analog - Is there an amplifier such that the gain is equal to the ratio of two potential differences?

I have been toying with some alternatives to transistors in building logic gates. I am particularly interested in the device I tried to summarize in the title of this post. The chip would have 8 pins: pins 1,2: voltage difference_1=V1 pins 3,4: voltage difference_2=V2 pins 5,6: power=V3 pins 7,8: output=V4

Essentially, I want: V4=(V1/V2)*V3 I would be happy with the following as well: I4=(V1/V2)*I3, with I=current (and I may ask about that in a separate post)

Answer

There's the AD734 -- not cheap but it should do what you want. (The U input isn't high-impedance; you have to drive it in a feedback loop.)

If you can deal with positive inputs only, and convert them to currents, you can do this with discrete transistors over a fairly wide range. (I tried and failed to find a reference -- basically you have a voltage loop where you take advantage of the logarithmic relationship between current and Vbe of a bipolar transistor)

edit: see Analog Devices appnote MT-079 for some more thoughts