The time domain modeling must determine what modes are available to the Tesla coil, their frequencies, Q factors and current profiles. It must then determine what composition of mode amplitudes and phases are required to match the starting conditions of the resonator. Finally, the predicted waveform and its Fourier spectrum can be generated.

As an end-to-end cross check on this whole process, a predicted secondary base current has been compared with actual waveforms as measured by Terry Fritz. These tests were carried out at low voltage using a solid state gap. This web page compares the results.

Test setup
Secondary base current was captured at a time resolution of 20nS, and modeled at the same time resolution. Raw data CSV 10k records, 174k bytes.

The coil was modeled at a spatial resolution of 500 steps for Cext, 300x300 for Ms, 32x32 for Cint, 1x300 for Mp, and 250 for Ctor.

We see reasonable agreement with the overall beat envelope, which indicates that the primary coupling is correctly determined. Slight error (~0.5%) in the frequencies of the first two modes results in a gradually increasing phase error across the trace. The primary loss resistance has been adjusted to match the observed decay rate - 0.3 ohms was required.

A good match is achieved on the first cycle of the base current, which is far from sinusoidal. The initial negative going transient, followed by a recovering ramp upwards, in which the 3rd mode is prominent, are reproduced in the model.

At the first base current notch, we again see a glimpse of mode 3 coming through, although by now the calculated phase is beginning to deteriorate. By the second notch, the phase of the higher modes is effectively random, and the amplitudes computed by the model are higher, due to the model's tendency to over-predict the higher mode Q factors. In the actual coil, these are decaying rather more rapidly.

The graph below shows a Fourier spectrum of the above waveforms.

The error in placement of the higher modes gradually increases with frequency, due mainly to the limited spatial resolution (32x32) of the internal capacitance determination. As a result, the model cannot be expected to predict the precise phase of the higher modes, beyond the first few cycles. Note the over-prediction of amplitudes for the 4th and higher modes. These are decaying rather more rapidly in the real coil.

The measured spectrum is exhibiting some intermodulation on components with less than 1% amplitude, as well as a clear second harmonic of the main two modes, at around -50dB. We cannot determine without further measurements whether these components arise from non-linearity in the coil or the instruments. Some rectification is occuring, as evidenced by the component appearing in the measured response down at the beat envelope frequency.

The quality of the measured traces, in terms of their low noise and freedom from interference, demonstrates the advantage of using a solid state gap for this kind of experimental work.