[Karl Uppiano]

wrote in message
ups.com...
Todd H. wrote:

So is distortion's root this nonlinearity?

I'd say that's a good way to look at it.

And if so, why does this nonlinearity always manifest itself as n-order
harmonics?

Great question. To appreciate it, math is involved, and that math
involved functions that have squared terms in them, among other
things. In the time domain, if you have a component whose transfer
function introduces

And how does clipping come into the picture?

Take an input of sine(t). The ideal output would G*sine(t) where G
is a linear multiplier representing the gain of the amplifier stage.

Clipping results when the the amplifier runs into the supply rail. In
the extremest case of clipping your sine wave looks like a square
wave. If you do a Fourier transform on a square wave you get a very
long equation that shows the square wave as a summation of sine waves
all harmonically related t othe original.

If the original input is at say 100Hz, the frequency components of
the square wave will be weighted sum of 100Hz 200Hz 300Hz 400Hz, ad
infinitum. I forget the specifics of the math, but mentally
envision an equation that takes the original sine wave, and adds sine
waves and successive harmonics. That's where you begin to
appreciatiate how clipping introduces new frequenies in the signal
that are multiples of the original. And hence, the term harmonic
distortion.


Thanks Todd for that reply. So let me rephrase so ensure I'm along the
right path:

- unwanted distortion is due to nonlinearities

- some nonlinearities exist even within the "linear" operation range of
the amplifier

- some nonlinearities exist when approaching the real-world limits
(power rails) of the amplifier

- It is not that the amplifier does anything special to add distortion
in terms of fundamental multiples, but rather when mathematically
transformed into the frequency domain (FFT) the distortion is
manifested that way.

Another question that comes to mind, then, is that if a wave is made up
of fundamental pure sines with different phases and frequencies (that
makes sense, I knew that one already), I guess I'm wondering why
amplifying, say a 1 kHz sine, doesn't introduce some 1.05 kHz sine as
some distortion coefficient. It would seem to me that if distortion is
caused by nonlinearities, then there must be an infininte collection of
possible nonlinearities that could incur the creation of a harmonic of
some decimal-multiple instead of whole-multiple of the fundamental.

Your thoughts?

No, a pure sine wave can only have integer harmonics. With a 1KHz pure
sinewave input, 2KHz is the next lowest frequency distortion component you
will ever see, no matter what.