# What's the relationship between harmonic distortion and intermodulation distortion?

So if you take a sine wave and put it through a non-linear transfer function, it experiences harmonic distortion, which produces other sine wave components at integer multiples of the original.

If you put 2 or more sine waves through the same non-linear transfer function, they experience intermodulation distortion, where the newly-produced partials are at sum and different frequencies from the originals.

But it seems strange that the 1-sine-wave case should be fundamentally different from the 2-or-more case.

As transfer functions with odd symmetry produce only odd-order harmonics, I thought maybe harmonic distortion is actually a form of intermodulation, where the single tone intermodulates with its negative frequency component, producing only odd harmonics (-10 and +10 are spaced 20 apart, producing intermodulation tones at 10+20 = 30, 10+20+20 = 50, 70, etc.) but that doesn't really work, because then why do even-symmetric transfer functions produce even-order harmonics and destroy the fundamental? And what happens when you distort a complex exponential that doesn't have a negative frequency component?

It isn't fundamentally different. Both IM signals also produce their own harmonic distortions, as well as the IM distortion. When there is only one signal, there is nothing to intermodulate with, so no IM. In a feedback circuit of course the harmonics themselves will produce IM distortion.

• Put 100 Hz into a full-wave rectifier and you get out 0 Hz, 200 Hz, 400 Hz, ... No more fundamental Oct 11 '12 at 2:05
• I'm speaking in the context of audio circuits :-| Oct 11 '12 at 2:36
• Meaning what? That circuits with even symmetry aren't used in audio? "The Octavia pedal and the the old Foxx Tone Machine (as well as the "new" Experience pedal, which is almost exactly the same circuit as the Foxx) use a form of full wave rectification followed by diode clippers and filtering." A Musical Distortion Primer Oct 11 '12 at 13:29
• @endolih OK, I'm referring to even-symmetry audio circuits like push-pull output stages, not full-wave rectifiers and effects pedals. Nov 12 '12 at 13:08
• push-pull amplifiers are odd symmetry, not even. Nov 13 '12 at 3:23

Harmonic Distortion is not related to intermodulation distortion. Here is another point I make, if you remove part of a sine wave, the harmonic spectrum exactly matches the harmonic content of that feature. Here is a shot of the peak of a sine wave clipped off, all by itself and its spectrum. Notice that the spectral pattern exactly matches the pattern of harmonic distortion of the clipped wave itself, but of course, the clipped wave has the fundamental in it too, obviously that would be missing from the clipping. This proves that harmonic distortion is related to the spectral content of that feature of the sinusoid, not to any "intermodulation." I can (and do) show an exact mathematical relationship between area and harmonic distortion, and it has nothing to do with intermodulation.

My book Distortion explains exactly where harmonic distortion comes from and it's not related to intermodulation distortion. Harmonics are caused by area, my article in LinkedIn proves it. The integral of time and voltage is energy, and that energy shows up as harmonic distortion.

• I'm not sure what you're trying to get at, but it's kind of obvious that the bottom waveform is simply a sine wave with the top waveform subtracted from it. Subtraction is a linear operation, so naturally, both would have the same spectrum (with the signs inverted -- something your magnitude plots doesn't show) with the addition of the sine wave itself in the lower spectrum. There's certainly nothing earth-shattering here. Also, the link to your book no longer works. Apr 10 '19 at 23:26
• It's kind of sad, really. I just reviewed some of your recent videos, and it's clear that you've latched onto a particular set of observations about the FFT, and you've completely missed the more general underlying concepts. Anyone who's been through an undergraduate engineering course has done the actual derivation of the Fourier Transform (in both its continuous and discrete forms), and understands that everything you're talking about are direct consequences of how the transform works. You haven't discovered any new fundamental "laws". Sorry! Sep 26 '21 at 15:50