The voltage doubler is based on the charge-pump principle of operation. A charge pump is a kind of DC-to-DC converter that uses capacitors for energetic charge storage to raise or lower voltage. Charge-pump circuits are capable of high efficiencies, sometimes as high as 90–95%, while being electrically simple circuits.
The circuit needs square wave pulses to drive the converter transistors. The frequency could be between 10-100KHz. Higher frequency gives lower output voltage ripple if capacitors stay the same. The pulses could come from a microcontroller or a simple hcmos rc oscillator, fig.2 below.
R1 value depends on the peak value of the input pulse train and is calculated like this:
$$R1=(Upeak-V_[BEsat])/I_B$$ If we choose the transistor base current to be =0.5mA, VBEsat 0.8V and Upeak 3.3V we get:
It is important to drive the transistors fully on and off for max efficiency so it may be needed to increase the base current to 1mA.
Brief circuit description:
At startup C3 charges up to the supply voltage minus two diode drops.
When Q1 switches on Q2 turns off and C2 is charged to the input supply voltage trough D1. When Q1 turns off, Q2 starts to conduct, and it will pull the negative terminal of C2 up to the input voltage terminal. At this point C2 delivers its charge to C3 trough D3 and the voltage on C3 starts rising to almost twice the input supply voltage. Then this cycle repeats.
This circuit is amazingly efficient. The supply current is just slightly more than twice the supply current. In this example the efficiency is 90%.
This efficiency at this low output current is hard to beat using commercial boost switching regulators.