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If I multiply a baseband signal \$A cos(C\omega t)\$ and a carrier signal \$B cos(D\omega t)\$, the result is \$\frac{AB}{2} [cos(C-D)\omega t+cos(C+D)\omega t]\$, which is a double sideband, suppressed carrier signal. My question is, how is the conversion gain defined in this situation? Would it be \$\frac{B}{2}\$ since the amplitude of each sideband is \$\frac{AB}{2}\$, or would it be \$B\$ since the total energy is spread among the two sidebands?

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You have to define what you mean by 'conversion gain'. Once you've done that, the question resolves itself.

Usually, when buying balanced mixers from a catalogue, the manufacturer specifies conversion gain as 'wanted sideband power' / 'input power', which results in a figure of -6dB for 'ideal' mixers. It's constant because in an RF mixer, the LO power is constant. But that's a physical system.

If you want to define derived terms from a mathematical formula, then the definition will yield whatever you put into it.

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