J- JL

Audio Distortion Measurements

by Steve Temme

/ .In the never ending quest for bettersound transmission, reinforcement, andreproduction, the electronics have beenextensively analyzed for distortion. Dis-tortion in the electroacoustic transduc-ers, while typically several orders ofmagnitude greater, has often been ne-glected or not even specified because ithas been difficult to measure and inter-pret. With a basic understanding oftransducer limitations, some knowledgeof human hearing, and the applicationof different distortion test methods, elec-troacoustic transducer distortion be-comes easier to measure and assess.

Introduction

All transducers have limitations, in-cluding our ears. There are many waysto describe these limitations, both ob-jectively through measurements, andsubjectively through personal listen-ing evaluations. The goal, of course, isto correlate what we measure withwhat we hear, and so to better under-stand how the transducer works. Thisin turn should help the designer tomake better performing and soundingelectroacoustic transducers faster thanby trial and error alone.

Before looking at distortion, somefundamentals must be understood. Itis pointless to discuss nonlinear meas-urements without having first per-formed some linear measurements. Forexample, what is the transducer’s fun-damental frequency, phase, and timeresponse. These typical measurementscan tell a lot about a transducer’s per-formance and are necessary for a bet-ter understanding of its nonlinear be-haviour. But these linear measure-ments cannot completely describe allof the inaccuracies we hear. For exam-ple, people often refer to the perceived

“clarity” in a long distance telephonecall or the “transparency” in a highquality loudspeaker system. It is veryunlikely that this condition can be com-pletely explained by linear measure-ments alone. Nonlinear analysis aidedby distortion measurements is prob-ably going to be more revealing as tothe limitations which most influencethis perception.

In order to clarify why and how tomeasure distortion in electroacoustictransducers, information will be pre-sented on psychoacoustics, transducermechanisms causing distortion, dis-tortion measurements without the needfor an anechoic chamber, and stand-ards for measuring distortion. Differ-ent test methods are discussed formeasuring random, harmonic, inter-

Brüel & Kjær

modulation, difference frequency, and ephones, and hearing aids will be pre-transient distortion. Practical exam- sented. Of course, most of what is dis-ples of distortion measurements made cussed can be equally applied to distor-on loudspeakers, microphones, tel- tion measurements on other transduc-

ers, electronics, and storage medias(e.g. headphones, amplifiers, tape re-corders, etc.).

Distortion Definition

Distortion occurs whenever the input/output transfer function alters thewaveform of a signal, discounting noise,interference, and amplification or at-tenuation (Fig. 1). Distortion can bedivided into two main categories [l].

a. Linear distortion: time and fre-quency dependent characteristics ofthe amplitude and phase responseof the transfer function, e.g. anideal equalizer. This occurs with nochanges in the frequency content ofthe input signal such that one fre-quency at the input results in onlyone frequency at the output.

b. Nonlineardistortion:changesin thefrequency content of the input sig-nal such that energy is transferredfrom one frequency at the input tomore than one frequency at the out-put. Nonlinear distortion productsusually have a fixed frequency rela-tionship to the excitation frequency.This phenomena is usually level de-pendent, e.g. clipping.

For convenience, the term fundamen-tal is defined herein as the linear por-tion of the response, and distortion asthe nonlinear portion of the responseof the device under test.

Ideal linear

Distortedsine wave

4

Distortedsine wave

-1- - Outpuisignal

-I--

Inputsignal

a. Ideal b. Symmetrical c. Asymmetricalaz?n%*e

Fig. 1 Nonlinear transfer characteristics

t= Pure tone excitation frequency (f)

I n = Analyzer frequency (Distortion Order N)

-I

N

I mnnnn . . . . . . . . . . . . . . . . . .I

bFrequency

Distortion Order Definition : N’” harmonic (Hs): N x f

Fig. 2 Harmonic distortion

A: Time Signal2

I/

1

V0

-1

-20 5m 10m 15m s 20m 25m

0

-20dB-40

-60

-80

B: Freq Spectrum, Magn, RMS dB re 1 .OOOV_RMS

1 b, HP H4 H6 b HlO

0.0 0 2k 0.4k 0.6k 0.8k Hz l.Ok 1.2k920.5.52~

0

-20dB

-40

-60

-80

A: Time Signal

0 5m 10m 15m s 20m 25m

B: Freq Spectrum, Magn, RMS dB re 1 .OOOV_RMS

0.0 0.2k 0.4k 0.6k 0.8k Hz l.Ok 1.2k93”55%L

Fig. 4 Positive and Negative Peak Limited Sine wave results inOdd Order Harmonics

Fig. 3 Positive Peak Limited Sine wave results in Even OrderHarmonics

2

Distortion OrderDistortion can be broken down intoindividual even and odd order compo-nents, for example, 2nd and 3’d har-monic distortion products (Fig. 2).

Asymmetrical system nonlinearitiescause only euen order distortion prod-ucts (Fig. lc). Signals, like the positivepeak limited sine wave, limited only onthe upper half-cycle (Fig. 3), containhigher amplitude even order harmon-ics than odd order harmonics. Sym-metrical system nonlinearities causeonly odd order distortion products (Fig.lb). Signals, like the positive and nega-tive limited sine wave (Fig. 4), whichwill look like a square wave if limitedenough, contain higher amplitude oddorder harmonics than even order har-monics.

Distortion is a relative measurement,usually referenced to the linear por-tion of the output signal both in ampli-tude and frequency. For example, totalharmonic distortion (THD) is usuallydescribed as a percentage of the powersum of all the harmonics to the powersum of all the harmonics plus the fun-damental (i.e. amplitude normaliza-tion).

H, = Harmonic response ofNth harmonic.

HI = Fundamental response.

The distortion response is usually plot-ted under the corresponding excita-tion frequency of the measured funda-mental response (i.e. frequency nor-malization). For example, the 2nd har-monic of 20 Hz occurs at 40 Hz and the3’d harmonic occurs at 60 Hz (Fig. 5a).Instead of plotting the harmonic dis-tortion products at their actual meas-ured frequency (Fig. 5b), their valuesare plotted at their excitation frequency(Fig. 5c). This can lead to some difficul-ties in evaluation due to the influencethat the passband and shape of thefundamental response have on the dis-tortion responses. For example, a peakat 1 kHz in the fundamental responsewill show up as a peak in the 2nd har-monic response at l/2 the frequencyand l/3 the frequency for the 3rd har-monic response (Fig. 5c). When follow-ing this convention it is easy to misin-terpret the relative distortion level.Typically when viewing such a graphas in Fig. 5c, it is the difference in thelevel that is observed between the dis-tortion and the fundamental at a par-ticular frequency (see Fig. 5c.: 3rd Har-

dB

t-

Low freq. High freq.r o l l off Passband roll off

I_ I w

4 Excitationf levelI

i

Measuredlevel

IH I Hz H3 I

I

I, 1 , ) ,! ,,,, , , , , ,,,, 1 , , , (,,,,, I~~~-, b20 40 60 100 lk 10k 20k 40 60 kHz f

9**.350e

Fig. 5a Simplified representation of a transducer with a limited frequency range and apeak at 1 kHz. Fundamental response (HJ, 2nd harmonic (HJ and 3rd harmonic (HJ of20 Hz

dBFundamental starts here

20 40 60 100 Ik 10k 20k 40 60 kHz f9.?0351~

Fig. 5b Distortion Responses at the Actual Measured Frequencies (assuming 100%constant distortion vs. frequency)

dB

After normalization, the Fundamental and all the harmonics start here

~~~~~

I ’l 100% 3ti Harmonic1 (normalized) II II I ,~~I~~~~1 I *~1~~-~1 1 ..n....r*

20 40 60 100 333l 500 lk 10k 20k 40 60 kHz f920352C

Fig. 5c Distortion Responses frequency normalized to the Fundamental Response

monic at 20 Hz). This explains why frequency scale. Significantly differ-harmonic components can appear to ent results will be obtained if the re-be higher in level than the fundamen- sponses in Fig. 5b and 5c are used total at the low end of the frequency scale compute THD.and lower in level at the high end of the

3

Psychoacoustics

The human ear’s sensitivity to soundvaries with frequency and level.Fletcher-Munson loudness curves de-scribe this relationship. These curvesindicate that tones at the low and highfrequency end of the audio band areless audible than tones of the sameamplitude in the middle frequencyband. This also applies to distortionproducts. For example, Moir found thatharmonic distortion below 400 Hz be-came increasingly harder to detect thanharmonic distortion above 400 Hz 121.

Distortion audibility is also a func-tion of sound duration. The ear has afinite time resolution. Moir has foundthat distortion due to clipping of a 4millisecond tone burst reached about10% before it was detectable, but in-creasing the pulse length to 20 milli-seconds reduced the “just detectable”distortion point to around 0.3% [2].

Another important psychoacousticphenomena is masking. Sounds in ourenvironment rarely occur in isolationas pure tones. The study of masking isconcerned with the interaction ofsounds. Tonal masking, for instance,deals with the change in the percep-tion threshold for a particular tone inthe presence of another tone (Fig. 6).Narrow band noise is used instead of apure tone for the masking frequency inorder to reduce “beating”, low frequencymodulation, when the probe tone ap-proaches the same frequency of themasking tone. Fig. 6 indicates thatmore masking occurs for frequenciesabove the masking tone than below [3].This becomes significant when discuss-ing the audibility of different kinds ofdistortion.

In the case of harmonic distortion,the fundamental masks the 2nd har-monic component more than the 3rdharmonic and very little for the higherharmonic components. This is anotherfrequency and level dependent phe-nomena. The masking threshold wid-ens in the low and high frequency endof the audio band and with increasingsound pressure level.

90dB80

Fig. 6 Masking threshold for a pure tone in the presence of narrow band noise centred at1 kHz (Zwicker, 1975). For a masking tone of 100 dB SPL, the 2nd Harmonic is maskedfor levels below 70 dB and the 3rd Harmonic is masked for levels below 60 dB SPL

A: Time Signal

“O 0.5

V

0.0

-0.5

-1.0 1 I I I0 5m 10m s 15m 20m

80

70

dB60

50

40

30

B: Freq Spectrum, Magn, RMS dB re 20.00pPar

0 lk 2k Hi! 3k

Fig. 7 Middle C (261.63 Hz) played by a Flute

The significant difference betweenthe two loudspeakers in Fig. 10, is thedramatic rise in the level of harmonicsabove the 12th harmonic. High orderharmonics as low as 60 dB below thefundamental can be quite audible 141.This is probably in part due to the largeshift in frequency from the fundamen-tal and the region in which these highorder harmonics fall, outside the mask-ing region and typically in the ear’smost sensitive frequency range.

Notice that in the “good”loudspeaker(Fig. lOa), the total harmonic distor-tion is actually higher than that for the“bad” (Fig. l0b), buzzing loudspeaker.This is because the 2nd and 3rd har-monic components dominate in levelcompared with the high order harmon-ics. Therefore, measuring just totalharmonic distortion is clearly notenough to completely describe the non-linear behaviour of an electroacoustictransducer. Therefore, to detect ruband buzz it is necessary to measurehigh order distortion products inde-pendent of both low order distortionproducts and background noise.

A: Freq.Spectrum: Near field, dB re 4V RMS at 200 Hz

-20

dB

-40

-60

0

-20

dB

-40

-60

t

IIk

“GOOD” Speaker

10%------_----------------------

G%THD

~ 1%

HI0 HZ00.1%

I I,, I2k 3k Hz 4k 5k

,: Freq.Spectrum: Near field, dB re 4V RMS at 200 Hz

+f I “BAD” Speaker

~-__--1--_--_~_~~T”~_--_____________

lk 2k 3k Hz 4k

All electroacoustic transducers possesssome asymmetrical nonlinearities.This could be due to an asymmetricmagnetic or electric field whosestrength changes with diaphragm po-sition. Electrostatic transducers, suchas condenser microphones, are usuallypolarized with a single fixed electrode.Consequently, the electric field be-comes stronger as the diaphragmmoves closer to the electrode. Dynamicor moving-coil transducers, such asmost loudspeakers, typically have anasymmetrical magnetic field, due tothe geometry of the pole piece, causingthe force on the voice coil to changewith position (Fig. 11 a). When the voicecoil is in its upper position, there isvery little of the pole piece inside it. Inits lower position, the pole piece acts asan iron core, thus raising self-induc-tion. This alternating magnetizationof the pole piece and asymmetricalforce create self-induction distortionand hysteresis distortion.

Short-circuiting ring Voice coil Pole piece

Fig. lla cross section of a loudspeaker “motor” with a “short-circuiting ring”

Therefore, even order distortion should indicate these asymmetricalproducts, especially at low frequencies nonlinearities. A good example of howwhere the displacement is greater, a loudspeaker manufacturer reduced

10%

1%

0.1%

9Z047&

Fig. 10 Resulting spectrum for a pure tone excitation (f) at 200 Hza) Upper curve shows a distortion spectrum of a normally functioning loudspeaker.THD = 6%b) Lower curve shows a distortion spectrum containing high order harmonics resultingfrom a “rubbing” voice coil caused by a bent frame. THD = 2%

Transducer Mechanisms Causing Distortion

Unequal magneticfield lines

this kind of distortion by adding a“short-circuiting ring” to counter bal-ance some of these asymmetrical

6

nonlinearities, can be seen in Fig. 11 b[51.

All electroacoustic transducers alsopossess some symmetrical nonlineari-ties. This could be the result of physi-cal limits on the diaphragm’s displace-ment or an actual limiting circuit suchas found in telephones to prevent hear-ing damage from excessively loud sig-nals. So, odd order distortion productsshould indicate these symmetric non-linearities. For example, when a voicecoil approaches the physical excursionlimits of the motor system. Again atlow frequencies, where the displace-ment becomes greater, odd order dis-tortion products should increase (Fig.llc).

It is interesting to note that in theprocess of reducing asymmetrical dis-tortion, with the short circuiting ring,some symmetrical distortion, 3rd har-monic, was reduced as well.

Measuring the 2nd, 3rd, and higherharmonics of a transducer can be veryrevealing as to some of the design prob-lems, but as already discussed, someharmonic distortion produced by thetransducer may not be especially dis-pleasing nor audible. Third harmonicdistortion in a tweeter, for example, at10 kHz occurs at 30 kHz. Clearly, thedistortion present at 30 kHz is notaudible, but it still represents a prob-lem. So what significance should beplaced on harmonic distortion prod-ucts? How and what levels are clearlyobjectionable, and are there any otherways that distortion can be producedthat might be more objectionable?

In the hope of answering these ques-tions, different distortion test methodsneed to be discussed with respect to;How well do they simulate real operat-ing conditions? Can they be correlatedwith each other and perceived distor-tion audibility? How easyunderstand and perform?

are they to 50

90

dB

80

70

60

50

Freauencv Response: dB re 20~ Pei7.4 V Q lm

2k

eb B&K Type2012

Fig. llb 2nd Harmonic Distortion reduced by the addition of an aluminium (AL) short-circuiting ring in the woofer’s motor. Measured in an anechoic chamber at 40 cm, 104 dBSPL at 1 kHz to give the equivalent at 1 meter for 96 dB SPL. (IEC Graph Standard87263 -same 25 dB/decade as in Fig. 27 using B&K chart paper)

90

dB

80

70

60

Frequency Response: dB re 20~ Pai7,4 V @ 1 m

20 200 Hz 2k 20k

Fig. llc 3rd Harmonic Distortion with the addition of an aluminium short-circuitingring in the woofer’s motor

7

Distortion Test Methods

It is possible to make theoretical mod-els for some of the nonlinear behaviourin transducers. But, under real operat-ing conditions, transducers and theirassociated electronics also exhibit non-linearities which are very difficult tomodel. This could be distortion due toabrupt or temporal changes in the in-put/output characteristics, such asthermal effects, saturation, and me-chanical fatigue. Capacitors, inductors,springs, and dampers all possess someof these nonlinearities. Consequently,the best solution and maybe the onlysolution, in this case, is to measuredistortion with the best tools avail-able. This has always been very diffi-cult for two main reasons: First, from apractical point of view, the question ofhow to separate out the distortion prod-ucts while at the same time simulatingreal operating conditions; Second, theproblem of getting instrumentation toperform tests quickly and accurately.

Real operating conditions vary fromapplication to application. For exam-ple, the spectral content and energy ofspeech is very different from that ofmusic. Therefore, maybe different testsignals should be used for telephonetesting as compared to loudspeakersdesigned for listening to music. Mostnatural sounds including speech andmusic are continuously changing.Therefore, real world signals tend to betransient, and contain many simulta-neous frequencies like a pulse (Fig.12).

The problem is how to isolate distor-tion products from the fundamentalresponse and noise.

Random Distortion (RD)One way to isolate the distortion prod-ucts and still use a broadband testsignal is to measure the coherence be-tween the input and the output signal.This can be performed by using a twochannel signal analyzer that can meas-ure the coherent and noncoherentpower of the device under test, forexample, a hearing aid (Fig. 13).

Coherent power is the part of thedevice’s output spectrum which is lin-early related to the input, while non-coherent power is the remainder. Non-coherence can be caused by distortion,noise, leakage or resolution bias er-rors, and uncompensated group de-lays. But with careful measurementprocedure, some of these factors can beeliminated or reduced so that distor-tion is the dominant factor fornoncoherence. A more thorough de-

600m

400m

V

200m

-2OOm

-60

dB

-80

-100

-120

A: Time Signal

0.0 0.5m 1 .Om s 1.5m 2.0m

B: Freq Spectrum, Magn, RMS dB re 1 .oooV_RMS

Broad Frequency Range .

20 200

Which part isl Linear ?0 Nonlinear?. Noise ?

Fig. 12 A Pulse and its Frequency Spectrum

HZ 20k

MultichannelAnalysis System

3550

Module:Noise Spectrumand equalization

\Ear Simulator

4157

\Hearing Aidunder Test

Fig. 13 Measurement setup for S-Channel measurement on Hearing Aids

scription of this technique can be foundin reference [63.

Measurements on hearing aids withcompressor circuits are particularlydifficult to perform because they usu-ally contain a microphone, an ampli-fier with signal processing, and a loud-speaker. Their response, like the ear,

changes depending on the level andfrequency content of the signal whichis applied. The family of curves in Fig.14a accurately represents the devicewhen the input is a sine wave. Buthearing aids are made to be used withcomplex signals such as speech ormusic. The sine result may not realis-

8

tically represent this intended use.One way to measure distortion with

a more realistic test signal, is to userandom noise with a speech-shapedspectrum and measure the ratio of thenoncoherent to coherent power (Fig.14b). Notice how the shape of the re-sponse is different from the sine test inFig. 14a.

While this provides a reasonable ap-proximation of real world operatingconditions, the end result is total ran-dom distortion. Since the device undertest is simultaneously being stimu-lated across its entire frequency range,there is no way to identify the type ofdistortion at a particular frequency.

Harmonic Distortion (HD)It turns out that the simplest and mostpractical way to separate out the indi-vidual distortion components from thelinear response is to use a sine wave asthe excitation signal. Since distortionis very level dependent, using a sinewave as the test signal makes inter-preting input and output levels verystraightforward. By sweeping the sinewave, the individual harmonic distor-tion components can be measured witha tracking filter so that individual har-monic distortion versus frequency canbe measured (Fig. 15a). Also noise willbe largely attenuated. Using a notchfilter (Fig. 15b) that only attenuatesthe fundamental and measures every-thing else will include not only totalharmonic distortion but noise as well.Noise in the case of electroacoustictransducer measurements is usuallyentirely due to background noise sincetransducers inherently have no self-noise. The one noticeable exception arehearing aids which have built-in elec-tronics. Also it is common for the back-ground noise to be higher than theelectroacoustic transducer’s distortion.

Because electroacoustic transducersusually have a nonflat response with alimited frequency range as was shownin Fig. 5. results for distortion meas-urements, especially for harmonic dis-tortion can be misleading and difficultto correlate with perceived distortion.

The transducer’s fundamental re-sponse can be viewed as a linear filterwhich is independent of the transduc-er’s nonlinearities. This linear filterwill alter the shape of the distortionresponse. Consequently, this can leadto an underestimation of the true dis-tortion, especially at the transducer’shigh frequency limit, (i.e. above l/3 theupper cutoff frequency for the 3rd har-monic). This can also lead to overesti-mations of the true distortion, espe-

40

Gain

30

d B

20

-10

Frequency Response, Magn dB re 1 ,O Pa/Pa

I 50

Fig. 14a Hearing aid with a varying response due to its built-in compressor. Frequencyresponse measured with stepped sine stimulus from 50 - 90 dB input level in 2 dBincrements

80

60dB

40

20

0

Frequency Response, Magn dB re 20 UPa

100 200 500 lk 2k Hz 5k 10k

Fig. 14b Coherent and Noncoherent Power output of a hearing aid measured using a 2-channel FFT analysis. Speech-weighted noise stimulus at 70 dB input level

dB

1 L b

IndividualTracking Filters

Overall noise level

Narrow band noiselevel

. w0 Hi Hz H, H, H, H, H, Hs 20 kHz f (lin)

R?“.w9r,

Fig. 15a Total Harmonic Distortion (THD) measured with a “tracking” filter (includesselected distortion components)

cially at the lower frequency limit.When reading a distortion responsegraph, it is important to keep in mindat what frequencies are the distortionproducts actually occurring and howdoes this level compare to the level ofthe fundamental at the excitation fre-quency.

Two-Tone Interaction DistortionAn interesting alternative to harmonicdistortion is to use two test tones andmeasure intermodulation distortion.Intermodulation distortion resultswhen signals with more than one fre-quency interact to produce frequencycomponents not found in the originalsignal. In practice, system nonlineari-ties cause inter-modulation distortion(IM) to occur due to amplitude and/orfrequency modulation of the higherfrequency components by the lowerfrequency components 171.

This is a more reasonable approxi-mation of a real world signal. Meas-urements with more than two test tonesare possible, but interpreting resultsbecome unmanageable and too com-plex. Although inter-modulation dis-tortion requires two signal generators,the purity of the signal generators isnot as important as with harmonicdistortion measurements since themeasured intermodulation compo-nents do not correspond with the har-monics of the individual signal genera-tors.

This is illustrated in Fig. 16a wheretwo sine waves at 100 Hz and 800 Hzare simultaneously introduced into anonlinear system. The resulting signalcontains distortion components whichare sidebands around 800 Hz. The fre-quencies of the sidebands are equal tothe sum and difference of the upperfrequency (800 Hz) and the integermultiples of the lower frequency: 800Hz +/- 100 Hz, 800 Hz +/- 200 Hz, 800Hz +/- 300 Hz, and so on.

Difference frequency distortion (Fig.16b) is a special case of intermodula-tion distortion which only considerscomponents which are the differenceand multiples of the difference betweenthe excitation frequencies. IM distor-tion considers both sum and differencecomponents.

Distortion order is used to describethe frequency relationship of a givendistortion component to the input sig-nal. For harmonic distortion, distor-tion order is equal to the harmonicnumber. For intermodulation distor-tion and difference frequency distor-tion, distortion order is equal to thesum of the absolute value of the fre-

10

Notch Filter at Fundamental

/dB _ _ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ Overall n o i s e level

Narrow band noiselevel

0 HI Hz H3 Ha Hs b H7 HB 20 kHz f (lin)92034&

Fig. 15b THD+N measured with a “notch”filter (includes overall noise level)

f, - f2II

ft + f2III f, + 2 f2l I1 I’ I

0 100 200 300 400 500 600 700 800 900 1 k 1,l k Hz7.508441

fl

Fig. 16a Illustration of IM distortion resulting from the interaction of a 100 Hz and 800Hz input signal

f2 fl

2 f, - f,

f1 - fzI

I I! I 2 f, - f,

2 f, -2 f* I I

I ; I i’ I

I II I I

I II I I I I 1 I I I I , P0 100 200 300 400 500 600 700 800 900 lk 1,lk Hz

7.5*.%%

3

Fig. 16b Difference frequency distortion resulting from a 800 Hz and 900 Hz inputsignal

quency coefficients (Fig. 17a and b). Anegative distortion order means thatthe measured distortion componentfalls below the higher of the two testtones.

Example: -3 IMThe distortion order off, - 2fi (Fig. 16a) isI1 I - I-21 = 3rdorderdistortion product

Positive even order difference fre-quency distortion products are equiva-lent to their negative even order coun-ter parts, except that they occur atnegative frequencies and are, there-fore, not measured.

It is important to be careful not tomeasure too low in frequency wherethe measured distortion componentfalls either too close to DC or one of the

test tones. Also, it is important not toinadvertently measure at harmonicmultiples of the test tones. This willinclude unwanted harmonic distortioncomponents. A good rule of thumb is tomeasure more than N times above thefixed tone (f,) for IM distortion. For DFdistortion measure more than N timesabove the delta frequency (f, - f,). N isthe greatest absolute value of the nega-tive distortion order.

I f,: Moving tone

f,: Fixed tone

t -N -3 -2 t 2 3 N

I f2 fl Frequency

Distortion Order Definition: Pos. Nth order IM: f, + ( N - 1) fz

Neg. Nth order IM: fr - (INI- 1) f,9.?05.%*

Example: -3 DF Fig. 17a ZM distortion order definitionIf Af=f,-f,=lOOHzwhen f,= 100 Hzand f, = 200 Hzthen 2fi- lfi= 0 Hzso the frequency sweepshould start above

f, & f?: Moving tones

Since music and speech consist of manydifferent frequencies occurring simul-taneously, the distortion test signalused should also contain more thanjust one frequency. This provides anopportunity to see how the systemcauses interaction between the vari-ous frequency components. A singletone cannot be used to measure inter-action phenomena, such as a full rangetransducer might cause when repro-ducing a broadband signal. Further-more, the sum and difference compo-nents arising in two-tone interactiondistortion have no harmonic musicalrelationships and hence can be quiteannoying. The difference components,in particular, are unlikely to be maskedby the two test tones since they appearat lower frequencies, outside the effec-tive masking curve region as was shownin Fig. 6.

(- even)

-2-4 -N

. . . .

Distortion Order Definition: Neg. even N”’ order DF:

Neg. odd N’” order DF:

Pos. odd Nm order DF:

Fig. 17b DF distortion order definition

42”” Harmonic Distortion

dBA

Another advantage of two-tone in-teraction distortion measurements isthat they can be used over the entirefrequency range of the system, whereasharmonic distortion measurementsbecome meaningless when the distor-tion products approach the system’sfrequency limits.

4 2”” Order Difference Frequency Distortion

dBpjjjq\)

- 2 DF: f, - f, f, fl HZ

Practical examples of DifferenceFrequency Distortion (DFD) meas-urementsAll transducers, including our ears,have some kind of frequency limits.Even the measurement equipmentused to measure the transducer undertest has frequency limits (e.g. the Brüel& Kjær Type 4133 measurement mi-crophone rolls off above 40 kHz). So thegoal is to get the distortion componentsto fall in the passband where they arenot attenuated and can be measured(Fig. 18). For electroacoustic transduc-

Fig. 18 Harmonic distortion components are attenuated by the high frequency roll-off ofthe system, while difference frequency distortion components remain inside the passbandof the system (assuming 100% distortion)

ers, this usually corresponds to peo-ple’s hearing range, as well.

A transmit measurement on a tel-ephone is a classic example of abandlimited device (Fig. 19). The tel-ephone interface provides the desiredline loading and DC powering whilethe artificial mouth and ear simulate

(- odd) 4 4 (+ odd)

-N -5 -3 3 5 N

. . . .rl n n . . . .

bf2 f, Frequency

( y) f, - ( y) f,

real operating conditions.Note the way that the -2 difference

frequency distortion rises with fre-quency in Fig. 20. This is probably dueto the limited maximum current deliv-ered to the telephone line. Govern-ment regulations require a limit toprevent saturation or line loading.

11

Notice how at the higher frequencies,the measured 2nd harmonic distortionunderestimates the true 2nd order dis-tortion due to the steep roll off which isactually desired because of the tel-ephone line’s limited transmissionbandwidth. If one were to judge thequality of this telephone based on themeasured 2nd harmonic distortion at 5kHz, one might think that 1% (-40 dB)distortion was inaudible. But in real-ity, the 2nd order distortion as meas-ured by the -2 difference frequencywould indicate 32% (-10 dB) distortionat 5 kHz and probably is very audible.

This is true both for transducer highfrequency limitations and for electronicfiltering which also imposes a highand/or low frequency limit. For exam-ple, a two-way loudspeaker system con-sisting of a low frequency woofer, acrossover filter network, and a highfrequency tweeter (Fig. 21a).

As can be seen in Fig. 21b, there is anincrease in level of the 3rd harmonicdistortion from approximately 800-1000 Hz. This region actually corre-sponds to the crossover frequency re-gion around 3 kHz (3 x 1 kHz). Above 1kHz the 3rd harmonic is greatly attenu-ated by the crossover filter. In com-parison, notice how the 3rd order differ-ence frequency distortion increases inthe crossover frequency region. Thereis a substantial peak in the response ofthe -3 difference frequency curve at thecrossover frequency of 3 kHz. Thisclearly indicates a problem with thecrossover design that might have beenoverlooked if only inspecting the 3rdharmonic distortion. In this case, abipolar electrolytic capacitor was usedin the design and its voltage rating wasexceeded causing it to saturate.

Practical examples of Intermodu-lation Distortion (IMD) measure-mentsIntermodulation distortion can also beused effectively to evaluate crossoverdesigns. If a transducer is excited witha fixed low frequency test tone, forexample near resonance to cause largediaphragm excursions, and anothertest tone that sweeps up in frequency,the resulting distortion will indicateboth amplitude modulation distortionand Doppler frequency modulation dis-tortion. The Doppler phenomena inloudspeakers occurs when a high fre-quency source is shifted by a low fre-quency.

Look at the IM distortion for the full-range loudspeaker with its single drivertrying to reproduce the entire frequencyrange (Fig. 22). There is a lot of 2ndorder IM distortion. This is quite audi-

12

rcAudio Analyzer

Ear Simulator for Telephonometry 4165

Telephone Interface5906/V/H 2517

Fig. 19 Measurement setup for measurement on telephones

20

dB 0

-20

-40

-60

Send Response: dB re 1V/Pa. L RGPr Fundamental

2 Difference Frequency

lk 2k Hz 5k 10k

Fig. 20 Fundamental, 2nd harmonic, and -2 difference frequency distortion for atelephone transmitter microphone. Input -6 dB Pa at the mouth simulator’s referencepoint (MRP), f,-f,=lOO Hz. LRGP is a telephone loudness rating standard

A3rd Harmonic Distortion

Low Pass FilterdB

High Pass Filter

Actual value

Hz -

*3rd Order Difference Frequency Distortion

dBLow Pass Filter High Pass Filter

Measured andactual value

-3DF:2f,-f,- f2 f,b

HZ%?058&

Fig. 21a Harmonic Distortion components are attenuated by filter networks while 3rdorder difference frequency components remain the same level as the excitation frequencies,f1 and 6 (assuming 100% distortion)

ble in the midfrequency range. If achamber music duet with a cello and aflute is played through a single driver,the driver might cause the high fre-quencies of the flute signal to be modu-lated by the low frequencies of the cellosignal. Look at the 2-way loudspeakersystem, the 2nd order IM distortiondrops dramatically above the crosso-ver point. So one would expect to heartwo distinct and clear musical instru-ments being reproduced.

Frequency Response: dB re 20 pPa/2.83V@ lm (1 W into 8n)

80dB

60

IM distortion is also very useful formeasuring microphone nonlinearities(Fig. 23). Microphone distortionis verydifficult to measure because typicallythe loudspeaker used to measure themicrophone will have greater ampli-tude response irregularities and dis-tortion than the microphone. Byweighting the output signal from thegenerator with the reciprocal responseof the loudspeaker’s fundamental, it ispossible to produce a constant soundpressure level versus frequency at themicrophone position. If separate testtones are fed to two separate loud-speakers, the loudspeakers’ harmonicdistortion will have no influence on themeasured intermodulation frequencycomponents. Consequently, only thedistortion of the microphones will bemeasured (Fig. 24).

0 I10

I Ilk HZ 10k 1 OOk

O?“dll,r

Fig. 21b Fundamental, 3rd harmonic, and -3 difference frequency distortion for 2-wayhome loudspeaker system with a crossover filter network. Measured in an anechoicchamber at 1 meter for 96 dB SPL at 1 kHz, fr - fz = 100 Hz

100Frequency Response: dB re 20 pPa/2.83 V @ 1 m

/ Fundamental

80dB

60

40

20

0100 lk HZ 10k 100k

0The advantage of using the IM dis-

tortion test method as opposed to dif-ference frequency distortion testmethod to measure microphones, isthat the setup requirements are less.The physical placement of the loud-speaker producing the fixed low fre-quency tone is not critical. It can beoptimally chosen for a high sound pres-sure level at one frequency, reducingthe requirements on the loudspeakerproducing the moving tone.

-20

dB

-40

-60

-80lk

- - - - - Spk 8: Full-range10k 1 OOk ^__.__

Transient DistortionSo far, all the distortion measurementsshown have been performed with oneor multiple continuous sine waves atone fixed level. As mentioned before,this is not very realistic. It would be alot more realistic if the distortion couldbe measured under typical transientconditions, (e.g. the snap of a snaredrum or a pizzicato passage played ona violin). In other words, high powerbut short in duration test signal. Thisis also essential in order not to destroythe transducer under test which typi-cally has two power ratings, continu-ous power and short term peak power.In addition, transducer distortion isvery sensitive to power level, espe-cially as the transducer nears its physi-cal limits.

Fig. 22 2nd order IM distortion of a Full-range and a 2-way loudspeaker system.Measured in an anechoic chamber at 1 meter for 96 dB SPL at 1 kHz. Fixed frequency,L = 41.2 Hz, the amplitude of ffJ was 4 times greater than (f>

“Equalized”Sound Sources

MicrophoneUnder Test

Audio Analyzer

L Audio PowerAmplifierWQ 0917

It is possible to put a lot of short term Fig. 23 Measurement setup for distortion measurements on microphones

13

energy into a transducer without de-stroying it by using a tone burst. Byperforming a properly windowed FFTon the measured response coming fromthe transducer (i.e. not including thebeginning and the end of the tone burst,(Fig. 25), it is possible to measure theindividual distortion orders (Fig. 26)181. In fact, two different frequencytone bursts can be applied simultane-ously to look at intermodulation ef-fects under high power levels. Unfor-tunately, the trade-off of this tech-nique is the measuring time since acontinuous sine sweep cannot be used.But by looking at the lower test leveldistortion measurements made with asine sweep, the number of frequencypoints can be reduced to look at themore problematic areas.

One more thing to mention aboutthis technique is that it can also indi-cate with more detail the onset of com-pression due to physical transducerlimitations. Transducers, as do ampli-fiers, also have various forms of hardand soft clipping/compression limits(e.g. Fig. 1). Does the distortion in-crease gradually or dramatically asthe input power increases? It could, forexample, depend on whether the voicecoil is hitting the bottom of the “mo-tor”, hard clipping, or the “spider” (loud-speaker’s centering mechanism) is be-ing stretched beyond its linear springregion, soft clipping. As the speakerapproaches overload, high-order har-monics increase dramatically. This isvery typical of dynamic drivers (Fig.26).

Frequency Response: Magn dB re lV/pbar3” I I I I / I I

-20

-40

-60

-6020 200 HZ 2k 20k

Fig. 24 IM distortion produced by an unidirectional dynamic microphone used for vocals.Input 120 dB SPL at the mouth simulator’s reference point (MRP), 6 = 82.44a, (1 bar = 10s Pa)

Hz, a2 =

A: Time Signal20 I I I I

-200 20m s 40m 60m

B: Time Signal300 IF Time window y

200 I ,Pa

100f Condition signal -W

0

-2000 20m s 40m 60m

Fig. 25 a) Upper curve shows a high level Tone Burst input signal with -20 dB relativeconditioning signal to minimize ringingb) Lower curve shows the tone burst reproduced by a loudspeaker. FFT analysis isperformed on windowed time data.

14

Other Distortion Test MethodsThere are many other alternative dis-tortion test methods, however, most ofthem tend to be a compromise betweenrandom distortion and harmonic dis-tortion test methods. The more com-plex the test signal, e.g. square waves,multi-sine, etc., the more difficult itbecomes to isolate individual distor-tion orders and relate it to a designproblem. In addition, it becomes diffi-cult to specify the test’s excitation leveland compare results to other test meth-ods. Acomprehensive nonlinear analy-sis requires that the device under testbe tested across its entire frequencyrange and at different excitation levels.

L

0.5k l.bk. Hi lik 2:Ok

Fig. 26 Harmonic Distortion of a dynamic loudspeaker at high output levels from lOO-110 dB SPL at 1 meter. Test signal is a 100 ms, 41 Hz tone burst. Measured in ananechoic chamber.

Traditional Requirements for Distortion Measurements

Distortion measurements have tradi-tionally required complex instrumen-tation and an anechoic chamber inorder to reduce background noise androom reflections. Distortion productsare hopefully much lower in amplitudethan the fundamental, typically -40 to-60 dB for a home loudspeaker, andtherefore require a large dynamicmeasuring range.

Traditionally, this meant sweepinga clean and stable signal generatoralong with a narrow, analog trackingfilter, in order to reduce backgroundnoise and isolate individual harmoniccomponents. An individual sweep wasperformed for each harmonic and hadto be performed slowly to avoid thetracking filter from dropping out dueto uncompensated time delay (Fig. 27).The slower the sweep, the more accu-rate the results, especially at low fre-quencies where the harmonic spacingis so small (e.g.. 2nd harmonic of 20 Hzis at 40 Hz and requires a very narrowfilter and a long averaging time). Thisof course took a long time!

Fig 27 Traditional harmonic distortion measurement performed using an analog signalgenerator, tracking filter, and chart recorder. “Glitches” at 200 Hz are the result ofswitching the tracking filter to a wider bandwidth to decrease the measurement time

In addition, room reflections can giving an exaggeration of the distor-cause large peaks and dips in the re- tion or vice-versa (a peak or dip of 20 -sponse (on the order of +/- 20 to 30 dB). 30 dB leads to an error of1000 - 3000%).Even though distortion measurements Therefore, it is necessary to have anare relative, the excitation frequency anechoic chamber or some other tech-may be at a dip while its harmonic nique to measure the free-field re-frequency component may lie at a peak sponse.

15

Distortion Measurements Without an Anechoic Chamber

It turns out that with today’s state-of-the-art digital filters and clever meas-urement algorithms 191, it is possibleto perform stepped, discreet tone meas-urements of individual distortion or-ders in a fraction of the time that itused to take with analog equipment.

The instrumentation pictured here,automatically selects the widest per-missible bandwidth filter that willmeasure the individual distortion com-ponent while rejecting the fundamen-tal and adjacent distortion components.If the background noise is a problem,longer averaging causes the effectivefilter to become narrower to reject noise.When performing a scan, the funda-mental and all the selected distortioncomponents are measured at each stepin the scan.

If there was a way to measure theelectroacoustic transducer’s nonlinearresponse without the room reflections,it would be possible to eliminate theneed for an anechoic chamber, assum-ing a good enough signal to noise ratioto achieve the necessary dynamicrange. One way to do this is to use atime selective technique which is capa-ble of isolating individual distortioncomponents. The TSR (Time SelectiveResponse) technique, in the Brüel &Kjær 2012 Audio Analyzer (Fig. 28),which rejects background noise andreflections, can track on individual har-monics (Fig. 29a) [l0].

The small differences between theanechoic and the TSR measurementsin Fig. 29b can be traced to two mainsources: 1) voice coil heating effectswhich generally make repeatable meas-urements on dynamic loudspeakers dif-ficult, and 2) the difference infrequencyresolution of the two measurements.The anechoic measurement was per-formed in l/12 octave steps, whereasthe TSR measurement has a frequencyresolution of 250 Hz.

Fig. 28 The 2012 Audio Analyzer allows fast distortron measurements in an ordanaryroom without the need for an anechoic chamber

t, +1Oms

I/

dB 4i

Reflections 42-f \

II \

I\ I\ 3f S=1OHz/msI f \I\ 4f -

I I I I \I ’5f 6f

6 II,,, b\ ‘?OO

I100 ‘,200 ’

I )400 500 600 f [Hz]

t, + 20 me I II IV I I w100 200 300 400 500 600 f WI

Fig. 29a Time Selective Measurements of Individual Harmonics

16

Distortion Standards and TestMethod ComparisonsObviously, when comparing one manu-facturer’s distortion specifications withanother’s, both manufacturers need toagree on the test conditions. For exam-ple, what is the percent 2nd and 3rdorder distortion versus frequency at“normal” and “loud” listening levels forloudspeaker A and loudspeaker B? Oneshould not have to calculate this fromgraphs and specifications. Least of all,one should not be expected to figureout if the manufacturer has measuredthe distortion correctly.

To date, several standards commit-tees, IEC, DIN, CCIF, and SMPTE,have tried to lay down some guidelinesfor distortion measurements. IEC 268discusses how to measure and specifyharmonic and intermodulation distor-tion but not difference frequency dis-tortion. CCIF discusses how to meas-ure difference frequency distortionwhere typically Af = 80 Hz and theindividual distortion orders are plot-ted versus the mean tone frequency,i.e. f, = (f, + f,) / 2. SMPTE discusseshow to measure IM distortion wherethe fixed low frequency tone is usuallyfrom 50 to 80 Hz and has an amplitudefour times greater than the swept tone.

Most of these standards discusschoosing excitation levels that will per-mit comparison of results for differenttechniques. The excitation used dur-ing the different trials has to be suchthat the peak value of the output is thesame in order to avoid peak clipping,for example as in Fig. 30.

100

dB

80

60

40

20

0

Freauencv Response. Magn dB re 20 uPti2.83 V @ 1 m

1 - Anechoic / /

Fig. 29b Comparison of harmonic distortion measurements made on a loudspeaker in ananechoic chamber and in an ordinary room using Time Selective Response technique

A: Time Signal: IM, f2=41.2Hz, fl =I kHz, a2=4al, sine wave = 1 OOHz2

1

V

0

-1

-2

Sine: a = 1.41 V,., IM: a, = 0.28 Vpak a2 = l.l3V,.,= 1 .oo VsMs = 0.20 v,,s = 0.80 Vsp_qs

B: Time Signal: DF, f2=900Hz, fl=l kHz, a2=al, sine wave = 1OOHz2 I I I

-2 \I0 10m \ 20m S 30m 40m

Sine: a = 1.41 Vpeak DF: a, = a, = 0,707 VWak= 1 .oo VRMS = 0.500 VsMs W”R”&

Fig. 30 The total peak value of the distortion test signal must be equal in order tocompare results for different distortion test methods:a) Single sine wave (e.g. Harmonic distortion) and a Two-tone signal consisting of Twosine waves with different amplitudes (e.g. Zntermodulation distortion, a2= 4aJb) Two-tone signal consisting of two sine waves of equal amplitude (e.g. DifferenceFrequency distortion, az = a,)

17

Conclusion

Nonlinear distortion measurementsand their interpretation can be compli-cated by the human ear’s perception ofdistortion, the passband nature of elec-troacoustic transducers, and measure-ment instrumentation requirements.

From a psychoacoustics or audibil-ity point of view, what is important iswhere the distortion products fall inrelation to the excitation frequency orfrequencies. Real world signals andoperating conditions will determinewhether these inherent transducernonlinearities will be excited and towhat extent. Unfortunately, real worldsignals such as music or speech are not

well defined or easy to control withrespect to power level, frequency con-tent, and duration. This makes it diffi-cult to isolate distbrtion products.

From a designer’s and a specifica-tion point of view, what is most impor-tant is knowing the distortion ordernormalized to the excitation frequencyfor a given input level and independ-ent of the passband. This is necessaryin order to determine what mecha-nisms in the transducer cause the dis-tortion (Table 1). This requires a welldefined and easy to control test signal,i.e. a sine wave. Furthermore, two-tone interaction and tone burst distor-

tion can be used to give a reasonablecompromise between real world oper-ating conditions and perceptibility. Inaddition, these test methods can bemade to be insensitive to the transduc-er’s nonflat passband response.

Maybe the difficulties in measuringand understanding distortion meas-urements are several orders of magni-tude more difficult than fundamentalmeasurements. But the informationand insight gained on how the trans-ducer works and its affect on the soundquality, can easily justify the addedeffort. After all, everything is relative,including distortion measurements.

Transducer Distortion and Recommended Test Methods

Type of Distortion Measurement Measurement Set-up Notes

General Cases

Displacement/Low frequencylimits

Force field imbalance/offset/misalignment

Diaphragm break-up/Highfrequency limits

Compression/Output level limit

Rub & buzz

3”’ harmonic response 5

2”” harmonic response

3’d DF response

TransientsFFT spectrum

High order harmonic &

Start measurement below resonance* Beware of passband influenceNarrow tracking filter on measured results

Start measurement below resonance Not very audibleNarrow tracking filter

Measure above 3(f, - fJ Match peak level of single tone,tj - fi = 80 Hz, a1 = a2 good correlation with audibility

Tone burst > 20ms Do not include beginning orend of burst

Excitation at resonance Typically > I-I,,Near field measurement

Crossover/filter effects 3d DF

2”d IM

Measure above 3(f, - fJfi - fz = 80 Hz, al = a2

fi at resonanceMeasure above 2 fi

Indicates electrical problems andfilter effectiveness

Reveals Doppler distortion

Special Cases

Signal processing/Sourcedependent

Microphones

Table 1

Coheren/Noncoherent power

2nd and 3rd IM

I Important to measure at differentoutput levels

Averaging, Shaped random noiseexcitation

fi at resonance, measure above 3 fiseparate generator outputs

* Resonance refers to transducersfirst resonant frequency

Total distortion onlyBeware of S/N problems

Needs 2 separate loudspeakers, onewith high output capability

92lw93e

18

Acknowledgement

The author would like to thank Christopher Struck, Martin Rung, Poul Ladegaard, John Bareham, Ole Zacho Pedersen,Henrik Biering and a special thanks to Peerless for their help.

This application note is based on a paper presented at the AES 11 th International Audio Test and Measurement Conference,Portland, Oregon, U.S.A., May 31,1992.

References

[ll

El

[31

[41

El

161

[71

[81

[91

no1

Ml

N. K. Taylor, “A Survey of Audio Distortion Measurement Techniques”,tory, Report No. 129/83,1983.

ITCA Technical Development Labora-

J. Moir, “Just Detectable Distortion”, Wireless World, vol. 87, no. 1541, Feb. 1981.

W. Yost and D. Nielsen, “Fundamentals of Hearing”, Holt, CBS College Publishing, 1985.

J. Bareham, “Automatic Quality Testing of Loudspeaker Electroacoustic Performance”, Brüel & Kjær ApplicationNote, BO 0141-11,1989.

K. Thorborg, “Short-circuiting Ring”, Peerless International Newsletter, no. 3,199l.

J. Bareham, “Hearing Aid Measurements Using Dual Channel Signal Analysis”, Brüel & Kjær Application Note,1989.

C. Thomsen and H. Møller, “Swept Measurements of Harmonic, Difference Frequency, and IntermodulationDistortion”, Brüel & Kjær Application Note, no. l5-098,1975.

D. Yong-Sheng, “A Tone-Burst Method for Measuring Loudspeaker Harmonic Distortion at High Power Levels”, J.Audio Eng. Soc., vol. 33, no. 3, March 1985.

C. Struck, “An Adaptive Scan Algorithm for Fast and Accurate Response Measurements”, Preprint 3171 (T-l),presented at the AES 91st Convention-New York, Oct. 1991.

C. Struck and H. Biering, “A New Technique for Fast Response Measurements Using Linear Swept Sine Excitation”,Preprint 3038 (F-6), presented at the AES 90th Convention- Paris, Feb. 1991.

M. Callendar, “Relationship between amplitudes of harmonics and intermodulation frequencies”, ElectronicEngineering, pp. 230-232, June 1951.

19

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