RF mixer

A circuit that multiplies two signals together to shift a signal from one frequency to another. If amplifiers add and filters select, the mixer translates: feed it your incoming radio signal and a clean local-oscillator tone, and out comes copies of the signal slid down (or up) to a new, easier-to-handle frequency. This is the heart of every superheterodyne radio and every modern transceiver.

The magic is trigonometry: multiplying cos(ω_RF·t) by cos(ω_LO·t) produces sum and difference frequencies, ω_RF ± ω_LO. The difference term — the intermediate frequency (IF) — carries your information at a lower frequency where filtering and digitizing are far cheaper. In ICs the favourite is the Gilbert-cell mixer, a clever stack of differential pairs switched by the LO; it gives conversion gain and good port isolation. The price of mixing is non-linearity, so mixers are major sources of unwanted IP3 products and spurious tones.