Micro energy harvesting battery charger

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I am looking for a circuit topology to be used as a micro power energy harvesting battery charger.

Here are the requirements:
An input impedance that is fairly constant in the 500 to 1000 ohm range;
The output would be a near constant voltage in the 1 to 5 volt range;
The output current would be rough proportional to the square of the input current.
The power handling ability to be in the 10 to 200 milliwatt range.

I am thinking of using a SMPS with some sort of nonlinear feedback element to make the output current roughly the square of the input current.

Is this possible?

If the input impedance is constant, the input current will be proportionally with the input voltage.
Their product (the input power) will be proportional with the input voltage.
Output voltage being constant, the current delivered can be only proportional with input voltage. This of course, considering efficiency close to 1.

If you are looking for supra-unitary devices, these are simply not possible.
Maybe if you give us more details we can understand what you actually want and we can help you. (if is not what i said, supra-unitary device).