In a standard mixer, we multiply two signals $x_1(t)$ and $x_2(t)$, each with units of volts $(V)$, and get at the output:
I have always thought that the output of mixing operation was another voltage signal. But how can this be? Looking at the units of the factors, we multiply a quantity of volts, $x_1(t)$, by another quantity of volts, $x_2(t)$. So shouldn't the units of $y(t)$ be $V\cdot V=V^2=W$?