esults of
that plan was asco, or maybe disaster. We had some sparks, but none where they belonged.
That was one of the most humiliating experiences of my career.
I learned several things from that experience. One is that the Tesla coil is more complex
than I had thought. Another was that there seemed to be a mismatch between theory and ex-
periment. At that time, at least, people would go through pages of high powered mathematics
and quit without giving an example of how to use all the formulas. Experimentalists would
sometimes make fun of the theorists, and give rules-of-thumb on how to make long sparks.
It was like I was hearing a debate on whether the best cooks use recipes or not. My mother
never used a recipe and I always enjoyed her cooking. However, my own talents are such that
if I am to cook anything t to eat, I need a recipe.
This book is written for people like me, challenged when faced with doing something
without a recipe or complete set of instructions. I will throw in things learned from other
Tesla coil builders, but will quickly admit that when it comes to making long sparks, there
are many who are far better than I.
I started asking questions about Tesla coils that any electrical engineer would ask. These
include:
1. What is the input impedance?
2. What are the fractions of input power that are dissipated in the spark itself, in elec-
tromagnetic radiation, the coil wire, the coil form, the toroid, the spark gap, and other
Solid State Tesla Coil by Dr. Gary L. Johnson
October 29, 2001 Chapter 1Introduction
12
circuit components?
3. Are there circuit models that allow these questions to be answered on the computer
before building and testing devices in open air?
4. What are the dierences between Tesla coils driven by or through spark gaps, vacuum
tubes, or solid state devices?
5. What are the important factors in producing long sparks (energy per bang, power input
at spark inception, rate of change of power, the coil, the toroid, etc.)?
One would expect the answers to these questions to come from a mix of theory and
experiment. One would develop a theory or model and then go to the laboratory to measure
parameters and check performance. The theory would then be adjusted to reect experimental
observations.
We now review a little Tesla coil history and look at the simplest model, the lumped
circuit element model.
1 History
Nikola Tesla (1856 - 1943) was one of the most important inventors in human history. He
had 112 U.S. patents and a similar number of patents outside the United States, including 30
in Germany, 14 in Australia, 13 in France, and 11 in Italy. He held patents in 23 countries,
including Cuba, India, Japan, Mexico, Rhodesia, and Transvaal. He invented the induction
motor and our present system of three-phase power in 1888 [20]. He invented the Tesla coil,
a resonant air-core transformer, in 1891. Then in 1893, he invented a system of wireless
transmission of intelligence. Although Marconi is commonly credited with the invention of
radio, the U.S. Supreme Court decided in 1943 that the Tesla Oscillator patented in 1900
had priority over Marconis patent which had been issued in 1904 [15].
Therefore Tesla
did the fundamental work in both power and communications, the major areas of electrical
engineering. These inventions have truly changed the course of human history.
After Tesla had invented three-phase power systems and wireless radio, he turned his
attention to further development of the Tesla coil. He built a large laboratory in Colorado
Springs in 1899 for this purpose. The Tesla secondary was about 51 feet in diameter. It was
in a wooden building in which no ferrous metals were used in construction [15]. There was
a massive 80-foot wooden tower, topped by a 200-foot mast on which perched a large copper
ball which he used as a transmitting antenna. The coil worked well. There are claims of
bolts of articial lightning over a hundred feet long, although Richard Hull asserts that from
Teslas notes, he never claimed a distance greater than 43 feet. From photographic evidence,
the maximum may have been closer to 22 feet [12].
Solid State Tesla Coil by Dr. Gary L. Johnson
October 29, 2001 Chapter 1Introduction
13
Tesla then abandoned the Colorado Springs Laboratory early in 1900, having learned
what he needed from that facility, and also having become somewhat unpopular as a result
of frequently knocking the local sub-station o line.
Since that time, it appears that no one has built a Tesla coil of both the size and perfor-
mance of the Colorado Springs coil. Apparently the only coil of that size was built by Robert
Golka at Wendover Air Force Base in Utah [8] and later moved to a facility near Leadville,
Colorado [9, 19]. The original purpose of this coil was to produce articial lightning for
testing the eects of lightning striking aircraft in ight. Golka determined that the average
voltage produced in Utah was about 10 MV, with the highest voltage observed being 25 MV.
Operation was spectacular, even if not quite at the level of the Colorado Springs coil.
When Golkas coil was moved to Leadville, however, it performed very poorly. Golka and
his associates were basically unable to properly tune the coil. There has been considerable
speculation over the reasons for the dierence in performance, but one problem seems to
be that we did not have adequate theoretical models for the design and operation of Tesla
coils. What appeared to be minor dierences in location and construction caused a major
decrease in performance. The number of variables was simply too large to allow for a purely
experimental optimization of performance before the coil was dismantled and moved early in
1990.
Some work on theoretical models has been performed by high energy physicists [6, 10,
1, 17, 18]. They are interested in high voltage capacitor discharges for research in plasma
physics and in the production of pulsed particle or radiation beams. The most common way
of producing such high voltage discharges is the Marx circuit, in which capacitors are charged
in parallel to a lower voltage and then discharged in series through a number of airgaps. The
Marx circuit requires the capacitor bank to be divided into sub-banks well-insulated from each
other and from ground. A Tesla coil oers an alternative method of charging the high voltage
capacitors. Discharges are reported in the range of 100 kA at 1 MV, with one report of 2.5
MV [10]. These models are all lumped parameter models.
There are a number of experimenters who build Tesla coils as a hobby. The Tesla Coil
Builders Association has several hundred members and a quarterly newsletter published by
Harry Goldman [7]. Harry has announced plans to stop publishing the newsletter at the end of
2001. The Tesla Coil Builders of Richmond has been a very active local group [11], although
their leader Richard Hull has recently become interested in other activities. A number of
manuals are available on how to build coils [16, 4, 5]. The one by Lee [16] is especially
well illustrated with pictures of capacitors and other components that might be needed for a
moderate sized Tesla coil. There is an Internet listserv (www.pupman.com) that has about
700 subscribers, which has been very helpful to me.
The brothers James and Kenneth Corum have done considerable work on distributed
models of Tesla coils in the past few years [2, 3]. They argue that lumped parameter models
are not adequate for all situations. Sometimes a distributed circuit analysis must be made. In
this case, the Tesla coil secondary and another component called the extra coil are considered
Solid State Tesla Coil by Dr. Gary L. Johnson
October 29, 2001 Chapter 1Introduction
14
as sections of transmission lines. This explains some of the eects in an elegant manner. They
have written a sophisticated computer program, TCTUTOR, to analyze Tesla coils. They
have also performed considerable historical research into Teslas notes made on his facility in
Colorado Springs [21].
The Tesla coil community is divided over the issue of lumped versus distributed models.
A majority favors the lumped model approach.
Some are outspoken in their belief that
distributed models are useless at best and just plain wrong on important issues. I confess to
being somewhere in the middle on this controversy. James Corum and I both have our Ph.D.s
in electromagnetic theory, so I can mostly understand what he says, and I therefore have a
natural orientation to the distributed approach. In my eyes, I am like a Baptist pastor of a
50 person congregation and James is like Billy Graham. That is, I hold him in awe. I have
heard the Corums speak several times, and have gotten caught up in their knowledge and
excitement.
On the other hand, I cannot honestly say that TCTUTOR has been helpful to me in
building and understanding Tesla coils. I can see signicant problems with distributed models,
which will be discussed later. And James, like many bright people, has a tendency to talk
down to us slow ones. This puts some people o, of course.
In this book we will look at both lumped and distributed models. We will point out
diculties with both.
We will look at some data, and ask which approach does best in
describing reality.
2 Classical Tesla Coil
A classical Tesla coil contains two stages of voltage increase. The rst is a conventional iron
core transformer that steps up the available line voltage to a voltage in the range of 12 to 50
kV, 60 Hz. The second is a resonant air core transformer (the Tesla coil itself) which steps up
the voltage to the range of 200 kV to 1 MV. The high voltage output is at a frequency much
higher than 60 H