Mixers are three port devices that can be active or passive, linear or nonlinear. They are used to modulate (upconvert) or demodulate (downconvert) a signal to change its frequency to be sent to a receiver or to demodulate at the receiving end to a lower frequency.
Two major mixer categories are switching and nonlinear. Nonlinear mixers allow for higher frequency upconversion, but are less prevalent due to their unpredictable performance. In the diagram above, the three ports are shown. The RF signal is the product or sum of the IF (intermediate frequency) and LO (Local Oscillator) signal during upconversion. Due to reciprocity, any mixer can be used for either upconversion or downconversion. For a downconversion mixer, the output is the IF and the RF is fed on the left hand side.
The above diagram illustrates the concept of frequency translation. In a receiver, the mixer translates the frequency from a higher RF frequency (frequency that the wave propagated wirelessly through air) to a lower Intermediate frequency. The mixer cannot be LTI; it must be either nonlinear or time varying. The mixer is used in conjunction with a filter to select either upper or lower sideband which are the result of the multiplication of two signals with different frequencies. These new frequencies are the sum or difference of the two frequencies at the two input ports.
In addition to frequency translation during modulation, RF mixers can also be used as phase comparators, such as in phase locked loops.
To maintain linearity and avoid distortion, the LO input should be roughly 10dB higher than the input RF signal (downconverter). Unfortunately this increases cost and so therein lies the tradeoff between cost and performance.