The mixer is a non-linear circuit, the non linear component par excellence is the diode because its response is not proportional to the input (voltage). As the diode is a non-linear component, when using a signal through the diode what happens is that it is going to be distorted, which will generate intermodulation components. If an input variable frequency signal and a local oscillator signal pass through a system with a second-order nonlinearity, the output signals will have components in the sum and difference frequencies.
