Finding the resonant frequency of a Tesla coil secondary
To get the best results from a Tesla coil, the primary and secondary need to be in tune, that is, oscillating at the same frequency. The secondary coil has its own resonant frequency based on its inductance and self-capacitance, and we tune the primary circuit (by adjusting its inductance and capacitance) to match this frequency. Today I’m going to find the resonant frequency of my newly wound secondary and also measure its Q factor, which is essentially a measure of how efficient the coil will be. See Q factor for more detail.
I cover the winding process for this secondary in a separate post.
Background
Resonant frequency is the natural frequency at which an LC circuit oscillates most efficiently. For a Tesla coil secondary, it’s determined by the coil’s inductance and capacitance, and represents the point of maximum voltage gain.
Q factor (quality factor) is a measure of resonance sharpness and energy efficiency. Higher Q means lower losses, narrower bandwidth, and higher voltage amplification. It’s calculated as \(Q = \frac{f_{\text{resonant}}}{\text{bandwidth}_{3\text{dB}}}\), where bandwidth is the frequency range between the half-power (-3dB) points.
Setup
To determine the resonant frequency, I’m using an oscilloscope with a built-in function generator. To find the Q factor, I’ll use the 3dB bandwidth method. The diagram below illustrates the basic setup.
Finding resonant frequency
The secondary coil acts as an LC circuit, with inductance from the winding and capacitance from the coil’s self-capacitance plus the top load. By sweeping the function generator from 200–500 kHz and measuring the voltage response, we can identify where the coil naturally resonates.
For this approximately ~823-turn, 80mm diameter secondary (turn count determined from measured resistance and wire specifications), resonance occurs at 430 kHz — shown by the peak voltage response in the centre image below.
| 420 kHz (below resonance) | 430 kHz (at resonance) | 440 kHz (above resonance) |
|---|---|---|
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Effect of body capacitance
One interesting phenomenon: when you’re near the coil, your body introduces parasitic capacitance to the circuit. This shifts the resonant frequency lower and reduces the Q factor. The video below demonstrates this detuning effect in real time.
Measuring Q factor
Todo…