The single cell led flashlight circuit is a self-oscillating boost converter. A typical white LED has its best power-efficiency combination at about 20mA, and needs about 3.3V. This makes for a power of about 66mW per LED. In this circuit are 7 series LEDs so we need a driver circuit that will provide about 23V at 20mA, when fed from a 1.2V NiMH rechargeable cell or from a 1.5V alkaline cell. When switching it on, R1 and D1 bias the transistor into the linear range, through the feedback winding on T1. That causes a current through the 18 turn winding, and thanks to the positive feedback the transistor is driven into saturation. At this moment there will be a base current defined like this: The 1.2V of the cell, plus the 0.2V induced in the feedback winding, minus the 0.7V base-emitter drop of the transistor, make a total of 0.7V, which applied to the 22 ohm resistor gives about 32mA base current. D1 is not conducting a significant current at this time, because the transistor clamps the base voltage to 0.7V and the 3 turn winding subtracts 0.2V from this, so that we end up with only 0.5V across the diode. This base current keeps the transistor in saturation until its collector current reaches approximately 1A, while the transformer loads up. At this point the transistor will start getting out of saturation, which makes the feedback voltage drop. This very quickly puts the transistor into blockage. The collector voltage will soar as T1 forces current to keep flowing, until D2 starts conducting and discharges the transformer into C2, by means of a quite narrow pulse. During operation this pulse is about 24V high, so that the feedback winding develops -4V, which results in applying about -3.3V to Q1′s base, enough to switch it off very fast, but not enough to make the base reverse-conduct. As soon as the transformer has fully discharged into C2, the voltage on it breaks down, and the transistor enters conduction to start a new cycle. The oscillating frequency is 30kHz, and the transformer operates at a peak flux density of 0.1 tesla, far away from saturation, and low enough to have very low loss. C2 has to eat the load pulses that start at about 1A, and has to keep the voltage constant enough to feed the LEDs an almost smooth DC. The value given works well. If anyone wants to build this circuit to run 24 hours a day for 30 years, it would be good to pick a capacitor rated for low ESR and a relatively high ripple current, but for flashlight use a plain standard 47μF, 35V electrolytic capacitor works great. C1 is not strictly necessary. With a good NiMH cell, the circuit works the same without it, so you can save a few cents here. But with the capacitor in place, the circuit keeps working better when the cell is almost fully discharged and its internal resistance gets higher, so it’s better to include it
