"George Dishman" wrote in message
...

"ralph sansbury" wrote in message
...
I still dont understand what you mean by the multiplication
of voltages arriving at the two gates of dual gate
transistor:

You produce the sum and difference frequencies by
making use of this identity:

sin(a) * cos(b) = [ sin(a+b) + sin(a-b) ] / 2

The right hand side contains the sum and difference
so is the output from the circuit. The function needed
on the right hand side is multiplication.

You mean the left hand side. Yes the summation is equal to
the product. And it is the summation that is produced by adding
the voltages at the dual gate transistor along with the input
frequencies.


The same
method works when using a wideband signal where each
component is shifted in frequency by the same amount.


My sense of this is that the sum of the voltages produces a
pattern
which contains a frequency which is the difference frequency
plus
the sum frequency plus the two input frequencies and that the
filters in the special circuits you refer to produce these
separate components???.

If you replace "the sum of the voltages" in the first
line by "the product of the voltages", the paragraph
is perfectly correct. The filters are conceptually
separate from the mixer but often merged in practice.

I think you are overlooking the basic physics here. You
have no reason
for the filters at the output of the dual gate transistor etc,
and
which are an integral 'part of the mixer but conceptually
separate', unless it
is to take the oscillation of voltage which results from the
addition of the
separate oscillating voltages and to produce the different
component frequencies as
different outputs. The difference frequency of oscillating
voltage is then
taken as the desired output.
Of course the mathematical equivalence between the specified
product
and the specified sum makes it mathematically correct to say that
the black box
circuit produces a product of the two input frequencies as well
as the two
input frequencies.
This is adequate for engineers once the circuit has been
designed. But the first designers of the
circuit had to know the physics and to put in the inductors and
capacitors in
a resonant configuration etc to get the desired output ie.
to design around the problem that voltages at the input can only
add.
Thus it is not quite physically correct to say that the
transistor multiplies the
input voltages
and more correct to say that the transistor adds the incoming
voltages such that
the resulting pattern can be written as the sum of the input
frequencies and the
difference frequency and the sum frequency and that the latter
two frequencies
are mathematically equivalent to the product of the frequencies
etc.
Ralph