Intermodulation Distortion (IMD) -- Why Don't We Like It?

DonH50

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A previous post discussed harmonic distortion (HD), but to most people intermodulation distortion (IMD) is far more objectionable. Why? Because IMD generates tones that are not harmonically related to the input signals, and these tones “stick out” more than tones that are harmonics of the input tones. They sound “off” to our ears.

As an example, I created two tones at around 523 Hz (C above middle C on a piano) and 661 Hz (the E above, the root and third of a major chord). I added 0.1 % second- and third-order distortion terms (x^2 and x^3) and plotted the spectrum.

IMD_1.JPG

You can see the two signal tones at -6 dB, and a group of distortion spurs (tones) around the signal. I used -6 dB (0.5 full-scale) because two signals added will peak at 0 dB when they are each at one-half full-scale. You can see that in the next picture, which shows a few cycles of the signal. The funny-looking waveform is a result of the two signals mixing together, adding and subtracting from each other at different times. Even though each signal alone would only reach 0.5, together they reach 1.0 when they are in phase so both signals add. The error signal is multiple by 100 to make it easier to see; otherwise, the 0.1 % error would be essentially invisible by eye.

IMD_2.JPG

Below is a zoom showing the bunched signals, and a table of all the frequencies present. Not only do we have harmonics of each signal, at 2x and 3x the fundamental tones, but also intermodulation sum and difference terms. That means that we get C and E, and their second and third octaves, but also a tone a little over high D, a little below a low C# from the second-order IMD. The third-order IMD gives back the fundamental tones (but in general out of phase, causing amplitude modulation), and tones around a couple of (lower and higher) G’s (not too bad), Bb (oops), and a strange tone about half-way between Ab and A (what?) As a matter of fact, none of the IMD tones lie exactly on a piano note. These added tones add dissonance not in the original chord structure, and our ears are pretty good at picking out this dissonance. Yuck.


IMD_3.JPG
IMD_4.JPG

So, IMD creates non-harmonic tones, tones that do not lie in the chord, and that sounds bad. One other note: IMD tones are actually higher in magnitude than HD tones. Theoretically, IMD-2 tones are 6.021 dB higher than HD-2 tones, and IMD-3 tones are 9.542 dB above the corresponding HD-3 tones. Adding insult to injury… This is another reason IMD is more important than HD in the real world.

The derivation of all this is straight-forward but tedious. Take a couple of signals represented by Vin=sin(2*pi*f1*t)+sin(2*pi*f2*t), then build a function using

Vout = Vin + HD2*Vin^2 + HD3*Vin^3

After expanding out the terms and plugging in various trig identities you will find the terms in the table above, and the relation between HD and IMD amplitudes.

Hope this is useful - Don
 
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dallasjustice

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thank you for this explanation. I read that IMD is also somehow related to phase distortion in amplifier's using poor feedback. I didn't really understand that. Is this true?
 

DonH50

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I do not know what is meant by "phase distortion" (or "poor feedback"). I don't think phase modulation alone adds frequency content, but in a feedback loop can amplitude-modulate the signal. Applied to any nonlinearity that can cause undesirable spurs, true. I would not make the tie to IMD, however. At least not after ten seconds' thought; been a while since I analyzed a PM signal. I could well be wrong.

I suspect what you are thinking about is transient intermodulation distortion, TIM, and that is related to phase delay in a feedback loop. In this case, the delay means the feedback signal gets back to the control point (input) too late to counteract the distortion and acts upon a later part of the signal (speaking loosely). The result is the signal is modulated by the feedback in a way that can increase, not decrease, distortion. TIM was a new term for audio, but problems of loop stability due to phase shift and other issues have been known since feedback was invented. The usual solution is to control the bandwidth appropriately by either increasing the feedback bandwidth or decreasing the signal bandwidth. Solutions may include other terms to stabilize the loop, such as feedforward paths or additional tricks to reduce TIM.
 

dallasjustice

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That's it! Sorry, I got my intermodulated distortions mixed up. :) Is there a generally accepted measurement for TIM?

I do not know what is meant by "phase distortion" (or "poor feedback"). I don't think phase modulation alone adds frequency content, but in a feedback loop can amplitude-modulate the signal. Applied to any nonlinearity that can cause undesirable spurs, true. I would not make the tie to IMD, however. At least not after ten seconds' thought; been a while since I analyzed a PM signal. I could well be wrong.

I suspect what you are thinking about is transient intermodulation distortion, TIM, and that is related to phase delay in a feedback loop. In this case, the delay means the feedback signal gets back to the control point (input) too late to counteract the distortion and acts upon a later part of the signal (speaking loosely). The result is the signal is modulated by the feedback in a way that can increase, not decrease, distortion. TIM was a new term for audio, but problems of loop stability due to phase shift and other issues have been known since feedback was invented. The usual solution is to control the bandwidth appropriately by either increasing the feedback bandwidth or decreasing the signal bandwidth. Solutions may include other terms to stabilize the loop, such as feedforward paths or additional tricks to reduce TIM.
 

Groucho

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A previous post discussed harmonic distortion (HD), but to most people intermodulation distortion (IMD) is far more objectionable.

Thank you for that informative post.

Is it worth making the distinction between harmonic and IM distortion because, presumably harmonic distortion without accompanying IMD is not possible unless listening to a single tone..? (or using some sophisticated DSP to identify the a signal's constituent tones and applying harmonic distortion to the individual tones before adding them back together again). I would assume that the sort of nonlinearity we encounter in amplifiers and speakers cannot cause harmonic distortion without also producing IMD. Yet people say they prefer even to odd harmonic distortion or whatever, and that they even prefer the 'right' harmonic distortion over no distortion. They are actually saying that they like the sound of certain types of IMD are they not?
 

DonH50

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I think it is worth making the distinction so people can know the difference, and because most audio component datasheets state THD but not IMD. And yes, if you have conventional circuits both HD and IMD are going to be present...

One important consideration is that second-order IMD produces tones at the sum and difference frequencies, which for two tones near each other means distortion tones that are fairly far away (around d.c. and 2x the signal frequencies). The farther apart the tones are, the less likely we are to notice the dissonance, at least IME and for reasonable (low) levels of distortion. Third-order IMD adds components at 2f1 +/- f2 and f1 +/- 2f2. The difference tones lie near the original signals, right where they can cause the most damage. So, there is some basis in my mind for prefering even-order over odd-order distortion terms.
 

amirm

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Great explanation as always Don! BTW, I think you mean "sum" and not "some" in your post above :).
 

Groucho

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One important consideration is that second-order IMD produces tones at the sum and difference frequencies, which for two tones near each other means distortion tones that are fairly far away (around d.c. and 2x the signal frequencies). The farther apart the tones are, the less likely we are to notice the dissonance, at least IME and for reasonable (low) levels of distortion. Third-order IMD adds components at 2f1 +/- f2 and f1 +/- 2f2. The difference tones lie near the original signals, right where they can cause the most damage. So, there is some basis in my mind for prefering even-order over odd-order distortion terms.

A very good point. I suppose it's true for sparse recordings featuring a solo voice or instrument, perhaps, but I would imagine that once you get a more complex signal it would be harder to see it 'by inspection' of the spectrum.
 

DonH50

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True that! Audio covers a huge frequency range (ten octaves) compared to most RF systems. Second- and higher-order products still fall in-band for the vast majority of audio signals. Any musical signal will essentially bury* all the distortion components, making it very hard to extract data from "real" signals. One reason distortion is a fairly poor metric for how a system sounds, unless it is pretty bad...


* "Bury" in the sense that spectral analysis is generally unfruitful; too many spurs, "grass" is too high...
 

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