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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 of magnitude greater, has often been ne-glected or not even specified because ithas been difficult to measure and inter-pret. With a basic understanding of transducer limitations, some knowledge

of 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 ways

to describe these limitations, both ob- jectively through measurements, and

subjectively 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 sounding electroacoustic 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 all

of the inaccuracies we hear. For exam-ple, people often refer to the perceived

“clarity” in a long distance telephone

call 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 to

the 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 

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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 than

harmonic 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 of sounds. 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 of distortion.

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 increasing sound pressure level.

90

dB

80

 Fig. 6  Masking threshold for a pure tone in the presence of narrow band noise centred  at1  kH z (Zwicker, 1975). For a masking tone of 100 dB SPL, the 2nd Harmonic is masked

 for levels below 70 dB and the 3rd Harmonic is masked for levels below 60 dB SPL

 A: Time Signa l

“O

 

0.5

V

0.0

-0.5

-1.0   I I I

0 5m   10m s

15m

20m

80

70

dB

60

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

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The significant difference betweenthe two loudspeakers in Fig. 10, is the

dramatic 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 not

enough to completely describe the non-linear behaviour of an electroacoustictransducer. Therefore, to detect ruband buzz it is necessary to measure

high order distortion products inde-pendent of both low order distortion

products 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

Ik

“GOOD” Speaker 

10%  _

G%THD

 

1%

HI0

HZ0

0.1%

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 diaphragm

moves closer to the electrode. Dynamicor moving-coil transducers, such as

most loudspeakers, typically have anasymmetrical magnetic field, due to

the geometry of the pole piece, causing the force on the voice coil to changewith position (Fig. 11 a). When the voice

coil is in its upper position, there isvery little of the pole piece inside it. Inits lower position, the pole piece acts as

an iron core, thus raising self-induc-tion. This alternating magnetization

of the pole piece and asymmetricalforce create self-induction distortion

and 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 asymmetrical

products, especially at low frequencies nonlinearities. A good example of how

where 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 resulting

 from 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

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nonlinearities, can be seen in Fig. 11 b

[5

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 products

should 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 very

revealing 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 clearly

objectionable, 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 dB

SPL at 1  kH z  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

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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 to

model. 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 measure

distortion 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 of how to separate out the distortion prod-ucts while at the same time simulating 

real operating conditions; Second, theproblem of getting instrumentation to

perform tests quickly and accurately.Real operating conditions vary from

application to application. For exam-ple, the spectral content and energy of 

speech is very different from that of music. 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 test

signal 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, for

example, 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 is

l Linear ?

0 Nonlinear?

. Noise ?

 Fig. 12 A Pulse and its Frequency Spectrum

HZ 20k

Multichannel Analysis 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 which

is applied. The family of curves in Fig.14a accurately represents the devicewhen the input is a sine wave. But

hearing aids are made to be used withcomplex signals such as speech ormusic. The sine result may not realis-

8

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

a more realistic test signal, is to userandom noise with a speech-shaped

spectrum 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 operating conditions, 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 of distortion 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 as

the excitation signal. Since distortionis very level dependent, using a sine

wave 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 can

be measured (Fig. 15a). Also noise willbe largely attenuated. Using a notch

filter (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 usually

entirely 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 the

electroacoustic transducer’s distortion.Because electroacoustic transducers

usually 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 difficult

to 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

  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

60

dB

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

Individual

Tracking Filters

Overall noise level

Narrow band noise

level

.

w

0  Hi  Hz  H,  H,  H,  H,  H,  Hs

20 kHz f (lin)

R?“.w9r,

 Fig. 15a Total Harmonic Distortion (THD)  measured with a “ t r a c k i ng ” filter (includes selected distortion components)

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Notice how at the higher frequencies,the measured 2nd harmonic distortion

underestimates the true 2nd  order dis-tortion due to the steep roll off which is

actually desired because of the tel-ephone line’s limited transmission

bandwidth. 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 electronic

filtering which also imposes a highand/or low frequency limit. For exam-

ple, a two-way loudspeaker system con-sisting of a low frequency woofer, a

crossover filter network, and a highfrequency tweeter (Fig. 21a).

 As can be seen in Fig. 21b,  there is anincrease in level of the 3rd harmonic

distortion 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 of the -3 difference frequency curve at the

crossover frequency of 3 kHz. Thisclearly indicates a problem with the

crossover design that might have beenoverlooked if only inspecting the 3rd

harmonic distortion. In this case, abipolar electrolytic capacitor was usedin the design and its voltage rating was

exceeded causing it to saturate.

Practical examples of Intermodu-lation Distortion (IMD)  measure-ments

Intermodulation distortion can also be

used effectively to evaluate crossoverdesigns. If a transducer is excited with

a fixed low frequency test tone, forexample near resonance to cause largediaphragm excursions, and anothertest tone that sweeps up in frequency,the resulting distortion will indicate

both 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 2nd

order IM distortion. This is quite audi-

12

r

c

 Audio Analyzer 

Ear Simulator  for Telephonometry 4165

Telephone Interface

5906/V/H  2517

 Fig. 19 Measurement setup for measurement on telephones

20

dB 0

-20

-40

-60

Send Response: dB re 1V/Pa. L RGP

r Fundamental

2 Difference Frequency

lk 2k Hz 5k  10k

 Fig. 20 Fundamental, 2nd harmonic, and -2 difference frequency distortion for a

telephone transmitter microphone. Input -6 dB Pa at the mouth simulator’s reference point (MRP),  

f -f =lOO

 Hz. LRGP is a telephone loudness rating standard

A

3rd Harmonic DistortionLow Pass Filter 

dBHigh Pass Filter 

 Actual value

Hz -

 

3rd Order Difference Frequency Distortion

dBLow Pass Filter High Pass Filter 

Measured and

actual 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,

f

and 6 (assuming 100% distortion)

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ble in the midfrequency range. If achamber music duet with a cello and a

flute 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)

80

dB

60

IM distortion is also very useful formeasuring microphone nonlinearities

(Fig. 23). Microphone distortionis very

difficult 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 is

possible to produce a constant soundpressure level versus frequency at the

microphone position. If separate testtones are fed to two separate loud-speakers, the loudspeakers’ harmonicdistortion will have no influence on the

measured intermodulation frequencycomponents. Consequently, only thedistortion of the microphones will bemeasured (Fig. 24).

0 I

10I

I

lk HZ  10k

1 OOk

O?“dll,r

 Fig. 21b Fundamental, 3rd harmonic, and -3 dif ference 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  kH z,  

fr - fz

 = 100 Hz

100

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

  Fundamental

80

dB

60

40

20

0

100 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, reducing the requirements on the loudspeakerproducing the moving tone.

-20

dB

-40

-60

-80

lk

- - - - - Spk 8:  Full-range

10k

1 OOk

^__.__

Transient Distortion

So far, all the distortion measurements

shown have been performed with oneor multiple continuous sine waves atone fixed level. As mentioned before,this is not very realistic. It would be a

lot more realistic if the distortion couldbe measured under typical transientconditions, (e.g. the snap of a snaredrum or a pizzicato passage played on

a violin). In other words, high powerbut short in duration test signal. Thisis also essential in order not to destroy

the 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

Microphone

Under Test

 Audio Analyzer 

L

 Audio Power  Amplifier WQ 0917

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

13

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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 spring region, soft clipping. As the speakerapproaches overload, high-order har-monics increase dramatically. This isvery typical of dynamic drivers (Fig.26) .

Frequency Response: Magn dB  relV/pbar

3”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 = 82.4  a

(1 bar = 10s  Pa) Hz, a2  =

 A: Time Signal

20I

I

I

I

-20

0 20m  s

40m 60m

B: Time Signal

300   I

F  Time window

200   I Pa

100

f

 Condition signal-W

0

-200

0 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 is

 performed on windowed time data.

14

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Other Distortion Test Methods

There are many other alternative dis-tortion test methods, however, most of them 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 design

problem. In addition, it becomes diffi-cult to specify the test’s excitation level

and 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.

 

0.5k

l . bk.

Hi   l i k 2: Ok

F ig. 26 Harmoni c Distortion of a dynamic loudspeaker at high output levels fr om lOO- 

110 dB  SPL at 1 meter. Test signal i s a 100 ms, 41 Hz tone burst. Measur ed in an 

anechoic chamber.

Traditional Requirements for Distortion Measurements

Distortion measurements have tradi-

tionally required complex instrumen-tation and an anechoic  chamber inorder to reduce background noise and

room 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 sweeping a clean and stable signal generatoralong with a narrow, analog tracking filter, 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 due

to uncompensated time delay (Fig. 27).The slower the sweep, the more accu-rate the results, especially at low fre-quencies where the harmonic spacing 

is 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!

Fi g 27 Traditional harmonic distortion measurement performed using an analog signal 

generator, tracking fi lter, and chart r ecorder. “Gli tches” at 200 Hz are the result of switching the tr acking f ilter 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.

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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 will

measure 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 nonlinear

response 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 dynamic

range. 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 measurements

in 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

 

dB   4

i

Reflections42-f

 

I\ 3f    S=1OHz/ms

I  

4f  

I I  I

\I  ’5f 

6f

6

II,,,  b

\

  ‘ ? O O

I

100‘ 2

I 400 500 600 f [Hz]

t, + 20 me I II   IV

 I Iw

100 200 300 400 500 600 f  W

 Fig. 29a Time Selective Measurements of Individual Harmonics

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Distortion Standards and TestMethod Comparisons

Obviously, when comparing  one manu-facturer’s distortion specifications withanother’s, both manufacturers need to

agree on the test conditions. For exam-ple, what is the percent 2nd and 3rd

order distortion versus frequency at

“normal” and “loud” listening levels forloudspeaker A and loudspeaker B? One

should 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 268

discusses 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 the

individual distortion orders are plot-ted versus the mean tone frequency,i.e. f = f,  +

f, /

 2. SMPTE discusses

how to measure IM distortion wherethe fixed low frequency tone is usuallyfrom 50 to 80 Hz and has an amplitude

four times greater than the swept tone.Most of these standards discuss

choosing 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

   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 OOHz

2

1

V

0

-1

-2

Sine: a = 1.41V,.,

IM: a, = 0.28Vpak

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 = 1OOHz

2 I

 

I

-2 \I0

  10m  \ 20m S 30m 40m

Sine: a = 1.41 Vpeak DF: a, = a, = 0,707 VWak

=.oo  VRMS

=

 0.500 VsMsW”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 Two sine waves with different amplitudes (e.g. Zntermodulation distortion,

a2=

 aJ

b) Two-tone signal consisting of two sine waves of equal amplitude (e.g. Difference Frequency distortion, az = a,)

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Conclusion

Nonlinear distortion measurementsand their interpretation can be compli-

cated by the human ear’s perception of distortion, 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 or

frequencies. Real world signals andoperating conditions will determinewhether these inherent transducernonlinearities will be excited and towhat extent. Unfortunately, real world

signals 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 di f f i -

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 order

normalized to the excitation frequencyfor a given input level and independ-ent of the passband. This is necessary

in 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. In

addition, these test methods can bemade to be insensitive to the transduc-

er’s nonflat passband  response.Maybe the difficulties in measuring 

and 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 sound

quality, 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

Transients

FFT spectrum

High order harmonic

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

Start measurement below resonance Not very audible

Narrow tracking filter

Measure above 3(f,  fJ Match peak level of single tone,tj  fi  = 80 Hz, a

= 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   d DF

2”d

 IM

Measure above 3(f,  fJ

fi

 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

 

Important to measure at differentoutput levels

 Averaging, Shaped random noiseexcitation

fi at resonance, measure above 3 fi

separate generator outputs

* Resonance refers to transducersfirst resonant frequency

Total distortion onlyBeware of S/N  problems

Needs 2 separate loudspeakers, onewith high output capability

92lw93e

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 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

[3

[4

l

  6

[7

[8

[9

o

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. Mø ller, “Swept Measurements of Harmonic, Difference Frequency, and Intermodulation

 Distortion”, 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.

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