Harmonic Distortion by Richard C. Heyser (Feb. 1976)

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by Richard C. Heyser

ONE TYPE of distortion a loudspeaker system can produce is the generation of extraneous harmonics when the system is driven by a single sustained tone. Thus, if a speaker drive signal consisting of a perfectly pure tone with no musical partials is reproduced with tonal harmonics in addition to the pure tone, then harmonic distortion has occurred. Since we are concerned with a sustained tone, the distortion components will consist of whole number harmonics of the fundamental pitch, that is the second, third, etc. harmonics of the fundamental pitch.

It is our belief that readers of Audio can relate more easily to musically based tones in distortion measurements than to test frequencies which might have a technical but non-musical basis. For that reason, we use test frequencies based upon the musical scale.

The test tones for these measurements were chosen with some care. First, the number of tones needed to be limited to keep the data from overwhelming the interpretation of performance. Second, it was decided that the span of the tones should encompass not only the usual range of fundamental notes produced by musical instruments, but also be placed to show possible speaker problems. Finally, the harmonic structure to be measured needed to be meaningfully related to both musical experience and to conventional speaker problems.

The three tones Bally chosen were E1 or 41.2 Hz, A2 or 110 Hz, and A4 or 440 Hz. E1 was chosen to represent the lowest fundamental one might generally find in music. The note is also near or below the low frequency cutoff of even the largest reproducing systems we might be called upon to test.

A2, in the octave below middle C, was chosen for its tonal position at the transition point one might conceive between bass and middle tones, as well as the fact that even the smallest systems should be able to reproduce it.

A4, a fundamental note for many instruments and vocalists, was chosen not only for its musical significance, but also because it is in the range where many speaker systems are in crossover or where the bass driver is running out of steam.

In those instances where the crossover is below 500 Hz, we replace A4 with a musical tone approximately a half octave below the actual crossover frequency.

Another reason for choosing these three frequencies is that the significant harmonics fill up the frequency range between the three chosen tones without overlap. In analysis of this measurement, the harmonics or distortion terms which are significant are the second harmonic (the same tone in the next higher octave) and the third harmonic (the fifth in the next octave). Fourth and higher harmonics are rarely of any significance when the speaker is driven within the maker's recommendations. When these harmonics do occur, they show up as an audible breakup or knocking, which usually signifies mechanical problems.

Measurement Scales

Harmonic distortion is measured in percent (%). The fundamental's level is defined as 100 percent at each point of our measurement, and the distortion component is given as a percentage of this level.

This percentage measurement of harmonic distortion can be related to musical experience in the following manner.

In an out-of-doors situation, the sound pressure will halve each time you double your distance to a source. If, for example, you were ten feet from a soloist and stepped back to twenty feet, the direct sound would be reduced by 6 dB. This would take a 100 per cent value at ten feet and reduce it to 50 percent at twenty feet. If you stepped back to forty feet , the reduction would be another 6 dB to produce a 12 dB pressure drop, or a change to 25 percent of the original ten foot level.

If you divide the harmonic percentage value into 100 this gives the distance you must move away to hear that level of sound. Ten per cent is a distance of 10 times, or 100 feet for our example where 10 feet was 100 per cent. This simplified analysis assumes free-field conditions for the direct sound and is a reasonable rule of thumb for those who would be able to relate this to out-doors concerts.

Thus a twenty percent third harmonic distortion of A2 could be musically equated to listening to two instruments.

One instrument is playing a pure A2 and is at a given subjective distance. The second instrument, representing the distortion, is playing the musical fifth in the next octave and is at an open air distance five times that of the fundamental instrument with respect to you.

The musical effect of the second or phantom instrument may not be great. In fact, the harmonic distortion of this type can subjectively enrich an otherwise dull sine wave. Beware, however, of the error of assuming that if the effect is benign for a sine wave, that it will be similarly all right for a complex musical tone. Complex musical tones are themselves composed of harmonics, and they may have that structure of harmonics altered because each harmonic in the original tone can act as an equivalent fundamental and produce additional distortion products. The result is not necessarily musically correct.

Harmonic distortion is also measured as a function of amplifier power. Each of the three fundamental tones we measure has its pressure for that value of power converted to the equivalent one-meter on-axis sound pressure level, and this is why each fundamental has a separate horizontal SPL scale.

The reason we do this is to give you a measure of the amount of relative distortion to be expected for wide-range program material that hasn't been modified by the use of tone controls. This lets you determine how loud you may play music for an acceptable distortion level and shows the amount of amplifier power demanded at that sound level. It also lets you see how much distortion can be expected if you equalize the speaker for "flat" amplitude.

Test Procedure

The actual method of measurement of harmonic distortion performed by Audio is a bit different from conventional methods. A narrow-bandwidth, Wiener matched filter is used, and it has been optimized for slightly less than a one-second time measurement. This filter has its center frequency of acceptance phase-locked to the appropriate harmonic of the actual sine-wave signal used to drive the speaker. A transmit attenuator, which is stepped in 2-dB increments, feeds the fundamental to the power amplifier used in the test. A receive attenuator, which compensates exactly relative to the transmit attenuator, reduces the microphone signal. In this way, the received level into the Weiner filter remains constant throughout the measurement.

When a measurement is to be made, the filter is "enabled" and a 980 millisecond burst of the fundamental is fed to the amplifier. At the end of this period, the transmit power is clocked off and the output of the filter transferred to a memory circuit. An X-Y plotter, which produces the original of the graph shown in the reviews, is programmed to draw a straight line between the previous distortion-versus-power value to the new distortion-versus-power value of the measurement just completed.

During the measurement, several precautionary techniques are used. First, an oscilloscope is used to view the normalized speaker output signal, which is also listened to over an auxiliary speaker system. This is done to discover rattles, buzzes, or other mechanical problems, which would indicate that the maximum safe power limit has been reached. The short power burst was chosen to prevent speaker damage, since sustained high power levels can soon char even the most robust speaker. As an additional precautionary measure, automatic equipment measures the instantaneous volt-amperes and the accumulated watt-seconds of energy and will quickly terminate a measurement if predetermined safe limits are exceeded.

One side benefit of these precautionary measures is that every power measurement is started from the same operating temperature. This has disclosed that some speakers "settle into" a tone burst within an acoustically significant period of time. The implication is that harmonic distortion in some speakers is a function of time as well as drive power.

This will be pointed out in reviews when it appears to be sonically significant.

The measuring microphone is placed in close proximity to the transducer under test. This is done to guarantee that polar response patterns will not give erroneous distortion readings.

What It Means

The first thing to keep in mind about these harmonic distortion measurements is that the magnitude of distortion is much higher for speakers than for amplifiers. Harmonic distortion in a speaker may be a thousand times greater at a robust sound level than in the amplifier driving that speaker.

The reason for this disparity in the magnitude of distortion and the relative "listenability" of speakers, amplifiers, and the other parts of the reproducing chain is a research subject much too deep to go into here. The basic point to remember is that the high percentage values of harmonic distortion for speakers relative to amplifiers is normal. However, do not assume that you cannot tell the difference between a good and a bad amplifier simply because the speaker through which you're listening to the two amplifiers has relatively higher distortion measurements. The differences between the two amps will be audible in most cases.

When checking the harmonic distortion graphs, note if the distortion increases smoothly with power level since deviations from a smooth curve can tell you a great deal. A nonlinear suspension is generally indicated by a second harmonic which is moderately high at lower power levels, say 1 per cent at 0.1 watt, and rises very slowly with increased power. Quite often some of these curves will actually drop with increasing drive level over a substantial range. In such a case, a second nonlinearity, such as an off-center voice coil, may become prominent at higher drive levels and cause a rapid rise of distortion. When this occurs in the lowest register, the sound is often muddy in tonal balance.

While generalities are of course hazardous, it can be stated that a distortion curve which does not rise smoothly with increasing drive level tends to invert the subjective ordering of the ways sounds behave when we hear them naturally. Such a distortion is perceived as something that's different or odd about the reproduced sound, but something you can't quite put your finger on.

Harmonic distortion will generally be higher for E1 than for A2 or A4. Usually, though not always, this will be because of greater cone excursion. If the distortion level rises smoothly with increases in power, then abruptly increases, the problem is probably due to cone motion. In the case of third harmonic increases, the voice coil may be running out of the linear region of the magnet structure. The sound in this case will be mushy and may subjectively appear louder than it actually is.

In all cases, the harmonic distortion should continually drop with a decrease in drive power. If, however, the distortion levels off and stays at a moderately high level even at 0.1 watt drive, the reproduced sound will definitely be colored by distortion.

(adapted from Audio magazine; Feb. 1976)

Also see:

Speaker Tests Polar Response by Richard C. Heyser (May 1975)

IM Distortion in Speaker Systems (Mar. 1976)

Understanding S/N Ratios (Sept. 1976)

Build a Low TIM Amplifier (Feb. 1976)

Reading VU Meters (Sept. 1976)

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