The standard analog multiplier circuit (i.e. multiplying two
analog signals to generate a product analog signal) sums the logs
of the inputs then takes the antilog to form the output. The log
and antilog functions are approximated using the base-emitter curve
of transistors. The rest of the circuit is opamps, which have
emitter coupled differential transistor amplifiers at their core.
This however is limited to positive values only, and is called a
one quadrant multiplier.
Perhaps you are asking instead about a type of analog multiplier
using two cross-connected emitter coupled differential transistor
amplifiers and several constant current sources for bias. The main
advantages of these is they can correctly handle negative numbers,
and are thus called four quadrant multipliers, and they are almost
trivial to integrate compared to the opamp version.