Additive mixers are usually resistor networks, surrounded by impedance matching and amplification stages.
Multiplying mixers have been done in a wide variety of ways. The most popular are diode mixers, gilbert cell mixers, diode ring mixers and switching mixers.
A diode mixer has two or more signals going into a diode. Whenever any signal pushes the voltage above the threshold of the diode, current will flow to the other side, but not back. If the inputs are the right voltages, the result is that the peaks of the new signal occur whenever either signal peaks, and the diode supplies the troughs by refusing to conduct backwards. The classic crystal set radio is a diode mixer, with a simple electronic filter between the antenna and mixer to eliminate unwanted radio stations. Cheap AM radios still use diode mixers.
Gilbert cell mixers are just an arrangement of transistors that multiplies the two signals. Surprisingly, the switching mixers (below) pass more power and usually insert less distortion.
Diode ring mixers are the original switching mixer. They have two transformers and an array of diodes in a ring. Basically, the transformers are arranged so that one signal switches the diodes to conduct in one direction, or the other direction. The other transformer pushes its signal through the diodes. Diode ring mixers are popular because the on/off mechanism injects less noise, and loses less signal power than other methods. Also, the transformers can be wound to match the impedances into and out of the mixer stage to the rest of the electroic system.
Switching mixers use an array of FETs or (in older days) vacuum tubes. These are used as electronic switches, to permit the other signal to go one direction, then the other. They are controlled by the signal being mixed. They are especially popular with digitally-controlled radios.
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