Why is distortion harmonic?

[dsavitsk]

When you put a 1KHz wave through an amp, for instance, you get 1KHz, 2KHz, 3KHz, ... etc. harmonic distortion components at the output. But, why aren't there non-harmonic components, 1.3KHz for instance?

[janneman]

Originally posted by dsavitsk
When you put a 1KHz wave through an amp, for instance, you get 1KHz, 2KHz, 3KHz, ... etc. harmonic distortion components at the output. But, why aren't there non-harmonic components, 1.3KHz for instance?

Good question. It has to do with the shape of the transfer characteristic of the devices. Suppose you have a pure squarelaw device and you input a sine wave with frequency f: sin(wt), where w=omega, or 2*pi*f. The square law means that at the output you get sin^2(wt). From mathematics we know that a sin^2(wt) = sin(2wt). There's your 2nd harmonic....

Amplifiers are never pure square law, but sometimes there are also 3rd order laws etc. All this leads to various mixtures of the fundamental and harmonics. But it can only be integer harmonics because of the mathematics involved.

Jan Didden

[HollowState]

I guess the simple answer is that distortion products are mathematically related. With only one frequency to work with there's a finite number of relationships which are multiples. With real world music, the possible relationships become much more complex and is called intermodulation distortion. (Not to mention transient IM from feedback.)

[janneman]

Originally posted by HollowState
I guess the simple answer is that distortion products are mathematically related. With only one frequency to work with there's a finite number of relationships which are multiples. With real world music, the possible relationships become much more complex and is called intermodulation distortion. (Not to mention transient IM from feedback.)

Yes, I'm not a mathematical genius, but I guess that it you get two frequencies like sin(w1t) and sin(w2t) and put them through a square law, you get sin(w(1+2)t) and sin(w(1-2)t) components.

Jan Didden

[tubelab.com]

When you put a single tone into an amplifier any "bad stuff" that happens to that tone happens at the same rate as the tone. IE 1000 times per second. Most distortions happen as the signal cross through the zero axis, or as they reverse direction, so it is easy to see how there are multiple opportunities for "stuff" to happen per cycle. These distortions are often called "harmonic distortion" for this reason.

Music is not just a single tone though. When you put two tones through an amplifier there will be some mixing of the two tones. If you put 100 Hz and 1000 Hz through a perfect amplifier you would get these two tones out. A real world amplifier would also give you some 900 Hz and some 1100 Hz from the intermingling of the two tones. These distortions are called "intermodulation distortion".

A real amplifier will have both types of distortion, so you will get 100 Hz, 1000 Hz (desired), 200 Hz, 2000 Hz (2nd harmonic) 900 Hz, 1100 Hz (IMD), 2100 Hz, 1900 Hz 1200 Hz 800 Hz (IMD of the 2nd harmonic) and so on.

Consider the IMD products of all of the harmonics and the IMD products from the residual power line hum and its harmonics (60 Hz, 120 Hz, 180 Hz etc.) and you can see how the picture (and the sound) gets cloudy real quick.

These are two common types of distortion that can be observed in steady state with an analyzer. There are other types of distortion that occur on transients and phase related distortions that are not easilly measured or observed. Music is composed of multiple tones and transients that change quickly. There are lots of opportunities for something to change, some of which aren't completely understood yet.

[Psychobiker]

As already covered, it'll be only the multiples/divisibles of the base frequency...hit A on the piano and As in the upper and lower registers ring in sympathy...

[EC8010]

The cheating answer is, "Because Fourier said so." More specifically, he showed that any repetitive waveform can be made up of a sinusoidal fundamental and a series of harmonics. Now, a distorted sine wave must be repetitive with each cycle (otherwise you'd get a different distortion depending on when you applied exactly the same signal). If you take the idea of applying a bust of sine wave at any time and getting the same answer each time a little further, you realise that any distortion must be higher in frequency (it can't be lower, because that would imply a result that changed depending on when you applied the signal). The distortion must be harmonically related to the input signal, otherwise it would beat with the input signal and produce a lower frequency, again causing a change dependent on when you applied your signal.l

[janneman]

Nice. Very good.

But, uhh, with 'bust' you probably meant 'burst' ?

Jan Didden

[Pano]

What a great question!

While not really an answer.... I do remember looking at the power supply of a single rail amp on the o'scope one day. Funny thing was, when a 1K signal ran thru the amp, there was 2K on the power supply.

Had to scratch my head for a bit before it dawned on me.
Each half of the 1K signal was pulling on the PSU, sagging it a bit. Thus double the rate, or 2 KHz.

As so well explained in the posts above, there's a lot of stuff like that going on.

[Jim McShane]

Originally posted by tubelab.com
When you put a single tone into an amplifier any "bad stuff" that happens to that tone happens at the same rate as the tone. IE 1000 times per second.

Any non-linearity in a circuit causes harmonics to be generated, regardless of whether the signal input to that circuit is a single frequency or multiple frequencies.

By definition, harmonics are multiples of the fundamental frequency. So a 2nd harmonic is 2000 Hz, a 3rd is 3000, etc.

So I don't think I understand what you are saying in the statement above...