The Joule Thief is a delightfully simple circuit that can light an

LED that requires 2V or more from a battery that is depleted to 1V or

less. There are three components in addition to the battery and LED: an

NPN transistor, a resistor and a double wound inductor. The key thing

about the inductor is that the same core shares two windings but in

opposite directions.

The explanation of how it works is simple enough, as long as you

already understand how inductors and transistors work. In other words,

it isn't simple at all! In short, the double wound inductor and

transistor conspire to generate a transient high voltage spike and so

turn LED on and off so rapidly that the human eye cannot perceive

it.

The idea of such a circuit is approaching its centenary but the name

itself is only around 20 years old. I recommend you check out Big Clive's web site as it was

he who came up with the name "Joule Thief". I also recommend this video in

which he constructs a circuit using some ninja-level soldering

skills.