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Data AcQuisition And Real-Time Analysis
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This results when two or more different frequency components interact within a nonlinear system. The output will then contain not only harmonics of the original frequencies, but also components at sum and difference frequencies that typically aren't harmonics of either input. This is also known as "intermodulation" or "IM" distortion (IMD), since the result is similar to multiplying two sinusoids together.

You can demonstrate these sum and difference products by using the STIM3A/DEMO setup described above for clipping distortion. Set the two sine waves to different frequencies and set both amplitudes over 50%. Clipping will appear on the composite waveform, but not on every cycle... only where both waves are aligned.

For example, set both levels to 60% and set the frequencies to 500 and 700 Hz. Notice that the most-positive waveform peaks are clipped, and that this happens about every 5 msec. (The same is true for negative peaks.) Now, 5 msec "just happens" to be the period of a 200 Hz wave, which is the difference between 500 and 700 Hz, and you will indeed see a 200 Hz peak in the spectrum, as well as one at the sum frequency of 1200 Hz.

In fact, you will see peaks at all multiples of 200 Hz. If we call the higher frequency f2 and the lower f1, then all these peaks represent "difference tones" at f2 - f1, 2f1 - f2, and all integer multiples Mf1 - Nf2. (Negative and positive frequencies are equivalent here.)


Many systems have milder nonlinearities than abrupt clipping, and are typically described by the order of the equation that relates the instantaneous output to input. A perfectly linear system with input X and gain A would produce output Y as:
  Y = AX
A system with nonlinearities would have the form:
    Y = AX + BX^2 + CX^3 + DX^4 + ...

In a two-tone intermodulation test, the 2nd order term B will cause intermodulation components to appear as an f2 - f1 difference tone. This is often referred to as the "quadratic" difference tone, as in the old "quadratic formula" for solving equations with squared terms. The 3rd order term C will result in a "cubic" difference tone at 2f1 - f2. By studying the locations and strengths of the distortion products, it is possible to gain insight about the nature of the system.

Intermodulation distortion is typically a problem when you are generating two tones from the same speaker or other source at high sound levels. Since any source is nonlinear at high levels, the sound output will include not only the two tones you desire (plus harmonic distortion products from each), but also intermodulation distortion products at inharmonic sum and difference frequencies.

It is particularly important to reduce intermodulation in loudspeaker and audio amplifier designs, since inharmonic distortion is subjectively much more objectionable to the ear than harmonic distortion. It is easily detected because it adds new tone frequencies that were not present in the original signal, and are thus not masked by harmonics of voices or instruments in the program material.


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