Bill,
You said:
" Any good technician will tell you it's an add and subtract process.
Any good engineer will bore you to tears with complicated mathematical
analysis.
Guess which answer is more useful for your purpose?"
Well of course...if you're only interested in what some of what comes out,
then it's an 'add and subtract process'. But isn't that our initial
definition of what we want a mixer to do? This is circular logic. You're
chasing your own tail.
The original question was more in the vein of 'by what mechanism does a
mixer produce sum and difference frequency components'. The correct answer
is that it implements the mathematical product of the two input signals, and
that product contains sum and difference frequencies in addition to a host
of other frequencies that includes the original frequencies, all their
harmonics, and every conceivable product of those frequencies and their
harmonics. It's not just a simple 'add and subtract'. It just so happens
that we're most interested in the sum and difference, but there is much,
much more going on.
The "answer that is most useful for the purpose" is not necessarily the most
simplistic. Consider the following profound statement from W.E. Deming:
"If you can't describe what you are doing as a process, then you don't know
what you are doing"
Joe W3JDR
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