What is mixer?

Question

Why the output signal is the product of the two input signals instead of addition?

Answer 1

The output is the product because a mixer always contains an active nonlinear device rather than linear components. A diode, a bipolar or an FET have nonliniear transfer functions which result in the product function. Take a bipolar. It has an exponential transfer function that can be expresses as a series of polynomials in X, X^2, x^3, x^4 etc. Each one of the polynomial terms yields different mixing products.