHz) actually appears in th e FF T outpu t a t 4MHz (10MHz 6MHz).The th ird ha rm onic (9MHz) appea rs a t 1MHz (10MHz 9MHz). The four thha rm onic (12MHz) appear s at 2MHz (12MHz 10MHz). Software r outines t operform these calculations are easily written.


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Two tone inter modulat ion distort ion can be mea sur ed by applying two spectra llypur e tones t o the ADC using th e circuit pr eviously shown in F igure 8.9. The conceptof second- or t hird -order inter cept point h as litt le mean ing when t esting ADCs fortwo reasons. Fir st, th e ADC acts as a ha rd limiter for out-of-ran ge signa ls, while anam plifier soft limits. Second, a s th e am plitude of th e tones is redu ced, th e value of the signal-related frequency spurs tends to become somewhat constant because of th e discontinu ous na tu re of th e ADC tr an sfer function. A "ha rd d istortion" floor isrea ched beyond which furt her r eduction in signal am plitude ha s litt le effect on th espur levels.

Fin ally, signal-to-noise plus distortion (S/N+D) can be calcula ted by t ak ing th e ra tioof th e rms signa l amplitu de to the rm s value of all oth er spectra l component s(excluding dc and f s /2). Fr om th e S/N+D value, th e effective n um ber of bits (ENOB)can be calculat ed. In some applicat ions, th e value of S/N+D without t he h ar monicsincluded is of int erest .

Becau se of th e sta tistical nat ur e of th e FF T ana lysis, ther e will be some var iability

in the output from run to run u nder identical test conditions. The data can besta bilized by averaging th e resu lts of several FF T run s. This will not lower th eaver age noise floor of th e FF T, but will reduce the var at ion in th e result s.

ANALYZING THE FFT OUTPUT

Single-to-Noise including Distortion: S/(N+D)

Effective Number of Bits: (ENOB)

Signal-to-Noise without distortion: SNR

Spurious Free Dynamic Range: SFDR

Harmonic Distortion

Total Harmonic Distortion: THD

THD + Noise (Same as S/N + D)

Two-Tone Intermodulation Distortion

Figure 8.23


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R E F E R E N C E S

1. Rober t A. Wit te, Distortion M easurem ents Using a S pectrum An alyzer ,RF Des ign , Sept ember, 1992, pp. 75-84.

2. Walt Kest er , Confu sed About A m plifier Distortion S pecs ?, Ana logDia logue , 27-1, 1993, pp. 27-29.

3. S y s t e m A p p l ic a t i o n s G u i d e , Analog Devices, 1993, Chapter 16.

4. F reder ick J . Ha r r is, On th e Use of Wind ows for Harm onic Ana lysiswith th e Discrete Fourier Tran sform , I E E E P r o c e e d in g s , Vol. 66, N o. 1,J an . 1978, pp. 51-83.

5 . Joey Doernbe rg, Hae -Seung Lee , David A. Hodges, Full S peed T estingof A/ D Converters , I E E E J o u r n a l o f S ol id S t a t e C ir c u i t s , Vol. SC-19,No. 6, Dec. 1984, pp. 820-827.

6. Brendan Coleman, Pa t Meehan, J ohn Reidy an d Pa t Weeks, Coherent S am pling Helps When S pecifying DS P A/ D Converters , E DN , October 15,1987, pp. 145-152.

7. Rober t W. Ramierez, T h e F F T: F u n d a m e n t a ls a n d C o n c e p t s ,Pr ent ice-Ha ll, 1985.

8. R. B. Bla ckm an an d J . W. Tu key, T h e M e a s u r e m e n t o f P o w e rS p e c t r a , Dover Publications, New York, 1958.

9 . Ja mes J . Colot t i , Digi ta l Dynamic Analys is of A/D Convers ionSystems Th rough Eva lua tion Software Ba sed on F FT/DFT Ana lysis,R F E x p o E a s t 1 98 7 P r o c e e d i n g s , Cardiff Publishing Co., pp. 245-272.

10 . H P J o u r n a l , Nov. 1982, Vol. 33, No. 11.

11 . H P P r o d u c t N ot e 5180A-2.

12 . H P J o u r n a l , April 1988, Vol. 39, No. 2.

13 . H P J o u r n a l , J un e 1988, Vol. 39, No. 3.

14. Da n Sh ein gold, E dit or , Ana log - to -Dig i t a l Conve r s ion Handbook ,T h i r d E d i t i on , Pr ent ice-Ha ll, 1986.

15. W. R. Bennet t , Spect ra of Quant ized Signals, B e ll S ys t e m Te c h n i c a lJ o u r n a l , No. 27, Ju ly 1948, pp. 446-472.

16 . La wr en ce R abin er a nd B er n a r d Gold , T h e o r y a n d Ap p l ic a t i o n o f D i gi t a l S i gn a l P r o c e s s in g , Pr ent ice-Hall, 1975.


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17. Mat thew Mahoney, DSP-Based Tes t ing o f Ana log an d Mixed-S igna lC i r c u i t s , IEE E Comput er S ociety Pr ess, Washingt on, D.C., 1987.

18 . I E E E Tr i a l -U s e S t a n d a r d f o r D i gi t i zi n g Wa v e f o r m R e c o r d e r s ,No. 1057-1988.

19. Rich ar d J . H iggin s, D ig i t a l S igna l P r oces s ing in VSLI , Pren tice-Ha ll,1990.

20. M. S. Gh au si a nd K. R. La ker , M o d e r n F i l t e r D e s i g n : Ac t i v e R C a n dS w i t ch e d C a p a c i t o r s , Pr ent ice Ha ll, 1981.

21. Mathcad 4.0 software package available from MathSoft , Inc.,201 Broadway, Ca mbr idge MA, 02139.

22 . S y s t e m A p p l ic a t i o n s G u i d e , Analog Devices, 1993, Chapter 8(Audio Applications), Chapter 9.

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