Tesla Secondary Simulation Project |

This project was started in May 2000 with the aim of exploring the fascinating
physics of self-resonant single-layer solenoids as used for Tesla transformer
secondaries.

We maintain a precision software model of the solenoid which is based on our
best theoretical understanding of the physics. This model
provides a platform for theoretical work and virtual experiments.

Site Contents |

Model
Modeling software.

Software Map
A summary of the project's software.

Theory Notes
Secondary Basics - pn2511.

More Theory Notes
Resonator Theory - pn1401.

Examples
Voltage and current distributions.

Virtual secondary database
A database of simulated secondary performance.

Various Formulae

Time domain modeling

Mode analyser
A program for analysing TC scope waveforms.

Stress Factors
Secondary voltage stress factors.

Equivalent Series Inductances
Tabulation by secondary shape.

Gallery
Simulations, animations, and sounds.

Coil models
A close look at the tuning of some coils.

Q Variations
Experiments looking at variation of secondary Q-factors.

GeoTC
A Javascript library for TC reactance calculations.

Miscellaneous

Introduction |

Tesla coils have been in use for over a century for high voltage testing,
particle accelerators, and other applications requiring upwards of 100 kV
at low to moderate radio frequencies. They are also capable of producing
entertaining displays of electrical discharges and their construction
has been developed to a fine art by several generations of dedicated coil
building enthusiasts. Despite this, there are many aspects of Tesla coil
design and operation which still appear to present a mystery, and in some
cases a great deal of poorly supported folklore has built up around them.

This project is an attempt to gather reliable information about just one
of these topics - the physics of Tesla secondary resonators.

Consisting of a close wound single layer air cored solenoid resonating at
its lowest self-resonant frequency in conjunction with a ground plane and
charge storing topload, the coil is excited either by a continuous wave
source, or by a power compression circuit usually consisting of the spark
triggered discharge of a storage capacitance. Each type of operation
places its own particular requirements on the secondary coil design,
and one of the aims of this project is to clarify these requirements by
examining and understanding the detailed behaviour of the resonator in
both of these modes of operation.

Some of the difficulty with understanding Tesla coil operation follows
as a result of the poor understanding of the resonant behaviour of close
wound solenoids. This research project aims to correct this deficiency,
by putting together a comprehensive quantitative theory of resonant
solenoids.

Progress and Conclusions |

We have established a set of differential equations which describe the
operation of a solenoid and we have demonstrated that the solutions
for small signal CW operation adequately predict the outcome of careful
measurements on Tesla resonators. From these fundamental equations of
the coil, we can put forward unambiguous definitions of the effective
secondary capacitance and other useful equivalent reactances, from which
a number of interesting and informative relationships are derived [pn2511], including precise expressions for
the input, output, and transfer impedances.

A detailed computational model has been set up for the precision
simulation of Tesla resonators. [model]. This
frequency domain, small signal model accurately predicts the spectrum
of resonant frequencies - better than 1% accuracy can be achieved up to
the 9/4 wave resonance and the model provides qualitative information
for higher frequencies.

The model has been applied to the task of mapping out the
performance of secondary resonators in small signal CW operation [vsd], from which semi-empirical formulae have been
obtained for the resonant frequencies and effective inductances [formulae].

Descriptions of the secondary resonator, and dual resonator Tesla coil,
have been derived in terms of integral operators. The integral equations
turn out to have the same mathematical form as those of the elementary
lumped approximation, except that the components of the lumped circuit
are replaced by the corresponding integral operators. These lead to an
eigenequation for the normal modes, the solution of which provides the
basis functions from which the time domain response of the resonator
is computed.

We have found that, contrary to commonly stated opinion, the longitudinal
capacitive coupling of the solenoid is a significant factor in determining
its behaviour, accounting for the bulk of the capacitive energy storage
at the higher modes. We find that longitudinal mutual capacitance works
to reduce the higher mode wave velocity and is the major influence
on dispersion. We also find that mutual inductive coupling acts to
raise the effective velocity at higher frequencies. Only when both
factors are taken into account can accurate predictions of the higher
mode frequencies be obtained.

The inability to predict Q factor persists and highlights both the lack
of an effective model of winding losses at high frequencies, and the
difficulty of quantifying all the other contributions to the energy loss
budget of the resonator.

Current Work |

After a couple of years of studying the linear behaviour of the TC, the main
thrust of the project now addresses the interaction of the coil with its
breakout loading. The main target is to model the formation of inhibited
leaders sufficiently well to predict breakout voltages and leader lengths.
Examination of the response of the system to transients induced by arc
discharges from the topload is also of interest.

For more detail, there is a
Things-to-do List.

Acknowledgments |

If you have found anything useful in these TSSP web pages, then it is due to the efforts of the following Tesla coil enthusiasts.

- Mark Rzeszotarski, Marco Denicolai, Marc Metlicka, Kurt Schraner, Bart Anderson, for their valuable contributions of careful resonator measurements. Anyone who has carried out accurate measurements on Tesla coils will appreciate the effort required to achieve reliable results.
- Terry Fritz, who despite being moderator of the busy pupman coil building list, somehow manages to find the time to carry out some long and careful experimental tests. Terry has been responsible for much of the experimental work necessary to validate the conclusions of this project.
- Malcolm Watts, Bert Hickman, and Boris Petkovic, for contributing some of their vast experience of Tesla coils, and for their vital help in ensuring that the work of this project conforms to the established laws of physics.
- Paul Nicholson, for software and documentation.

and also to several others who, by keeping an eye on things through the mailing list and occasionally chipping in, help us to feel that these efforts are relevant and worthwhile to the Tesla coil building community.

Maintainer