Two-tone output of a linear resonant circuit

A linear time-invariant circuit sends each sinusoidal input to an output at the same frequency, multiplied by its complex transfer function. Two inputs therefore give the sum of two phase-shifted sinusoids. If their output amplitudes are equal, the sum factors into a carrier at the mean frequency and a signed cosine envelope at half the frequency difference. The envelope magnitude repeats at the full difference frequency. Unequal amplitudes give a nonzero minimum; a nonlinear detector is needed to generate a separate difference-frequency signal.