Intermodulation difference frequencies and symmetrical distortion

[Malcolm Irving]

Rod Elliot presents some very interesting experiments which demonstrate that symmetrical distortion creates far less intermodulation sum and difference frequencies than asymmetrical distortion:
IMD - Something New

I was reminded of this recently when I compared an overdrive pedal that I have with a (supposedly) identical new one. The new one has far more difference frequency than the old one. (Lack of tweaking in the factory perhaps?)

Any thoughts or experience on this? In particular, does anyone know a theoretical basis for Rod’s findings?

[frus]

there was a whole thread about that article recently

http://music-electronics-forum.com/t41113/

[jazbo8]

Any thoughts or experience on this? In particular, does anyone know a theoretical basis for Rod’s findings?

Not sure if there is a theoretical basis for his finding... because:

1) symmetrical clipping produces only odd harmonics; so there are less difference frequecy products, i.e., there is no f_odd±f_even products, therefore there is less IMD;
2) asymmetrical clipping contains both odd and even harmonics, so there are more difference frequency products, which suggests that there should be more IMD components;

So why is it "new" to find that asymmetrical clipping has higher IMD than symmetrical clipping?

[Malcolm Irving]

Yes, it makes sense. With two sine wave inputs, f1 and f2, into an asymmetric nonlinearity, the first few additional terms in the output would be at frequencies (f1+f1), (f2+f2), (f1+f2), (f1-f2), i.e. second harmonics and sum and difference frequencies.

But with a symmetric nonlinearity the first additional terms would be 3rd harmonics (f1+f1+f1) and (f2+f2+f2). The sum and difference frequencies (f1+f2) and (f1-f2) won’t fit the pattern. Although terms like (f1+f1+f2), (f1+f2+f2), etc. might. But that is just guesswork on my part - I’m hoping someone might be able to point to some Fourier analysis to explain it.

[jazbo8]

I recall seeing some online program that could display half-wave and full-wave rectified spectrum's, from which you can see how the addition of even harmonics to the odd harmonics result in many more IM products, i.e., you can see more spikes in the spectrum, which should be matched by the Fourier transform.

[Malcolm Irving]

Thanks to a very knowledgeable person (DF96) on another forum (diyAudio) I have found out that symmetric distortion produces only odd-order intermodulation products, such as (2f1 + f2), (2f2 - f1) etc. In particular, it cannot create the difference frequency (f1-f2) as that is an even-order intermodulation product.

I think this is quite interesting, because I find the difference frequency below a distorted power chord to be a big nuisance!

Could be another reason why folks like overloaded push-pull power stages.

OK, I know a lot of other folks prefer overloaded single-ended power stages.

[uneumann]

Thanks to a very knowledgeable person (DF96) on another forum (diyAudio) I have found out that symmetric distortion produces only odd-order intermodulation products, such as (2f1 + f2), (2f2 - f1) etc. In particular, it cannot create the difference frequency (f1-f2) as that is an even-order intermodulation product.

I think this is quite interesting, because I find the difference frequency below a distorted power chord to be a big nuisance!

Could be another reason why folks like overloaded push-pull power stages.

OK, I know a lot of other folks prefer overloaded single-ended power stages.

Interesting... so symmetric distortion produces a low IM product with a higher pitch. I'm just walking through the implications here...

I find 1/2 steps to be particularly revealing for distortion character. Open A (117 Hz) with a G# (104 Hz) is a tough case. You're saying that the lower IM product will be 2*104 - 117 = 91 Hz, vs 13 Hz for asymmetric distortion. My sense is that the 13 Hz is a problem even though you can't really hear 13 Hz. It has a "throbbing" or modulating effect that makes me cringe. Reducing the low freq IM products produced by a circuit could only help, IMO. Of course HP filters are used after distortion to filter out lows - but symmetric distortion could produce less of the LFs to begin with. Did I get this right?

So dual diode clippers have that property. As do LIO-stage preamp clippers.... as do PP output stages.

[Malcolm Irving]

Yes, those are the kind of implications that I’m thinking about.

I’m particularly bothered by power chords like A (110.0Hz) with E (164.8Hz). (Note this is not a ‘perfect fifth’ because of equal temperament.) The difference frequency 54.8Hz is approximately an octave below the A. To me that lower A is just getting in the way of the bass player. Also, if you bend the strings a bit, the low intermodulation product ‘wanders around’, creating more havoc.

I’m not so bothered about the higher frequency IM products as they just seem to become part of the overall ‘fuzz’.

[nickb]

Here is an FFT of showing IMD products for sym' and asym' cases.

The differences in magnitude and placement are clear. It's not so much that the sym case has many products missing but rather that it has them at different amplitudes and frequencies, most notably around 3.1kHz / 3.2Khz in the sym case instead of around 2.1KHz in the sym case.

[Malcolm Irving]

Here is an FFT of showing IMD products for sym' and asym' cases. ...

Are you putting two sine waves into the input? If so, what are their frequencies?

[nickb]

Sorry, I forgot to put that important info in! Yes, 1KHz and 1.1Khz

[Malcolm Irving]

The difference frequency is 100Hz and it does seem to be substantially reduced in the symmetric distortion case compared to the asymmetric case, although I expected it to be eliminated completely.

[nickb]

The difference frequency is 100Hz and it does seem to be substantially reduced in the symmetric distortion case compared to the asymmetric case, although I expected it to be eliminated completely.

Practically speaking you are correct. At -45dB I would consider that inaudible.

Edit: Or 65dB below 1KHz and 1.1KHz.

[Malcolm Irving]

.... At -45dB I would consider that inaudible....

Great! That's what I want for my power chords!

Seems like the second of the two 'identical' overdrive pedals, that I mentioned in the opening post, wasn't tweaked properly at the factory to get the distortion symmetrical enough.
Maybe I'll open it up and see if there are any pre-sets in there.

[nickb]

Great! That's what I want for my power chords!

Seems like the second of the two 'identical' overdrive pedals, that I mentioned in the opening post, wasn't tweaked properly at the factory to get the distortion symmetrical enough.
Maybe I'll open it up and see if there are any pre-sets in there.

It's a great observation. I see quite a few pedals that are deliberately made asym'. I just modded one for someone the other day to make it symmetrical as I thought it sounded better. Now I know why. Thx!