How Does a Radio Mixer Work?

Simply put, if you combine two frequencies, the result is the sum of the two frequencies, as well as the difference of the two frequencies

See

http://www.electronics-radio.com/articles/radio/receivers/rf-mixer/rf-mixing-basics.php

let me correct a common mistake ...mixer is not a sum and difference frequency signal producer!

its any device having non-linear transfer characteristics .it is simply like our "mixer".it produces many components of frequencies sum ,difference ,secondorder sum second oerder difference .the no: of frequency components generated depends on the extent nonlinerarity of the device transfer characteristics .for more details visit the url:

togglezero.

True..... but I was trying to keep it simple.

He is trying to learn the basics. For practical use, It produces the sum and differences. These are the signals that are used. Don't complicate things with harmonics and noise that are later filtered out anyways.