# Calculating capacitance for high voltage doublers

I am working on a power supply for a tesla coil, and keep having really annoying problems with MOTS (microwave oven transformer).

We have a bunch of microwave capacitors and diodes, which we are attempting to increase the voltage with those, plus two little 1nf 10kv caps in parallel with the diodes.

Weird problems

So we decided to fire up a voltage doubler, and the results were amazing! We had arcs finally breaking way over a foot and a half, but unfortunately, one capacitor failed, and we realized that maybe it is a good idea for a safety gap!

So, we replaced the capacitor with something a tiny bit off value (like from .9µF to .8µf) and the arcs were horrible, they started at a few mm and broke at a few cm.

So what is making a huge difference with the caps just a tiny bit different in value, and how can I calculate the right capacitor to use?

Does it have to do with resonance?, because I can get the inductance of the secondary with my handy LCR meter.

I left the MOTS at school and I forget the exact secondary inductance, but I believe it was in the Fifteen Henry ballpark.

Schematic:

• Please post a schematic and/or a photo of your current setup. Remember that people around here help for fun, and guessing a schematic or a setup is little or no fun. Apr 27 '14 at 12:49
• @VladimirCravero sorry about that, added a little schematic; ignore the stuff to the right of the red line Apr 27 '14 at 12:56
• no problem. just add references in your question to the parts now... I believe you have changed $C_m$ but that's not so clear. If possible for such a setup a photo would help too... And would definitely be cool Apr 27 '14 at 13:00
• My guess would be that you actually blew both of the Cm capacitors, but only one of them showed physical damage. Have you measured them? Apr 27 '14 at 18:08
• i'll measure tomarrow. I believe one worked though, the other was a dead short, and I am pretty sure I measured it. Apr 27 '14 at 20:35

The quality or limit to current in the secondary will be based on the ESR of Ct and Primary of Tesla coil. Tesla's patent, indicated only use high quality Mica Capacitor material

My recommendation;

Ditch the ceramic cap and look for high quality mica material or cap made from same.

Get a platinum tip automotive sparkplug which should arc at 8kV in air or adjust gap to desired protection level. Keep in mind that ionization has a time lag and overvoltage will occur before air gap protects the capacitor. Consider using spark plugs for all your gaps and tune the gap for the desired breakdown voltage.

The ESR of the gap will drop with rising current due to current density. This has a negative differential resistance and the value of this negative ESR also limits current, where a very low negative ESR generates very high V = L di/dt into the coil.

Higher Resonant frequency is better and just as important as ESR of all the elements in the Tesla primary coil loop.

So ideal is ESR is infinite with open gap and 0 Ohm during ionization, thus di/dt becomes infinite. In practise di/dt is limited by stray capacitance and self capacitance of Tesla coil( which determines self resonant frequency (2PI*f)^2=1/LC (impulse response will show this on floating scope probe shunted to ground clip as a small a loop antenna) and I is limited by ESR or effective series resistance. For better scope results use 1 turn coil around current path and terminate 50 Ohm coax with 50 Ohms at scope. THis will yield rise times of <1ns and low voltage into 50 Ohms from which you can now calculate power of the pulse as V^2/50*t, where t= PW50

So in summary, high self resonant frequency coil and low ESR mica caps and spark plug protect any caps used to prevent failure ( which results in carbon trees)

A poor substitute for Mica may be thick film Plastic like Polyester, Polyurethane which are expensive much better than ceramic for ESR and leakage. (Edit, Your MOT caps are probably one of these. the second stage Tesla air core step up transformer with the Donut terminal on top for reducing E-field gradients ought to extend your arcs to 10x what you are getting now from the MOT. If you create a free-space antenna grid you can also capture energy from static electrification and generate even greater energy pulses with a resonant pulse and single panel antenna grid as air gap capacitor to earth >10m below) If you perfect this, you might even get it to self resonate sustained arcs without 120Vac ;)