Joule Thief Operation and Formula
I've been researching the self oscillating boost converter for a few days now. The technical name for it's operation is boundary conduction mode / Critical conduction mode.
The absolute value of the inductor is not critical as long as it is big enough (> 50uh). The inductor will only affect the frequency that the circuit runs at - bigger = lower frequency.
The important thing is to get a suitable switching transistor with a low Vce(sat) at the peak current the circuit operates at.
If you know what load you want to drive then you can calculate the peak current easily enough. You only need to know the wanted output voltage, output current, saturation voltage of the transistor, forward voltage of the rectifier (for a smoothed output) and the input voltage.
Output power = output voltage x output current
To get the peak current the formula is:
Ipk = Po ( ( 2/(Vs - Vce )) + ( 2/(Vo - Vs + Vd) ) )
Where:
Ipk = Peak current.
Po = Output power.
Vs = Supply Voltage.
Vce = Transistor saturation voltage.
Vo = Output voltage.
Vd = Output smoothing diode forward voltage.
I have built a joule thief type circuit, measured the voltages and currents and the formula gives roughly the right answer. I say roughly due to the use of a not to accurate old oscilloscope used for the peak current / saturation voltage measurements. At low voltage, a small error in the transistor saturation voltage will have a large impact on the calculation of the peak current. A small re-arrangement of the above formula can give you the likely maximum output power if you can measure the peak current.
Trying to set the peak current in a practical circuit is the difficult bit as every transistor has it's own value of gain, meaning that the base drive resistor needs to be adjusted for a particular transistor. The power supplied to the circuit from the battery will be higher due to losses. Using a good switching transistor and a fast diode will help minimise the losses.
Hope this is of use to someone....