a mixer

A mixer is the part that shifts a signal from one frequency to another without changing the information it carries. Despite the name it does not blend signals like an audio mixer adds voices; instead it multiplies two signals together, and the magic of multiplication is that it creates new frequencies that were not in either input. This is how a radio takes a station up at, say, 100 MHz and slides it down to a convenient fixed frequency the rest of the receiver can handle comfortably.

The mechanism is multiplication, and a trig identity tells the whole story. If you multiply two sine waves at frequencies f1 and f2, the result contains two new tones: their sum (f1 + f2) and their difference (f1 - f2). So feed a mixer an incoming radio signal at 100 MHz and a locally generated tone (the local oscillator) at 90 MHz, and out come components at 190 MHz and 10 MHz. A filter then keeps the one you want, here the 10 MHz difference, which carries exactly the same modulation as the original but at a far more convenient frequency. Real mixers are built from diodes or transistors that act as fast switches; switching is a form of multiplying, which is why a humble diode ring can convert frequencies.

Mixers are the heart of frequency conversion and the superheterodyne receiver that powers almost every radio and phone. They appear twice over in transceivers: down-converting received signals and up-converting signals to transmit. Honest caveats worth knowing early: a mixer is not noiseless or distortion-free. It produces both the sum and difference plus unwanted spurious products, so good filtering is essential. It has an image frequency problem, a second input frequency that lands on the same output and must be filtered out before mixing. And passive diode mixers have conversion loss, they output less than they take in, so they often sit after an LNA that has already lifted the signal.