Step 5: The 'Impossible' Joule Thief
A few changes allow this to happen: First, the coil must have a Secondary with at least 3 times as many turns as the Primary, and the LED is connected between the Base (-) and the Collector (+) of the transistor. The circuit cannot start at this voltage, but, once given a jump (with a 1v jolt), it is very stable, drawing a measly 7-milliAmps from the supply.
A look at the scope's reading tells us how it works. The top (yellow) trace shows the voltage slowly growing, which increases the drive on the Base, forcing the transistor to conduct harder. This stops when the supply cannot drive the coil any more. The base drive disappears, the field collapses, producing the pulse. This induces a negative pulse on the Base (Blue trace) which is 3-times greater. By placing the LED across this, it has enough power to light, if dimly. The falling edge of the pulse pushes the transistor back into conducting mode and the cycle continues.