Wave distorsion in multiplying, switching or sampling mixers

Conceptually, engineers tend to replace mixers by multipliers, controlled switches or samplers. It is clear that these models lead to very different signal processing operations and therefore are in general incompatible. In the special case that the mixers are used as frequency translation devices and one is interested in the first lower or upper conversion band only, the equivalence between these models is shown for general multiple tone input signals. Distortion of the shape of the converted temporal waveforms is shown to occur. Fortunately, this distortion does not jeopardize the measurement results obtained by mixing or sampling waveform measurement front ends as the envelope of the modulated signal is shown to be insensitive to the type of distortion at hand.