If I use a step up transformer (flyback for example) for primary to boost the voltage to 10 kV which (flyback) has a resonant frequency around 30-50 kHz, and the primary coil has a res. freq. of 500 kHz, does my primary still resonate at 500 kHz?
Does the capacitor change the resonance frequency of the primary coil? If yes, how to measure that?
Does it matter if I use AC or DC step up transformer for driving the primary with spark gap? What is the difference?
A flyback transformer is not a resonant transformer, so its output frequency (which, by the way, is not a resonant frequency) has less of an effect. In fact, most modern flyback transformers have a built-in rectifier diode, which means the output is DC. When using flyback transformers in Tesla coil applications, you usually use this DC to charge the primary tank capacitor. When the voltage across the capacitor reaches a sufficient voltage, the spark gap fires and dumps the energy from the capacitor into the primary coil. This LC circuit is what resonates at the resonant frequency. The output frequency of the flyback transformer, if used correctly, should not have much of an effect.
Posting a schematic of your setup would have been helpful, but since you didn't provide one I based this answer on the classic circuit that uses a transformer with a rectified output.
So here are your answers:
- If you use the correct circuit, the resonant frequency will stay the same
- The capacitor is the heart of the circuit and its interaction with the inductance of the primary coil is what creates the resonance. The formula is F=1/(2⋅pi⋅sqrt(L⋅C)) where F is the resonant frequency, L is the inductance of the primary coil, and C is the capacitance of the primary capacitor
- An AC transformer must be matched perfectly with the capacitor in order to make it as efficient as possible. The capacitor must have a capacitance that can be charged fully during each half-cycle of the AC wave. With a high voltage DC supply the cap takes as long as it needs to charge up, and the spark gap fires when it's ready.
In reality it's more complicated than this but this is the basic operation.