The resonant frequency of this arrangement is determined by the values of the ballast inductance L and the tank capacitance C. The frequency is not affected by the winding resistance R or any resistive ballast added. (Typically the resonant frequency will lie between 10Hz and 500Hz.)
Resonance will occur regardless of whether the transformer is ballasted at the primary or the secondary, but it is easier to understand if we assume the ballast inductance is in series with the secondary side of the transformer. If this assumption is made then we can consider the HV transformer as presenting a stiff HV supply so the circuit can be simplified to get that shown on the left. The values of L and R are derived from an actual 10kv/100mA Neon sign transformer.

It demonstrates four things:-

1.It shows how important it is to use correctly set safety gaps to prevent excessive voltage rise if using a capacitor which is close to “matched” size.
2.It shows that the tank capacitance effectively cancels out the ballast inductance near the resonant frequency. In this example at 50Hz the current is 2A which is the result of current limiting by only the winding resistance. The inductive ballasting effect of the magnetic shunts is eliminated.
3.It shows that current will be drawn from the supply even though no power is being taken from the system yet. (There is no spark gap to discharge the capacitor.) The current flowing is reactive current and represents energy “sloshing” in and out of the tank capacitor as it is charged in opposing directions by the positive and negative cycles of the supply.
4.It shows the “shape” of the LC resonant response before the effect of a spark gap is introduced.
The addition of a correctly set spark gap will limit the amount of voltage rise permitted whilst still getting the benefit of the increased charging current.

Resonant charging can take place with both neon sign transformers and inductively ballasted power transformers. The only difference is that the ballast is built into the neon transformer. Power transformers, however, have much lower internal losses. This results in a higher Q value and causes more intense voltage and current rises around the resonant frequency.

Due to the intensity of the resonant rise effect, it is not always desirable to use a “matched” capacitor which causes resonance at exactly the line frequency. The graph below shows the effect of using “smaller than resonant” and “larger than resonant” capacitors on the same 10kv/100mA neon supply. (The supply still has no spark gap connected, only the tank capacitor.)

Spark gap misfires,

Because resonant voltage rise thrives on time, (time required for the voltage to build-up,) it is worth considering what would happen if our spark gap was to accidentally miss a firing. If a rotary gap misfires, there cannot be another firing until the next time that the electrodes are aligned. This means that when a firing is missed there is twice as long between discharges of the tank capacitor, and this allows the voltage to ring up to a higher voltage.

Computer based simulation packages such as PSpice are ideal for predicting what would actually happen in such circumstances without risking any expensive components.