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January 10th 04, 09:38 PM

In article ,
(Joer) writes:

I'm trying to settle a debate with a friend, and my knowledge of
mixers is pretty rusty.

Say you have a receiver whose IF is 455 kHz, and it's tuned to a
station at 1500 kHz. If all's working OK, at the output of the mixer
you should have four frequencies:

1500 (original signal)
1955 (oscillator signal - osc. working above the signal freq.)
3455 (sum)
455 (difference)

My question is by what process does the mixer produce the 3455 and 455
frequencies. I say it's an add and subtract process, my friend says
(via mathematics) it's a multiplication process. Who's right?

Neither and both! :-)

It depends on the definitions of "linearity," "mixing," and "adding."

In a perfect linear circuit, two or more signals can exist as separate
entities, none affecting any other. You can "mix" them (inject them)
with the group of signals. Since the circuit is perfectly linear, no new
frequencies are added which are attributed to a sum or difference of
existing frequency signal components.

In sound recording "mixing" and "adding" always refers to operation
with nearly-perfect linear circuits to a recording medium.

"Mixers" in radios are highly non-linear. Some are outright switches
(Tayloe Mixer), some are very nearly on-off switches (diode rings),
and some use gross distortion of normally-linear characteristics
(tubes, particularly pentagrids...and Gilbert Cell double-differential
transistor structures). NON-LINEARITY creates new frequencies.

Mixing (in a mixer circuit) an incoming signal with a local oscillator
creates a mathematical sum and difference of the signal and the
LO frequencies...in addition to the existing signal and LO
frequencies passing through the mixer circuit (balanced mixers will
suppress the LO and double-balanced mixers can suppress the
signal frequency as well).

In this process of mixer circuit mixing, the new frequency products
(using "products" in a very general sense, not just multiplication)
still retain the amplitudes of the original. The signal's amplitude
containing AM sidebands is repeated at the new sum and difference
frequencies. Relative phase is also preserved. If the signal has
modulation components due to FM or PM, those appear on the new
sum and difference frequencies. If the much-stronger LO contains
any AM, FM, or PM, that is repeated on the new sum and difference
frequency components as AM, FM, or PM.

It gets worse. :-) The LO is seldom a pure sinewave so it has
harmonic content. New sum and difference frequencies will exist
as a result of LO harmonics! [most of those are simply filtered
out, dissipated, rejected] Scoping an LO injection waveform on
a wideband oscilloscope might come as a shock... :-)

The "process" is all due to NON-LINEARITY. The mixer output
contains the original signals plus components at frequencies
which are the sum and difference of the original...plus a few more.

Mathematics is used as a way of explaining the non-linear mixing
process. That isn't the full explaination but it is close enough.
Don't get caught up in plus and minus signs on equations and
too much argument over that...nor of the mathematical purists
who play games with term re-arrangements and "hidden meanings."

Non-linearity of all amplifiers will cause heterodyne creations. A
low-level example is the intermodulation distortion values such as
"IP3.".

Len Anderson
retired (from regular hours) electronic engineer person

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