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)
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
I think an OTA (Operation Transconductance Amplifier, http://en.wikipedia.org/wiki/Operational_transconductance_amplifier) can do does at least the multiplication part of what you want, but it is far from a one-chip solution to your problem. Division of voltages seems to be a hard problem (and searching is difficult because the term 'voltage divider' means something else!). One approach would be conversion to a log scale, substracting, and conversion back to linear.
If your application involves just divisions and multiplactions it might be an idea to do everything in the log domain, convert ony at the inputs and outputs.
An example of an OTA is the LM13700 (http://www.ti.com/lit/ds/symlink/lm13700.pdf): two differential voltage inputs, and one current input that sets the transconductanes (== the multiplication factor), and the output is a current.
You did not state the accuracy, speed, range, etc you need. Within ceratin limits a microcontroller with 4 A/D inputs and one D/A output would do the trick nicely.
