[Todd H.]

writes:

How is it created?

Any time you go through a non-linear component in the audio chain, you
have the potential for distortion.

For instance, let's take the scenario of an all-analog, all pure
class-A staged amplifier.. My *assumption* is that in an ideal model,
this scenario would generate no distortion,

Yup, whatever came out would be exactly X dB louder than the input,
and no new frequencies would be generated.

but in using real-world components, distortion is still generated.a

Correct. It has to do with the non-linear nature of transistors and
tubes that we have to use to take energy out of a power supply and add
it to an audio signal to make that audio signal bigger.

I understand that there exist what are called "nonlinearities" in
the amplifier, where at some input levels, a change of the input
voltage causes a particular change in the output voltage, but at
some other input level voltage, the same change in voltage (just
offset from the original) would cause a different amount of change
in the output.

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.

Some quick background-- I've got an EE degree in electrical and
computer engineering with emhpasis on the digital realm of circuit
design. But I've been trying to go back and "fill in the details" in
the analog world due to my heavy interest in audio. So while I easily
understand some EE topics, others I may not have as fundamental a
grasp

My EE had a bit of DSP but focused quite a big on analog signal
processing. Such a broad field, so no shame in it!

Think in terms of a fourier sreies representation of a square wave, or
how a fourier series' coefficients for higher frequencies would be
changed when you try to represent a clipped signal as a function of an
undistorted sine wave, and your brain will wrap around it pretty
quickly.

Best Regards,
--
/"\ ASCII Ribbon Campaign | Todd H
\ / | http://www.toddh.net/
X Promoting good netiquette | http://triplethreatband.com/
/ \ http://www.toddh.net/netiquette/ | http://myspace.com/mytriplethreatband