Are there well known simple operationnal amplifier circuits designs to make purely analog squaring amplifier (for experimental analog computing)?

Question

In order to make analog calculation (for analog regulator simulation), what would be the means to make an squaring amplifier ?

• There is an obvious solution with a multiplier circuit as pointed here;
• I also imagined using a mosfet like in the following drawing and in this case I would need another similar circuit for the negative part of the signal;

but before trying to effectively design it, I wondered if there would be other well known simple solution.

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Edit : Some people seem to dislike the application of analog computing. Just think of it as an educational application.

Edit2 : To make things more precise, let's say that to avoid saturation problems, the identity element would be 10v, So for a 1v input we get a 0.1v output and for a 0.1v input, we get 1mV output, and it would be even better if we had a circuit which would give the same positive output for the same negative inputs.

Answer 1

This circuit will do squaring. I leave calibration, and temperature compensation, to you.

What is the bandwidth? at 1mA input, the 2N3904 will have about 40pF Cbe (computed from Ftau). With 100 ohm resistors, thus 4nanosecond Tau on nodes, BW is about 40MHz.

^{simulate this circuit – Schematic created using CircuitLab}