Below is a proof of concept circuit which needs improvement. The part values shown will run a high efficiency red LED with a Vf of 1.9V from only 2 nicads, right down to 2 volts. For a white LED you will need more batteries and you must increase the 1.0K resistor to a higher value. Current sensing at a mere 18mV over 1ohm makes this stepdown switcher efficient, but efficiency can be increased by using a larger inductor, improving transistor switching speed, or by increasing the value of the 1.0K resistor. Positive feedback from the driver transistor back into the current mirror through the 47K hysterisys resistor ensures that this circuit behaves as a switching power supply, however it could be used in linear mode if this resistor and the inductor were removed. The two transistors in the current mirror should be somewhat matched, in other words they should be by the same manufacturer and manufactured around the same time. Swap the two transistors if you have any trouble.
If the battery voltage exceeds the 18mA Vf of the LED by 100mV, the voltage accross the 1ohm current sense resistor is picked up by the current mirror and the circuit starts to buck through the inductor.
I do not gaurantee the accuracy or safety of any information herein.
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