Audio Distortion Measurements
by Steve Temme

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

V

J

Introduction
All transducers have limitations, in­cluding our ears. There are many ways
to describe these limitations, both ob­
jectively through measurements, andsubjectively through personal listen­ing 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
electro acoustic transducers faster t h a n
by trial and error alone.
Before looking at distortion, somefundamentals must be understood. It
is pointless to discuss nonlinear meas­
urements without having first per­formed some linear measurements. For
example, what is the transducer's fundamental frequency, phase, and time
response. These typical measurements
can tell a lot about a transducer's performance and are necessary for a better understanding of its nonlinear behaviour. But these linear measurements cannot completely describe allof the inaccuracies we hear. For exampie, people often refer to the perceived"clarity" in a long distance telephone
call or the "transparency" in a highquality loudspeaker system. It is very
unlikely that this condition can be completely explained by linear measurements alone. Nonlinear analysis aided
by distortion measurements is probably going to be more revealing as tothe limitations which most influence
this perception.

In order to clarify why and how tomeasure distortion in electroacoustic
transducers, information will be presented on psychoacoustics, transducer
mechanisms causing distortion, distortion measurements without the needfor an anechoic chamber, and standards for measuring distortion. Different test methods are discussed formeasuring random, harmonic, inter-modulation, difference frequency, andtransient distortion. Practical examples of distortion measurements madeon loudspeakers, microphones, tel-ephones, and hearing aids will be presented. Of course, most of what is discussed can be equally applied to distortion measurements on other transduc-

ers, electronics, and storage medias(e.g. headphones, amplifiers, tape recorders, etc.).

Distortion Definition
Distortion occurs whenever the input/
output transfer function alters the
waveform of a signal, discounting noise,interference, and amplification or at­
tenuation (Fig. 1). Distortion can bedivided into two main categories [1].
a. Linear distortion: time and fre­quency dependent characteristics ofthe amplitude and phase responseof the transfer function, e.g. an
ideal equalizer. This occurs with nochanges in the frequency content of
the input signal such that one fre­quency at the input results in only
one frequency at the output.
. , r ,.
,.
,
. ,,b. Nonlinear distortion: changes in 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 products
usually have a fixed frequency rela­tionship to the excitation frequency.
This phenomena is usually level de­pendent, e.g. clipping.
For convenience, the term fundamental is defined herein as the linear por­tion of the response, and distortion as
the nonlinear portion of the responseof the device under test.

Fig. 1 Nonlinear transfer characteristics

Fig. 2 Harmonic distortion

Fig. 3 Positive Peak Limited Sine wave results in Even Order
Harmonics

2

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

Distortion Order
Distortion can be broken down into
individual even and odd order compo­ndrdnents, for example, 2 and 3 har­monic distortion products (Fig. 2).
Asymmetrical system nonlinearities
cause only even order distortion products (Fig. lc). Signals, like the positive
peak limited sine wave, limited only on
the upper half-cycle (Fig. 3), containhigher amplitude even order harmon­
ics than odd order harmonics. Symmetrical system nonlinearities cause
only odd order distortion products (Fig.
lb). Signals, like the positive andnegative limited sine wave (Fig. 4), which
will look like a square wave if limited
enough contain higher amplitude odd
, , '
. .,
, ,
order harmonics than even order harmonies.
Distortion is a relative measurement,
usually referenced to the linear por­tion of the output signal both in ampli­
tude and frequency. For example, total
harmonic distortion (THD) is usuallydescribed as a percentage of the powersum of all the harmonics to the powersum of all the harmonics plus the fun­damental (i.e. amplitude normaliza­tion).
% T H D = -1 0 0 V g 2 2 + H

iHf+Hi+Hl

Fig

5a Simli ied'P f
representation of a transducer with a limited frequency
range and ardpeak at 1 kHz. Fundamental response (HJ, 2nd harmonic (HJ and 3 harmonic (HJ of
20 Hz

^-

Hi

HN = Harmonic response ofth
N harmonic.
H1 = Fundamental response.
The distortion response is usually plotted under the corresponding excitation frequency of the measured funda­
mental response (i.e. frequency nor­ndmalization). For example, the 2 har­monic of 20 Hz occurs at 40 Hz and therd
3 harmonic occurs at 60 Hz (Fig. 5a).
Instead of plotting the harmonic dis­tortion products at their actual meas­
ured frequency (Fig. 5b), their values
are 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 dis­tortion responses. For example, a peakat 1 kHz in the fundamental responsendwill show up as a peak in the 2 har­monic response at 1/2 the frequencyrdand 1/3 the frequency for the 3 har­monic response (Fig. 5c). When following 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 distortion and the fundamental at a parrd
ticular frequency (see Fig. 5c.: 3 Har-

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

Fig. 5c Distortion Responses frequency normalized to the Fundamental Responsemonic at 20 Hz). This explains why
harmonic components can appear tobe higher in level than the fundamental at the low end of the frequency scaleand lower in level at the high end of thefrequency scale. Significantly different results will be obtained if the responses in Fig. 5b and 5c are used tocompute THD.

3

Psychoacoustics
The human ear's sensitivity to soundvaries with frequency and level.
Fletcher-Munson loudness curves de­scribe this relationship. These curvesindicate that tones at the low and highfrequency end of the audio band areless audible than tones of the same
amplitude in the middle frequency
band. This also applies to distortion
products. For example, Moir found that
harmonic distortion below 400 Hz be­
came increasingly harder to detect thanharmonic distortion above 400 Hz [2].
Distortion audibility is also a func­tion of sound duration. The ear has afinite time resolution. Moir has foundthat distortion due to clipping of a 4
millisecond tone burst reached about
10% before it was detectable, but in­creasing the pulse length to 20 miiliseconds reduced the "just detectable"
distortion point to around 0.3% [21.
Another important psychoacoustic
phenomena is masking. Sounds in ourenvironment rarely occur in isolation
as 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 in
the presence of another tone (Fig. 6).
Narrow band noise is used instead of apure tone for the masking frequency inorder to reduce "beating", low frequency
modulation, when the probe tone ap­
proaches the same frequency of themasking tone. Fig. 6 indicates that
more masking occurs for frequencies
above 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,ndthe fundamental masks the 2 har­rdmonic component more than the 3harmonic and very little for the higher
harmonic components. This is anotherfrequency and level dependent phe­nomena. The masking threshold wid­
ens in the low and high frequency endof the audio band and with increasing
sound pressure level.

4^ Q Masking threshold for a pure tone in the presence of narrow band noise centred at
i kHz (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^-

7

Middle C (261.63 Hz) played by a FluteThe harmonic structure of musicalinstruments may also mask harmonic
distortion products. The amount ofmasking will vary depending on thetype of instrument and music.
For example the flute (Fig. 7) has
fewer and relatively lower harmonics
than the guitar (Fig. 8). The flute
sounds more "pure" while the guitarsounds more "rich". Consequently, har­monic distortion introduced by a loud­speaker when reproducing guitar mu­
sic will be harder to detect than when
reproducing flute music.
Some people think that vacuum tube
electronics also sound pleasingly "rich"or "warm". Their nonlinearity, typi­cally more asymmetric than symmet­
ric, occurs more gradually with level
than most transistors and results insofter clipping. Therefore, they mayndhave relatively high 2 order distor­
tion but very little high order distor­
tion. Furthermore, even order distor­tion, especially integer multiples
2,4,8,16..., coincides with perfect oc­
tave intervals on the musical scale. So
adding a certain amount of even orderdistortion to the original music signal
is generally quite tolerable and some­times even pleasant.
Odd order distortion, resulting fromsymmetrical clipping, for example, gen­erally sounds "fuzzy" and "grainy". The
human ear is not very tolerant to thiskind of distortion. In fact the harder
the clipping, the greater the number ofhigher order harmonics. At some point,
probably above the 15th harmonic,
these high frequency components be­
gin to sound separate from the funda­
mental. They become two distinct
sounds. A defective rubbing voice coilin a loudspeaker is a good example of
this.
A "rub and buzz" measurement isperformed by placing the microphonein the nearfield of the loudspeaker, as
near to the loudspeaker cone as possi­
ble, to achieve the best signal to noise
ratio (Fig. 9). The excitation frequency
should be near or at the loudspeaker's
resonant frequency and at as high alevel as possible to achieve maximum
cone excursion.

Fig. 8 Middle C (261.63 Hz) played by a classical Guitar

Fig. 9 Measurement setup for Rub and Buzz measurement on a loudspeaker

5The significant difference between
the two loudspeakers in Fig. 10, is thedramatic rise in the level of harmonics
above the 12th harmonic. High orderharmonics as low as 60 dB below thefundamental can be quite audible [4].
This is probably in part due to the large
shift 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's
most sensitive frequency range.
Notice that in the "good" loudspeaker(Fig. 10a), the total harmonic distor­
tion is actually higher t h a n t h a t for the"bad" (Fig. 10b), buzzing loudspeaker.
ndrdThis is because the 2 and 3 har­monic components dominate in levelcompared with the high order harmon­
ics. Therefore, measuring just total
harmonic distortion is clearly notenough to completely describe the non­linear behaviour of an electroacoustic
transducer. Therefore, to detect rub
and buzz it is necessary to measurehigh order distortion products inde­
pendent of both low order distortion
products and background noise.

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
All electroacoustic transducers possess
some asymmetrical nonlinearities.
This could be due to an asymmetricm a g n e t i c or electric field whosestrength changes with diaphragm po­sition. Electrostatic transducers, suchas condenser microphones, are usually
polarized with a single fixed electrode.
Consequently, the electric field be­comes stronger as t h e d i a p h r a g mmoves closer to the electrode. Dynamic
or moving-coil transducers, such as
most loudspeakers, typically have an
asymmetrical magnetic field, due tothe geometry of the pole piece, causing
the 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. In
its lower position, the pole piece acts as
an iron core, thus raising self-induc­tion. This alternating magnetizationof the pole piece and asymmetricalforce create self-induction distortionand hysteresis distortion.
Therefore, even order distortion
products, especially at low frequencies
where the displacement is greater,

6

Fig. 11a Cross section of a loudspeaker "motor" with a "short-circuiting ring"should indicate these asymmetricalnonlinearities. A good example of how
a loudspeaker manufacturer reduced

this kind of distortion by adding a"short-circuiting ring" to counter balance some of t h e s e a s y m m e t r i c a lnonlinearities, can be seen in Fig. l i b[5].
All electroacoustic transducers also
possess some symmetrical nonlineari­ties. This could be the result of physi­
cal limits on the diaphragm's displace­ment or an actual limiting circuit suchas found in telephones to prevent hear­ing damage from excessively loud sig­
nals. So, odd order distortion products
should indicate these symmetric nonlinearities. For example, when a voicecoil approaches the physical excursion
limits of the motor system. Again at
low frequencies, where the displace­ment becomes greater, odd order dis­tortion products should increase (Fig.
lie).
It is interesting to note t h a t in theprocess of reducing asymmetrical dis­tortion, with the short circuiting ring,rdsome symmetrical distortion, 3 har­monic, was reduced as well.
ndrd
Measuring the 2 , 3 , and higher
harmonics of a transducer can be verv
revealing as to some of the design prob,
. °
..
, ,.
,
lems, but as already discussed, someharmonic distortion produced by thetransducer may not be especially dis­pleasing nor audible. Third harmonic
distortion in a tweeter, for example, at
10 kHz occurs at 30 kHz. Clearly, thedistortion present at 30 kHz is not
audible, 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 t h a t distortion can be producedt h a t might be more objectionable?
In the hope of answering these ques­
tions, different distortion test methods
need 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 easy are they tounderstand and perform?

Fig. lib 2nd Harmonic Distortion reduced by the addition ofan aluminium (AL) shortcircuiting ring in the woofer's motor. Measured in an anechoic chamber at 40 cm, 104 dB
1 kHz
to
1
ter
r
f%J?
*™'*f "Pjvalent«?
™ f° ^ *?SPL. (IEC Graph Standard
87263 — same 25 dB/decade as in rig. 27 using B&K chart paper)

Fig. lie 3rd Harmonic Distortion with the addition of an aluminium short-circuiting
ring in the woofer's motor

7

Distortion Test Methods
It is possible to make theoretical mod­els for some of the nonlinear behaviour
in transducers. But, under real operat­
ing conditions, transducers and theirassociated electronics also exhibit nonlinearities which are very difficult tomodel. This could be distortion due toabrupt or temporal changes in the in­put/output characteristics, such as
thermal effects, saturation, and me­
chanical fatigue. Capacitors, inductors,
springs, and dampers all possess someof these nonlinearities. Consequently,
the best solution and maybe the only
solution, in this case, is to measure
distortion with the best tools avail­able. 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 fromapplication to application. For exam­
ple, the spectral content and energy ofspeech is very different from that ofmusic. Therefore, maybe different test
signals should be used for telephone
testing as compared to loudspeakers
designed for listening to music. Most
natural 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 fundamental
response and noise.

Fig. 12 A Pulse and its Frequency Spectrum

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 noncoherent
power of the device under test, for_ _P '°i
P i
Coherent power is the part of thedevice's output spectrum which is lin­
early related to the input, while non­coherent power is the remainder. Noncoherence can be caused by distortion,
noise, leakage or resolution bias errors, and uncompensated group delays. But with careful measurement
procedure, some of these factors can beeliminated or reduced so that distortion is t h e d o m i n a n t factor fornoncoherence. A more thorough de-

8

Fig- 13 Measurement setup for 2-Channel measurement on Hearing Aidss crip tion of this technique can be foundin reference [6].
Measurements on hearing aids withcompressor circuits are particularly
difficult to perform because they usually contain a microphone, an amplifier with signal processing, and a loudspeaker. 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 device
when 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-tically represent this intended use.
One way to measure distortion witha more realistic test signal, is to use
random noise with a speech-shaped
spectrum and measure the ratio of thenoncoherent to coherent power (Fig.
14b). Notice how the shape of the re­sponse is different from the sine test in
Fig. 14a.
While this provides a reasonable ap­
proximation of real world operating
conditions, the end result is total random distortion. Since the device under
test is simultaneously being stimu­
lated across its entire frequency range,
there is no way to identify the type of
distortion at a particular frequency.
H a r m o n i c D i s t o r t i o n (HD)It turns out t h a t the simplest and mostpractical way to separate out the indi­vidual distortion components from thelinear response is to use a sine wave as
the excitation signal Since distortion
,
j ,
.
n j
is very level dependent, using a sine
wave as the test signal makes inter­preting input and output levels verystraightforward. By sweeping the sine
wave, the individual harmonic distor­
tion components can be measured witha tracking filter so t h a t individual har­monic distortion versus frequency canbe measured (Fig. 15a). Also noise will
be largely attenuated. Using a notch
filter (Fig. 15b) t h a t only attenuates
the fundamental and measures every­
thing else will include not only total
harmonic distortion but noise as well.
Noise in the case of electroacoustic
transducer measurements is usuallyentirely due to background noise sincetransducers inherently have no self,i,.
minoise. The one noticeable exception arehearing aids which have built-in elec­
tronics. Also it is common for the back­ground noise to be higher t h a n theelectroacoustic 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 dis­tortion can be misleading and difficult
to correlate with perceived distortion.
The transducer's fundamental re­sponse can be viewed as a linear filter
which is independent of the transduc­
er's nonlinearities. This linear filter
will alter the shape of the distortion
response. Consequently, this can leadto an underestimation of the true dis­tortion, especially at the transducer's
high frequency limit, (i.e. above 1/3 therdupper cutoff frequency for the 3 harmonic). This can also lead to overestimations of the true distortion, espe-

F^S- 14a Hearing aid with a varying response due to its built-in compressor. Frequency
response measured with stepped sine stimulus from 50 - 90 dB input level in 2 dB
incrementsFi

14eren am^\' ^ l' *Noncoherent Power output of a hearing aid measured using a 2channel bb 1 analysis. Speech-weighted noise stimulus at 70 dB input levelaFig- l&~ Total Harmonic Distortion (THD) measured with a "tracking" filter (includes
selected distortion components)

9

cially at the lower frequency limit.
When reading a distortion responsegraph, it is important to keep in mind
at what frequencies are the distortion
products actually occurring and how
does this level compare to the level ofthe fundamental at the excitation frequency.
Two-Tone Interaction Distortion
An interesting alternative to harmonic
distortion is to use two test tones andmeasure intermodulation distortion.
Intermodulation distortion results
when signals with more than one frequency interact to produce frequency
components not found in the original
signal. In practice, system nonlinearities cause intermodulation distortion(IM) to occur due to amplitude and/or
frequency modulation of the higher
frequency components by the lower
frequency components [7].
This is a more reasonable approxi­
mation of a real world signal. Meas­
urements with more than two test tones
are possible, but interpreting results
become unmanageable and too com­
plex. Although intermodulation dis­tortion requires two signal generators,
the purity of the signal generators is
not as important as with harmonic
distortion measurements since themeasured intermodulation compo­
nents do not correspond with the harmonies of the individual signal generators.
This is illustrated in Fig. 16a where
two sine waves at 100 Hz and 800 Hz
are simultaneously introduced into a
nonlinear system. The resulting signal
contains distortion components which
are sidebands around 800 Hz. The fre­quencies of the sidebands are equal to
the sum and difference of the upper
frequency (800 Hz) and the integer
multiples of the lower frequency: 800
Hz +/-100 Hz, 800 Hz +/- 200 Hz, 800
Hz +/- 300 Hz, and so on.
Difference frequency distortion (Fig.
16b) is a special case of intermodula­tion distortion which only considers
components which are the difference
and multiples of the difference between
the excitation frequencies. IM distor­
tion considers both sum and differencecomponents.
Distortion order is used to describe
the frequency relationship of a given
distortion component to the input signal. For harmonic distortion, distortion order is equal to the harmonic
number. For intermodulation distortion and difference frequency distortion, distortion order is equal to thesum of the absolute value of the fre-10A/ ^ o t c h R | t e r a t Fundamental
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tig. 15b 1HD+N measured with a notch fitter (mctudes overall noise level)iuustration
Hz input signal
Fig

16a

0fIM distortion resulting from the interaction of a 100 Hz and 800

Fig. 16b Difference frequency distortion resulting from a 800 Hz and 900 Hz input
signalquency coefficients (Fig. 17a and b). A
negative distortion order means thatthe measured distortion component
falls below the higher of the two test
tones.
Example: - 3 IM
The distortion order of
fj - 2f 2 (Fig. 16a) is
111 - 1-21 = 3rd orderdistortion product

Positive even order difference frequency distortion products are equivalent to their negative even order counter parts, except that they occur at
negative frequencies and are, therefore, not measured.
It is important to be careful not tomeasure too low in frequency where
the measured distortion component
falls either too close to DC or one of thetest tones. Also, it is important not to
inadvertently measure at harmonic
multiples of the test tones. This will
include unwanted harmonic distortion
components. A good rule of thumb is tomeasure more than N times above thefixed tone (f2) for IM distortion. For DF
distortion measure more than N times
above the delta frequency (f: - f2). N is
the greatest absolute value of the nega­tive distortion order.
Example: - 3 DF
If A f = f 1 - f 2 = 1 0 0 H z
when
f2 = 100 Hz
andfx = 200 Hz
then 2f 2 -lf 1 =0 Hz
so the frequency sweep
should start above
I-3 I-100 Hz = 300 Hz
Since music and speech consist of manydifferent frequencies occurring simul­
taneously, the distortion test signal
used should also contain more thanjust one frequency. This provides anopportunity to see how the systemcauses interaction between the vari­
ous frequency components. A single
tone cannot be used to measure interaction phenomena, such as a full range
transducer might cause when repro­
ducing a broadband signal. Further­more, the sum and difference compo­
nents arising in two-tone interaction
distortion have no harmonic musicalrelationships and hence can be quiteannoying. The difference components,
in particular, are unlikely to be masked
by the two test tones since they appear
at lower frequencies, outside the effec­
tive masking curve region as was shownin Fig. 6.
Another advantage of two-tone in­teraction distortion measurements isthat they can be used over the entire
frequency range of the system, whereas
harmonic distortion measurements
become meaningless when the distor­
tion products approach the system's
frequency limits.
Practical examples of Difference
Frequency Distortion (DFD) measurements
All transducers, including our ears,
have some kind of frequency limits.
Even the measurement equipmentused to measure the transducer under
testhasfrequencylimits(e.g.theBruel& Kjaer Type 4133 measurement microphone rolls offabove 40 kHz). So thegoal is to get the distortion components
to fall in the passband where they are
not attenuated and can be measured(Fig. 18).Forelectroacoustictransduc-Fig. 17a IM distortion order definition

F

&

17h

DF

distortion order definition^ig. }g 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 peopie's hearing range, as well.
A transmit measurement on a telephone is a classic example of abandlimited device (Fig. 19). The telephone interface provides the desiredline loading and DC powering while
the artificial mouth and ear simulate

real operating conditions.
Note the way that the -2 difference
frequency distortion rises with frequencyinFig. 20. This is probably due
to the limited maximum current delivered to the telephone line. Government regulations require a limit toprevent saturation or line loading.

11

Notice how at the higher frequencies,ndthe measured 2 harmonic distortionndunderestimates the true 2 order dis­tortion due to the steep roll off which isactually desired because of the tel­ephone line's limited t r a n s m i s s i o nbandwidth. If one were to judge thequality of this telephone based on thendmeasured 2 harmonic distortion at 5
kHz, one might think t h a t 1 % (-40 dB)
distortion was inaudible. But in real­ndity, the 2 order distortion as meas­
ured by the -2 difference frequency
would indicate 32% (-10 dB) distortion
at 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 con­sisting of a low frequency woofer, acrossover filter network, and a highfrequency tweeter (Fig. 21a).
As can be seen in Fig. 21b, there is anrdincrease in level of the 3 harmonic
distortion from approximately 8001000 Hz. This region actually corre­
sponds to the crossover frequency re­gion around 3 kHz ( 3 x 1 kHz). Above 1rd
kHz the 3 harmonic is greatly attenu­
ated by the crossover filter. In com­rdparison, notice how the 3 order differ­ence frequency distortion increases in
the crossover frequency region. Thereis a substantial peak in the response of
the -3 difference frequency curve at thecrossover frequency of 3 kHz. This
clearly indicates a problem with thecrossover design t h a t might have beenrd
overlooked if only inspecting the 3harmonic distortion. In this case, abipolar electrolytic capacitor was usedin the design and its voltage rating was
exceeded causing it to saturate.
Practical e x a m p l e s of Intermodul a t i o n D i s t o r t i o n (IMD) m e a s u r e ments
Intermodulation distortion can also be
used effectively to evaluate crossoverdesigns. If a transducer is excited witha fixed low frequency test tone, forexample near resonance to cause large
diaphragm excursions, and anothertest tone t h a t sweeps up in frequency,
the resulting distortion will indicate
both amplitude modulation distortionand Doppler frequency modulation dis­tortion. The Doppler phenomena inloudspeakers occurs when a high fre­quency source is shifted by a low fre­quency.
Look at the IM distortion for the fullrange loudspeaker with its single driver
trying to reproduce the entire frequencyndrange (Fig. 22). There is a lot of 2order IM distortion. This is quite audi12

Fig

19

Measurement setup for measurement on telephones

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

Fig. 21a Harmonic Distortion components are attenuated by filter networks while 3rdorder difference frequency components remain the same level as the excitation frequencies,andfi
f2 (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 fre­quencies of the flute signal to be modu­
lated by the low frequencies of the cellosignal. Look at the 2-way loudspeakerndsystem, the 2 order IM distortion
drops dramatically above the crosso­
ver point. So one would expect to hear
two distinct and clear musical instru­
ments being reproduced.
IM distortion is also very useful formeasuring microphone nonlinearities(Fig. 23). Microphone distortion is very
difficult to measure because typicallythe loudspeaker used to measure themicrophone will have greater ampli­
tude response irregularities and dis­t o r t i o n t h a n t h e m i c r o p h o n e . By
weighting the output signal from thegenerator with the reciprocal responseof the loudspeaker's fundamental, it ispossible to produce a constant soundpressure level versus frequency at the
microphone position. If separate test
tones are fed to two separate loud­speakers, the loudspeakers' harmonic
distortion will have no influence on themeasured intermodulation frequency
components. Consequently, only the
distortion of the microphones will bemeasured (Fig. 24).

Fig. 21b Fundamental, 3rd harmonic, and -3 difference frequency distortion for 2-way
home loudspeaker system with a crossover filter network. Measured in an anechoic
chamber at 1 meter for 96 dB SPL at 1 kHz, frf2= 100 Hz

The advantage of using the IM dis­tortion test method as opposed to dif­ference frequency d i s t o r t i o n t e s tmethod to measure microphones, isthat the setup requirements are less.
The physical placement of the loud­speaker producing the fixed low fre­quency tone is not critical. It can be
optimally chosen for a high sound pres­sure level at one frequency, reducing
the requirements on the loudspeakerproducing the moving tone.

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,
f2= 41.2 Hz, the amplitude ofif^) was 4 times greater than (fjTransient Distortion
So far, all the distortion measurements
shown have been performed with one
or multiple continuous sine waves at
one fixed level. As mentioned before,
this is not very realistic. It would be a
lot more realistic if the distortion could
be measured under typical transientconditions, (e.g. the snap of a snare
drum or a pizzicato passage played ona violin). In other words, high power
but short in duration test signal. Thisis also essential in order not to destroy
the transducer under test which typi­cally 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.
It is possible to put a lot of short term

^8- ^ Measurement setup for distortion measurements on microphones
413

energy into a transducer without de­stroying it by using a tone burst. By
performing a properly windowed FFTon the measured response coming fromthe transducer (i.e. not including the
beginning and the end ofthe tone burst,(Fig. 25), it is possible to measure theindividual distortion orders (Fig. 26)[8]. In fact, two different frequency
tone bursts can be applied simultane­
ously to look at intermodulation ef­
fects under high power levels. Unfor­
tunately, the trade-off of this tech­nique is the measuring time since a
continuous sine sweep cannot be used.
But by looking at the lower test level
distortion measurements made with asine sweep, the number of frequency
points can be reduced to look at themore problematic areas.
One more thing to mention about
this techniaue is t h a t it can also indicate with more detail the onset of compression due to physical transducer
limitations. Transducers, as do ampli­
fiers, also have various forms of hardand soft clipping/compression limits(e.g. Fig. 1). Does the distortion in­crease gradually or dramatically as
the input power increases? It could, forexample, depend on whether the voicecoil is hitting the bottom of the "mo­tor", hard clipping, or the "spider" (loud­speaker's centring mechanism) is be­
ing stretched beyond its linear spring
region, soft clipping. As the speakerapproaches overload, high-order har­monics increase dramatically. This isvery typical of dynamic drivers (Fig.
26).

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), f2 = 82.4 Hz, a2 =
4a (1 bar =1Q5Pa)*

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

14

Other D i s t o r t i o n Test M e t h o d s
There are many other alternative dis­tortion test methods, however, most ofthem tend to be a compromise between
random distortion and harmonic dis­tortion test methods. The more com­plex the test signal, e.g. square waves,multi-sine, etc., the more difficult it
becomes 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 meth­ods . A comprehensive nonlinear analy­
sis requires t h a t the device under test
be tested across its entire frequency
range and at different excitation levels.

Fig. 26 Harmonic Distortion of a dynamic loudspeaker at high output levels from 100110 dB SPL at 1 meter. Test signal is a 100 ms, 41 Hz tone burst. Measured in an
anechoic chamber.

Traditional Requirements for Distortion Measurements
Distortion measurements have tradi­tionally required complex instrumen­
tation and an anechoic chamber inorder to reduce background noise androom reflections. Distortion products
are hopefully much lower in amplitudet h a n the fundamental, typically -40 to-60 dB for a home loudspeaker, andtherefore require a large dynamic
measuring range.
Traditionally, this meant sweeping
a clean and stable signal generator
along with a narrow, analog tracking
filter, in order to reduce backgroundnoise and isolate individual harmoniccomponents. An individual sweep was
performed for each harmonic and had
to be performed slowly to avoid thetracking filter from dropping out due
to uncompensated time delay (Fig. 27).
The slower the sweep, the more accurate the results, especially at low frequencies where the harmonic spacingndis so small (e.g.. 2 harmonic of 20 Hz
is at 40 Hz and requires a very narrowfilter and a long averaging time). Thisof course took a long time!

pig 27 Traditional harmonic distortion measurement performed using an analog signal
generator, 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 cancause large peaks and dips in the response(ontheorderof+/-20 to30dB).
Even though distortion measurements
are relative, the excitation frequency
may be at a dip while its harmonicfrequency component may lie at a peakgiving an exaggeration of the distortion or vice-versa (a peak or dip of 20 30 dB leads to an error ofl 000-3000%).
Therefore, it is necessary to have ananechoic chamber or some other technique to measure the free-field response.

15

Distortion Measurements Without an Anechoic Chamber
It turns out that with today's state-ofthe-art digital filters and clever meas­
urement algorithms [9], it is possible
to perform stepped, discreet tone meas­
urements of individual distortion or­ders in a fraction of the time that it
used to take with analog equipment.
The instrumentation pictured here,
automatically selects the widest per­missible bandwidth filter t h a t willmeasure the individual distortion com­ponent while rejecting the fundamen­
tal and adj acent distortion components.
If the background noise is a problem,
longer averaging causes the effective
filter to become narrower to reject noise.
When performing a scan, the funda­
mental and all the selected distortion
components 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 ratio
to achieve t h e necessary dynamic
range. One way to do this is to use atime selective technique which is capa­
ble of isolating individual distortion
components. The TSR (Time Selective
Response) technique, in the Bruel &Kjaer 2012 Audio Analyzer (Fig. 28),
which rejects background noise andreflections, can track on individual har­monics (Fig. 29a) [10].
The small differences between theanechoic and the TSR measurements
in Fig. 29b can be traced to two main
sources: 1) voice coil heating effects
which generally make repeatable meas­
urements on dynamic loudspeakers dif­ficult, and 2) the difference in frequency
resolution of the two measurements.
The anechoic measurement was per­formed in 1/12 octave steps, whereas
the TSR measurement has a frequency
resolution of 250 Hz.

16

Fig. 28 The 2012 Audio Analyzer allows fast distortion measurements in an ordinaryroom^thout the need for an anechoic chamber

Fig. 29a Time Selective Measurements of Individual Harmonics

Distortion Standards and Test
Method ComparisonsObviously, when comparing one manu­
facturer's distortion specifications withanother's, both manufacturers need toagree on the test conditions. For exam­ndrdple, what is the percent 2 and 3order 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 measured
the distortion correctly.
To date, several standards commit­
tees, IEC, DIN, CCIF, and SMPTE,
have tried to lay down some guidelines
for distortion measurements. IEC 268
discusses how to measure and specify
harmonic and intermodulation distortion but not difference frequency distortion. CCIF discusses how to meas­
ure difference frequency distortion
where typically Af = 80 Hz and theindividual distortion orders are plot­
ted versus the mean tone frequency,
i.e. f = (f + f9) / 2. SMPTE discusses
III_L

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

how to measure IM distortion where
the fixed low frequency tone is usuallyfrom 50 to 80 Hz and has an amplitude
four times greater t h a n the swept tone.
Most of these s t a n d a r d s discusschoosing excitation levels t h a t will per­mit comparison of results for different
techniques. The excitation used dur­ing the different trials has to be sucht h a t the peak value of the output is thesame in order to avoid peak clipping,for example as in Fig. 30.

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. Intermodulation distortion, a2= 4ax)b) Two-tone signal consisting of two sine waves of equal amplitude (e.g. Difference
Frequency distortion, a2~ a2)17Conclusion
Nonlinear distortion measurements
and their interpretation can be complicated by the human ear's perception of
distortion, the passband nature of electroacoustic transducers, and measurement instrumentation requirements.
From a psychoacoustics or audibility point of view, what is important iswhere the distortion products fall in
relation to the excitation frequency orfrequencies. Real world signals andoperating conditions will determine
whether these inherent transducer
nonlinearities will be excited and towhat extent. Unfortunately, real world
signals such as music or speech are notwell defined or easy to control withrespect to power level, frequency content, and duration. This makes it difficult to isolate distortion products.
From a designer's and a specification point of view, what is most important is knowing the distortion ordernormalized to the excitation frequency
for a given input level and independent of the passband- This is necessary
in order to determine what mechanisms in the transducer cause the distortion (Table 1). This requires a welldefined and easy to control test signal,
i.e. a sine wave. Furthermore, twotone interaction and tone burst distor-

tion can be used to give a reasonable
compromise between real world operating conditions and perceptibility. In
addition, these test methods can bemade to be insensitive to the transducer's nonflat passband response.
Maybe the difficulties in measuring
and understanding distortion measurements are several orders of magnitude more difficult than fundamental
measurements. But the informationand insight gained on how the transducer works and its affect on the soundquality, can easily justify the added
effort-After all, everything is relative,
including distortion measurements.

Transducer Distortion a n d R e c o m m e n d e d Test Methods

Type of Distortion
Distortion

Measurement

Notes
Notes

Measurement Set-up
Set-upGeneral Cases
Displacement/Low frequency
frequency
limits3 rrdd harmonic response 88

Start measurement below resonance*
Narrow tracking filter
filter

Beware of passband influence
on measured results

Force field
field imbalance/offset/
imbalance/offset/
misalignment

2 n d harmonic response
response

Start measurement below resonanceNarrow tracking filter

Not very audible

Diaphragm break-up/High
break-up/High
frequency limits
limits3rrdd DF response
response

Measure above 3(fL - ff2)
2)
f2 - f2 = 80 Hz, aL = a2fiMatch peak level of single tone,
good correlation with audibility

Compression/Output level limit
limitTransientTransient 5
FFT spectrum
spectrum

Tone burst > 20ms

Do not include beginning or
end of burst

Rub & buzz

High order harmonics 55

Excitation at resonance
Near field
field measurement

Typically > H 15

Crossover/filter effects
effects3rrdd DFDF

Measure above 3(fx - f22)
fx — f2 = 80 Hz, ax = a2

Indicates electrical problems andfilter effectivenesseffectiveness

2

nd

IM

filterf2 at resonanceresonance
Measure above 2 ff22

Reveals Doppler distortion

SpecialI Cases
SpeciaSignal processing/Source
processing/Source
dependent

Coherent/Noncoherent power

Averaging, Shaped random noise
excitation

Total distortion only
Beware of S/N problems

Microphones

2 nd and 3 r d IM

f2 at resonance, measure above 3 ff22
Separate generator outputs
outputs

Needs 2 separate loudspeakers, onewith high output capability

5* Resonance refers to transducers
first
first resonant frequency
frequency

Table 1
Table

18

Important to measure at different
different
ouput levels

920893e920893e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 AES11 th International Audio Test and Measurement Conference,
Portland, Oregon, U.S.A., May 31,1992.

References[I]

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

Techniques", ITCA Technical Development Labora­[2]

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

[3]

W. Yost and D. Nielsen, "Fundamentals[4]

J. Bareham, "Automatic Quality Testing of Loudspeaker Electroacoustic Performance", Briiel & Kjser Applicationof Hearing", Holt, CBS College Publishing, 1985.

Note, BO 0141-11,1989.
[5]

K. Thorborg, "Short-circuiting Ring", Peerless International Newsletter, no. 3,1991.

[6]

J. Bareham, "Hearing Aid Measurements Using Dual Channel Signal Analysis", Briiel & Kjaer Application Note,
1989.
C. Thomsen and H. M0ller, "Swept Measurements of Harmonic, Difference Frequency, andIntermodulation
Distortion", Briiel & Kjser Application Note, no. 15-098,1975.

[7]

[81

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.

[9]

C. Struck, "An Adaptive Scan Algorithm for Fast and Accurate Response Measurements",
presented at the AES 91st Convention-New York, Oct. 1991.

[10]

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.

[II]

M. Callendar, "Relationship between amplitudes
Engineering, pp. 230-232, J u n e 1951.

of harmonics

and intermodulation

Preprint 3171 (T-l),frequencies",

Electronic19English BO 0385-11