An electronics circuit which performs multiplication of two or more analog input voltages is called **analog multiplier** circuit. Multiplier circuits are used in mathematical operation like squares, square root extractor, frequency doublers etc. Such mathematical operation is required in variety of application like in communication circuit such as amplitude modulation, phase modulation, frequency modulation, phase detection, instrumentation and control application used to measure velocity, acceleration, automatic gain control, instantaneous power, true rms calculation, rectifier phase shift detection, in oscillators circuits, solve non-linear calculation and others.

Another application of analog multiplier circuits is in instrumentation
and control circuits, where they are used to measure various parameters
such as velocity, acceleration, instantaneous power, true RMS
calculation, and phase shift detection. They are also used in
oscillators circuits to solve non-linear calculations and in other
circuits requiring complex mathematical operations.

An analog multiplier is designed using log and antilog amplifiers and summing amplifier. The following shows how analog multiplier circuit diagram.

In the circuit above the op-amp 1 and op-amp 2 are log amplifiers which produces logarithm of the input signals V1 and V2 respectively. The output of this log amplifier is summed by the op-amp 3. The sum of two log signals is equivalent to multiplication of the two signals V1 and V2. In the final stage, the antilog or exponential amplifier 4 transforms the log(V1V2) into voltage multiplication of V1 and V2.

In the above log and antilog amplifier used can either be designed with diode or transistor. These amplifier were explained in the following tutorials.

- How does Log and Anti-Log Amplifiers work?

- How does Log Amplifier using transistor work?

- How does Antilog amplifier using Diode work?

- How does Antilog Amplifier with Transistor work?

In conclusion, analog multiplier circuits are an essential component of
modern electronics and find application in a wide range of fields such
as communication, instrumentation, and control. They are used to perform
complex mathematical operations like multiplication, squaring, and
square root extraction, making them an indispensable tool for engineers
and scientists.