A lot of good stuff here and unfortunately some digression.

It might help here if you think this way. The basic RF or as you say,
superhetrodyne mixer, does what it does by instantaneous voltages
multiplication of the _instantaneous voltages_ of the two signals. There
are many types of these RF mixers, but the one which is modeled with this
concept will only give you the two frequencies as Roy's trig identity shows.
You can take a spreadsheet and put a sine wave of one freq in one column and
another freq in another column (use a pretty small angle step, say 1 degree
or less - be careful the degree/radian issue doesn't mess you up) then make
a formula in a third column which is A*B. You will see that the resulting
"product" column has variations which are not the two input frequencies. It
may not me real clear, but if it wiggles faster or slower that the
originals, then it is a different frequency. (now I gotta do this so I see
what it looks like for my self). However, better yet.....
The neatest example of this is to put the exact same frequency in both
inputs columns! Then the "wiggles" of the sine wave will be very obvious.
There will be no doubt about what is coming out of the multiplication.
God, I love spreadsheets. (sorry here, the beginning of a sentence is
capitalized).

Why does this Mister Wizzard stunt work? Because a circuit is doing
something to the voltages present at any given time, and in this case it is
a product thing.

SO, YES you do get the "Sum" and "Difference" frequencies out, so if you
want to call that addition / subtraction while working "in the frequency
domain" that's ok with me. However, all this other garbage holds, just the
same.

If you make a circuit which gives as its output the product of the two input
voltages, Roy's formula holds and you get the sum and difference frequencies
only. This is what we commonly call a "balanced mixer". The term
"balanced" comes from the concept that in this type, if you get the circuit
set up or "balanced" just right, the two input signals don't appear at the
output and the trig identity holds. I suppose it can be called the ideal
type.

When you get into what is commonly called "modulation", you still have this
type of instantaneous voltage multiplication, but usually, like in a Plate
modulated Tube transmitter, it is not so perfect and some of the original
input signals get through to the output (though the audio can't make it out
to the antenna) and you get carrier (one of the input signals) as well.
(I'm not going to get into the 'does the carrier vary in amplitude' or
sideband arguments here.)

All this talk about many more than the two frequencies is the result of what
we call "higher order" non linearities. This is just a way to describe
distortion that keeps the original sine waves from being perfect sine waves
in a circuit.

Also, the sampling talk will just confuse this basic issue, so I advise
ignoring it for now.

FWIW: the model in my brain can somewhat consider time variant the same as
non linearity since you get out something which ain't a simple scaled
version of the input...
73, Steve K;9;D:C:I

How'm I doin' Roy & Reg?

"W3JDR" wrote in message
...
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