The mathematical equations which describe the operation of the resonating solenoid are too difficult for us to solve analytically. We therefore rely heavily on a numerical computational model as a means of generating testable predictions of resonator performance. This page introduces that model.
This is a precision model of a closewound single-layer solenoid with
a non-conductive core, operating perpendicular to a ground plane -
the configuration typically used as a resonating secondary in Tesla coils.
We employ a non-uniform transmission line model extended by additional current and voltage injections to enable accurate representation of the solenoid's longitudinal coupling due to internal capacitance and mutual inductance. A detailed capacitance matrix is obtained from the geometry of the resonator and its surroundings by means of a boundary element method, and the mutual inductance profile is generated by summing contributions from elementary current filaments. The software solves the integral equations of the solenoid in the frequency domain for steady state operation, and in the time domain for impulsed operation. The model will compute the normal modes of single and dual resonator configurations, along with the time domain response to a given set of starting conditions.
The model has only two arbitrary constants which calibrate loss factors, and is otherwise constructed from reasonable physical models, parameterised by input measurements of only lengths and turns.
Factors taken into account by the model are:
As currently implemented, the software model:
At present, the model does not:
Estimate of frequency prediction error limits: 1/4 wave, +/- 4%; 3/4 wave, +/- 3%; 5/4 wave, +/- 3%;
Results of comparison tests.
Software Map An overview of the software.
Examples Voltage and current distributions.
The software at present is not available for download because several parts are still a work-in-progress. Documentation, too, is also limited, but if you really want to run it, please email to request a tar file of the C source, scripts, and makefile for Linux.