Analog computing question - how to implement X^Y=Z

[rtarbell]

An attempt at a thought provoking question for the analog computing types:

In the world of analog circuits, how would one implement the function

X ^ Y = Vout?

That is, a circuit block with two inputs, X and Y (inputs can be voltage or current). The output voltage (or current) is equal to the input X, raised to the power of Y (Y is also an input).

One way I can think of doing it is:

X ^ Y = exp(y * ln(x))

This uses a logarithmic amplifier, exponential amplifier, and one multiplier. Are there other ways/circuits to implement this function?

[zigzagflux]

They do make analog multipliers in integrated circuit form. On Semi used to, at least.

[jcx]

Analog Devices is a big player in analog function blocks:
Analog Multipliers/Dividers | Other Products | Analog Devices
also look for log amps


but today single chip flash uC with ADC and DAC can give good results for applcations that fit the resolution and speed of the digital implementation

[SoNic_real_one]

One log amp for the X signal (X needs to be positive).
The result feed into a multiplier with Y.
The third result fed to a good OpAmp that has in the feedback network another log amplifier (to result the exp function).