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# What Capacitor size for a 4 stack MOT Tesla coil?

I have just bought a 4 stack MOT transformer in a case and oil filled it says 8.6kv on it but no idea of amperage, I have a large variable ballast and hooked it up to my test jacobs ladder and it pulls about 10amp and really fires the ladder well.

My coil has a 6inch by 29inch winding on the secondary and a Synchronous spark gap (200bps) but I cant seem to get a decent spark off it

I have an MMC of 44.0nF @20kv at the moment

## Discussions

4 years ago

That depends on the resonant frequency of the secondary and the inductance of the primary. Once you know the inductance of the secondary and the capacitive loading on it (partially determined by the topload as well as surrounding objects), say it is 100KHz, then you can calculate the inductance of the primary by the number of turns used (relative permeability of air), and using the resonant frequency formula you can calculate the final capacitance value needed for the LC circuit to ring at the right frequency to achieve the largest sparks.

However, as you might notice, there are a lot of unknowns here, and not even taking into account parasitic properties of any of the components. IMO the secondary capacitance is the hardest to figure out because it is entirely dependant on the surrounding. And what this means is that the coil needs to be tuned when in different conditions, and even with different power level outputs! (the circuit will detune as the size of the sparks increase.)

To get the inductance, you can use the formula L = (µ*N^2*A / l )where L is inductance, µ is permeability of the transformer core, in this case air (1), N is the number of turns, A is the cross-sectional area of the coil, and finally l is the length of the coil. That is a lot, but luckily there are calculators online to allow you to cheat on the math and get answers quicker.