Hi folks,

I've been delving deep into capacitors as of late. The two equations (Q=CV & E=CV

^{2}/2) have been bugging me.

The first one is a linear relationship, because as capacitance or voltage increases then charge increases linearly.

The second one is an exponential relationship, because as voltage increases then energy increases exponentially.

If it is possible to increase voltage in a linear fashion then we effectively gain the difference between CV and CV

^{2}/2.

Most voltage multipliers work in a linear fashion. As the number of stages increases then the voltage increases by the source voltage, e.g. if source voltage was 12V and we had a 5 stage multiplier (Greinacher/Cockcroftâ€“Walton multiplier, Dickson charge pump etc.), then the voltages across each stage would be 12V, 24V, 36V, 48V, 60V, 72V (I'm deliberately ignoring any circuit losses, diode voltage drops etc.).

I then found something called an exponential voltage multiplier which piqued my interest. In an exponential voltage multiplier, each successive stage doubles the preceding stage's output voltage. For example, if the source voltage was 12V, and again we had a 5 stage multiplier, then the voltages across each stage would be 12V, 24V, 48V, 96V, 192V, 384V.

European patent application 88305898.4 - Compensated exponential voltage multiplier for electroluminescent displays made for very interesting reading. It describes in fine detail a scheme to multiply voltage like I described above.

In short, the example in the patent starts with a 2.5uF capacitor and 15V source voltage. It has 5 stages and halves the capacitance and doubles the voltage for each successive stage. Ultimately it ends up with 0.04uF (actually 0.03906uF) charged to 960V.

2.5uF charged to 15V has 0.0000375 Coulombs and 0.00028125 Joules.

0.03906uF charged to 960V has 0.0000375 Coulombs 0.018 Joules.

You can see that there was a deliberate action in the patent to halve the capacitance when the voltage doubled. This maintains the charge at a constant level through the pipeline of stages. The energy, however, increases exponentially. The output energy is 64x the input energy.

You can have as many stages as you desire, and increasing the frequency increases the output voltage according to the patent.

The secret seems to be in the control scheme. It's a bit cryptic and I'm trying to decypher it at the moment. I've put together a simulation and it isn't working entirely according to the patent, but that's because of the logic that I've implemented so far. The voltage is indeed multiplied in the first 3 stages, but at the moment the last 2 stages are ouputting the same voltage as the 3rd stage. Some more work to do.

Firefox just crashed, so I lost some work. Argh! I'll be continuing the simulated circuit this evening and hope to post an example later.

Seems promising so far.