IM Distortion in Speaker Systems (Mar. 1976)

by Richard C. Heyser

IF A MUSICAL tone is altered in its properties by the presence of a second tone, this is described as intermodulation. When we listen to natural sound, separate musical voices are usually due to separate instruments. When we reproduce a signal through amplifiers and loudspeakers, these otherwise separate voices must share the same channel. The mere presence of one voice may then modify the other if there is not enough "shoulder room" for both. This jostling may take the form of an alteration of the dynamic level of each or even a slight modulation of the pitch. Timbre and dynamics are most noticeably affected, and the subjective image of what should be a completely separate instrument modifying, by its presence, another completely separate instrument can be quite unnatural.

Test Procedure

In order a provide a measurement of this distortion, Audio uses two pure musical tones mixed in equal level. There are many classes of inter modulation, but one that is readily identifiable is due to the woofer which is called upon to reproduce the lowest bass as well as a major piece of the musical spectrum containing fundamentals.

Audio has settled on a low bass tone of E1, which is 41.2 Hz, and the tone of A4, which is 440 Hz, as a standard for this particular test. If the speaker which reproduces E1 is not called upon to pass A4, then we choose a musical tone about a half octave within the band which it is suppose to handle.

E1 and A4 are mixed at equal voltage level into the speaker, and A4 is our primary concern in the reproduced signal. We want to know how A4 is modulated by the presence of E1.

Both a spectrum analyzer and special coherent filter are used for this test. The output from the test microphone is measured on a spectrum analyzer to determine the power spectral density of sidebands about 440 Hz due to the 41 Hz. The bandwidth of this analyzer can be made as narrow as 2 Hz, and the exact frequency under test is measured by a frequency counter. The total power in the side bands about 440 Hz is measured as a percentage of the power in the unmodulated 440 Hz. This is the percentage value of IM which we plot as a function of drive power. The power level in watts on this plot is average power expressed as the square of a measured voltage divided by the resistor equal to the stated loudspeaker impedance, usually 8 ohms. The voltage is the peak value of the composite 440 Hz and 41 Hz presented to the speaker divided by the square root of two. This is done to be consistent with amplifier standards. On the curve we supply, the peak power is thus twice the indicated "average" power, just as though it were a single sine wave.

The IM is calculated on the basis of power where each component adds quadratically. From a voltage standpoint, this is the square root of the sum of the squares of the components. It is a one-number measurement which can be used as a relative measure between speakers. Furthermore, a perfect speaker will have no IM distortion.

That's fine, but there are many researchers who believe that this number and fifty cents will buy a cup of coffee in most restaurants. Audio supplies this measurement because we believe intermodulation distortion is a very real thing and somebody should pioneer the making of such a measurement, rather than sit around and haggle about whether the measurement should be made. We deliberately use a power spectrum basis because that is conventional in testing cartridges and amplifiers. You can thus use this measurement for speakers exactly as you would for amplifiers.

We don't stop there, however. Besides the spectrum analyzer, we use two specially developed coherent filters to view the intermodulation on a oscilloscope. We coherently multiply the microphone output against the exact 440-Hz signal in order to know precise amplitude and phase relationships of the acoustic tone. We first up convert to 225 kHz where a precision goniometer/phase shifter is available. Then, the signal is coherently down converted to zero frequency into an in-phase and a quadrature component. The original 440-Hz sine wave is now two d.c. voltages. These are viewed on an X-Y oscilloscope. A second filter using quadrature integrate and dump circuits is also available for oscilloscope view.

When the 41 Hz modulates the 440 Hz, we can independently measure both the angle modulation and amplitude modulation on the 440 Hz. In addition, we can measure the precise shift in static phase due to the 41 Hz and the exact change in average power.

Now we have a different ball game.

Not only can we measure Doppler versus amplitude, but we can spot static cone displacement due to heavy drive in a nonlinear magnetic structure. This lets us describe the IM plot in a much more meaningful manner than had we depended upon a power spectrum measurement.

If the nature of the distortion above a certain power level is different than that at lower levels and can give rise to a different sonic effect, we state this fact in the review. This means the IM curve is now more valuable in its comparative ranking.

The IM test that is printed is, of course, a test of only the woofer. To test the tweeter, two tones of equal level are again used but they lie in the frequency range covered by that speaker. The spectrum analyzer is used to check the intermodulation fragments for this case. This data is only reported if it discloses something significant.

Interpretation

One of the first things which is evident in the intermodulation distortion of speakers is the magnitude of distortion. An audio aficionado who would not consider buying an amplifier with more than one tenth of one per cent distortion at any level must view as incredulous that "good sounding" speaker which runs a neat three per cent at his normal listening levels. Rest assured this is not unusual, and the speaker may "listen" very well at this level of distortion.

Just as in amplifiers, a lower distortion on a power spectrum basis may not mean a cleaner reproduction. However, the distortion should rise smoothly from a low level at low power. Sudden changes in curvature are undesirable because they may signify a change in form of the inter modulation.

Distortion levels above 5 percent generally indicate noticeable subjective modification of the sound. The type of intermodulation enters into this. There is a sonic difference between tremolo and vibrato as a modulation of one musical note by another.

Compare the harmonic and intermodulation distortion measurements for each speaker as some measure of how it may sound. Remember, that in order to keep the peak power the same value, the average 440-Hz power level in the IM measurement is 6 dB (one fourth) less than the average 440 Hz power level in the harmonic distortion. Read the harmonic distortion curve at 1 watt and the IM curve at 4 watts to get those measurements corresponding to the same loudness of 440 Hz. How loud the 440 Hz is in your listening environment can be obtained from the one-meter SPL reading on the harmonic distortion plot.

The IM test, plus the supporting narrative Audio supplies, can give a fair idea how low bass can modulate other musical components, whether this is due to a thundering classic organ or a chest-thumping kick drum.

(Audio magazine; Mar. 1976)

Also see:

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

Understanding S/N Ratios (Sept. 1976)

Build a Low TIM Amplifier (Feb. 1976)

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