Is there a circuit for precise microwatt power regulation with variable load?

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A circuit is needed for precise microwatt power regulation with a variable load, ideally using a small shunt resistor to obtain a voltage proportional to output current and an analog multiplier IC to regulate output voltage. The challenge lies in operating within the microwatt range (e.g., 10mV across 100 Ohms) while maintaining acceptable accuracy, as existing multiplier chips are typically designed for higher voltages. The discussion highlights the importance of understanding the dynamic nature of the load and suggests that low-power op-amps can be utilized for effective regulation. A proposed solution involves logarithmic amplifiers and a comparator for preset regulation, with a desired output range of 5-500 µW. Modifications to existing circuits may be necessary to achieve the desired performance.
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I am looking for a circuit that takes a voltage to preselect a power and than outputs that power through a variable load.

I have already seen a circuit that does this. The setup is easy:
You take a small shunt resistor to get a voltage proportional to the output current, and you also take the the output voltage, and multiply the two voltages together with an analog multiplier IC. The multiplied voltages you compare with the input voltage and regulate the output voltage with an op amp accordingly. This might sound confusing but it's very easy.

My problem is this: I need to do this in the microwatts range with a load that's R<100 \Omega the multiplier chips I saw seem to be constructed for input of maybe U = 3V and the absolute errors look unacceptable.
Can anyone recommend a circuit or a chip?
 
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Can you post the range of output voltages and currents you are wanting to control and monitor? A microwatt would be 10mV across 100 Ohms (100uA). How much above and below those voltages and currents do you want to go?

How dynamic is the load? Can it vary with some frequency, or is it set and stays that value for a while?
 
I think the main dynamic range limitation of analog multipliers is the output circuit which is an anti-log curcuit. The two input channels are logarithmic amplifiers (matched diodes in the feedback loop-I have used transdiode connection) which are added in a regular summing junction configuration. This output has a high dynamic range. All three opamps can be low power. need to run this into a comparator for preset regulation. This is good enough to use as a control function.
 
I think I already have a kind of solution now. But just to give you an Idea. Maybe I'd like to give something like 5-500 \mu \mathrm{W} on a 100\Omega. The input voltages for the circuit should be maybe 0.1-1 V the working voltage can be whatever.
This should work with some modification: http://electronicdesign.com/Articles/ArticleID/14194/14194.html
 
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