Background
The classic frequency mixer is a multiplier. Multiplying two sinewaves produces just the sum and difference frequencies; the input frequencies are suppressed, and, in theory, there are no other heterodyne products. In practice, the multiplier is not perfect, and the input frequencies and other heterodyne products will be present.
An actual multiplier is not needed. The significant requirement is a nonlinearity, and at microwave frequencies it is easier to use a nonlinearity rather than an ideal multiplier. A Taylor series expansion of a nonlinearity will show multiplications that give rise to the desired higher order products.
Design goals for mixers seek to select the desired heterodyne products and suppress the undesired ones.
Diode mixers.
Overdriven diode bridge mixers. Drive signal looks like odd harmonic waveform (essentially a square wave).
Read more about this topic: Subharmonic Mixer
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