How a mixer makes a new frequency from two

A mixer combines two signals to make new frequencies: their difference and their sum. Feed it 100 kHz and 110 kHz and out come 10 kHz and 210 kHz. It only works with something non-linear in the path, a diode, a transistor or a multiplier, because simply adding two signals never creates a new frequency. Radios use the difference to move every station they tune to one fixed frequency: that's the superheterodyne receiver.

Adding isn't mixing

Put 100 kHz and 110 kHz on one wire. Where their peaks line up the sum is twice as big; a moment later they cancel. The swelling and fading repeats at the difference, 10 kHz: a beat, like two guitar strings slightly out of tune. But look at the spectrum and there's still only 100 and 110 kHz. A filter tuned to 10 kHz finds nothing to pass. Any linear circuit, however it's built, can only scale and delay the frequencies it's given.

Multiply them

The product of two sines contains exactly the difference and the sum. A diode does a rough version of that multiplication: it conducts on the crests of the combined wave and not the troughs, so what comes through really does contain a 10 kHz component.

A diode mixer

Send the two tones through a diode into a resistor with a capacitor across it. The RC must hold the voltage between carrier crests but still follow the beat. Its time constant has to sit between the two periods: longer than a 100 kHz cycle, 10 µs, and short against the 10 kHz beat, 100 µs.

That gives a 10 kHz output about 1.47 V in size. With 10 pF, 0.1 µs, the output follows the carriers themselves; with 100 nF, 1 ms, it smooths the beat away.

The superheterodyne

Mix the incoming station with an oscillator inside the radio, the local oscillator, and keep the difference. Tune the oscillator 455 kHz above whichever station you want, and every station comes out at 455 kHz, the intermediate frequency. One fixed, carefully built filter and amplifier then handle all of them. To hear 1 MHz, set the oscillator to 1.455 MHz; to hear 1.2 MHz, set it to 1.655 MHz.

Where else mixing appears

Spectrum analysers sweep a mixer's oscillator to scan a band. Musicians tune by listening for the beat to slow to nothing. And unwanted mixing is a real problem too: two strong signals hitting an overloaded amplifier mix inside it and create new frequencies that weren't there, called intermodulation.