What are the principal frequencies that appear at the output of a mixer?

A mixer is a fundamental non-linear circuit used in radio receivers and transmitters to shift signals from one frequency to another. It takes two input signals—typically an incoming RF signal (F1) and a local oscillator signal (F2). Because the mixing process relies on non-linear components (like diodes or specialized transistors), it mathematically multiplies the signals. This process naturally outputs a predictable set of principal frequencies: the original two input frequencies (F1 and F2), their sum (F1 + F2), and their difference (F1 - F2 or F2 - F1). The desired sum or difference frequency is then selected by a bandpass filter (often as an Intermediate Frequency, or IF) while the others are rejected. Distractors involving square roots or fixed constants like 1.414 have no mathematical basis in heterodyning.