Corums New Tesla Coil Theory Paper

Hi Bill and All,

At 02:41 AM 10/22/1999 -0600, you wrote:
>Original Poster: wysock-at-ttr-dot-com 
>To the Tesla List.
>First, I apologize, for any frustrations and inconvenience, in the
>original posting of Kenneth and Dr. James Corum's major paper
>on the subject of treating a Tesla Coil as a "lumped circuit
>analysis model" or a "distributed circuit analysis model."  Ken
>Corum has taken the appropriate steps, to make the entire article
>much more readable, as well as editing a few typographical 
>The reason this article appears on my web site, is in whole and
>part, because I personally support and defend the assertions and
>claims, made by both the authors; not to mention that the Corum's
>analysis work on Tesla has been, and continues to be, the subject
>of great debate, in the simulation, analysis and theoretical modeling
>realms of Tesla Coil design.

Many many thanks for making this paper available at:


I really like your web site,  straight forward and to the point.  You and your
Web Master have done a great job!

>This feature paper is published on my web site, with full permission
>and authorization from both of the authors, with the intent of
>shedding new light, on this subject.

I really appreciate the Corums making their paper available in this way!!  In
the past, their papers have been hard to get IMHO.  Putting it on the Internet
in this way makes the paper instantly available to everyone.  At one point, I
thought they just wrote these papers to earn extra money.  However, this very
public and free offering of their paper blows that theory out of the water.  I
hope that is the ONLY theory of mine to fall in all this!  :O)   Even though I
mostly find myself disagreeing with them, they certainly provide a catalyst for
some great ideas and discussions.

>Please do not e-mail me, with any questions, arguements or
>debates on this subject.  I have neither the time or energy to
>reply.  I simply am saying that I support the author's work
>and statements.

No problem!  We'll let you escape from being "caught in the middle" of this one
;-)  However, as far as I know, the Corums are not on this list (only Chip
knows such things if he bothers to try).  So you may want to pass on the
discussions as you see fit.  I know they are busy and all and don't like
getting into the arguing stuff....  That's cool.

Of course, "I" can't let this go without my comments on the paper since I am
sort of on the other side of the fence on this one.  I happened to know about
this paper and read it a week ago so I have had time to think about it more
than most.  I have also had limited discussions with Bill Wysock and Malcolm
Watts about it this week.  It is sort of awkward being the moderator when
something "controversial" like this comes along that I am involved in...  Of
course, this clarifies the "great division" in Tesla coil theory that exists
these days in a wonderful way for all to enjoy!

So, let's get it on!

"Terry's Thoughts on the Corum's New Paper" 

        I can't help but comment on the new paper by Kenneth and James Corum. 
The paper "Class Notes:  Tesla Coils and the Failure of Lumped-Element Circuit
Theory" directly disputes a number of modern ideas about Tesla coil operation. 
I would like to clarify "my" position on a number of the points raised in that

        Much of the paper's statements are based on the "coherence theory" or
resonant rise effects that the Corums have explained in previous papers.  This
theory states that when the primary arc is quenched, the secondary system will
be free to ring independently and the voltage rise will only be limited by the
VSWR (a function of Q) of the secondary system.  I would point to the following
flaws with that theory.

1.      The secondary system has a relatively fixed secondary capacitance that
must be charged to increase voltage.  The moment the gap quenches, the energy
in the system is fixed and any additional voltage rise will require additional
energy to the secondary system which is not possible.  If one simply takes a
sine generator and excites the secondary system, very high voltage increases
can be created.  However, the sine wave generator is supplying a continuous
source of energy to the system that is not available a real operating coil with
a fixed amount of energy per discharge cycle.

2.      The VSWR voltage rise theory does not consider the enormous system
losses in a Tesla coil.  Once streamers and other losses are added into the
system.  The system Q drops dramatically.  This large system loss effectively
damps any resonant rise effects.

3.      The resonant rise theory has never been demonstrated by myself or
despite many attempts.  In fact, repeating experiments that the Corum's
describe in previous papers as carefully as possible, have failed to show ANY
evidence of this effect.

4.      They state that the secondary voltage is proportional to the equation
"Vmax = S x Vmin" where S is the standing wave ratio.  This has not been
independently demonstrated in any way.

Much of the paper's dispute with lumped element Tesla coil models is based on
the fact that a lumped element inductor has equal current entering and leaving
the coil were a real Tesla coil secondary does not.  However, NO lumped element
model ever assumed that.  The work of Medhurst demonstrated that the current
decreases along the secondary, due to capacitive charging of the space around
the coil, in his landmark paper of 1947.  Every lumped element representation
of a secondary coil has an inductor in parallel with a capacitor representing
the self-capacitance of the secondary.  This allows two lumped elements, the
inductance and self-capacitance, to represent the very complex secondary
behavior.  Papers, like my "Modeled and Actual Voltage and Current Waveforms
within a Tesla coil", use this method to represent the secondary and
demonstrate, through actual measurement, it's validity.

        The paper talks much of higher order standing waves or overtones that
can be set up on bare coils.  I would submit that this is not applicable to
real Tesla coils for the following reasons.

1.      Tesla coils only operate acceptably at the fundamental frequency.

2.      The tests use a continuous sine wave generator.  They should use a
primary capacitor and inductor circuit driven from a sine wave if anything. 
This is important since a real primary coil does not drive the secondary from a
point at the base but rather a large area at the base of the coil.  It is much
harder to set up standing waves using the large area mutual induction of the
primary to secondary.  This is why they emphasize that the primary circuit must
quench for the VSWR effects to take place.  A pulsed or arbitrary function
generator simulating a real Tesla coil drive signal would be a much better
energy source.

3.      These coils are not terminated as practically all Tesla coils are.
is important because a terminated coil has far greater top current than an
un-terminated coil.  Also, the effects of the self and terminal capacitance
serve to greatly damp higher order harmonics when a top terminal is present.

4.      The tests are done without any load or losses.  If one adds a 5pF
capacitor in series with a 220K ohm resistor (a typical streamer load) the
standing waves are not nearly as easy to create.

They should use a pulse driven primary circuit, a top terminal, and add a load
to represent streamers.  Then the test would be fairly accurate.   Although,
only operation at the fundamental frequency would be easy to demonstrate. 

However, I too have done such harmonic tests and the graphs are at:

        Another point, that was very surprising, was their "Test II" experiment
which they base a number of claims on.  They simply find the resonant frequency
of a bare coil and add a terminal to the top.  They note that the frequency
shift is less than would be predicted from simply adding the self capacitance
of the bare secondary to the bare terminal's measured capacitance.  This effect
has been known and basically understood since Tesla's original work 100 years
ago.  No modern theory, lumped element or otherwise, would predict any
different outcome.  It has been a long standing difficulty to predict how a
given terminal will add to the self capacitance field of a given secondary coil
and what the final operating frequency would be.  Lumped parameter theory does
not solve this problem.  However, my own "E-Tesla5" program solves that problem
by computer iteration.  That program also generates data to accurately map the
voltage fields around a given secondary / terminal configuration (see
http://users.better-dot-org/tfritz/Vdist1.jpg). The program is not based on 1/4
wave, standing wave, or VSWR effects in any way (the voltage distributions are
empirically derived and they do not match the above) but it can predict a
coil's behavior within the arbitrary 5% figure they mention.  In fact, the
program can predict systems that do not even remotely adhere to the old wire
length ideas as well as ones that adhere well.

        The paper still relies on 1/4 wave effects.  Many coils have been built
with various wire lengths.  Many have wire lengths similar to the wavelength of
the coil's fundamental frequency.  Many have wire lengths far from that value. 
Everything else being equal, wire length has never been demonstrated to have
any effect on a coils performance due to propagation time or 1/4 wave effects. 
The phase shifts that such a theory predicts have not been observed and have
been demonstrate not to exist.  Other theories have long since taken the place
of the old wire length ideas.  The new theories accurately predict the behavior
of Tesla coils, without exception, despite the fact that they do not use VSWR,
1/4 wave, standing wave, resonant rise, or coherence theories.

        I should also point out that the distributed capacitance of a bare or
terminated Tesla coil is far from uniform.  This gives a non 1/4 sine voltage
function along the length of the coil.  The voltage builds up slowly at the
base due to the proximity of the ground and primary.  This produces a high
capacitance at the base that can absorb more electrostatic energy without
producing nearly as great of voltage rise.  The voltage then builds fairly
linearly until the large top capacitance of an un-terminated coil reduces the
voltage again or the terminated coil case where the voltage continues to rise
(see http://users.better-dot-org/tfritz/DistGraph.jpg).  The distribution is close
to a "Vm x l^e" function.  This plays havoc with trying to determine the
transmission line characteristics of a Tesla coil since the normal transmission
line models assume that the per-distance coefficients (RLGC) are constant along
the length of the line.  However, there are equivalent values that may
suffice.  Although, the "real" transmission line effects are lost in that
case.  Note also that the shunt capacitance term (C of RLGC) has a substantial
series resistance that most equations do not consider.  Thus, one may be able
to fit the transmission line parameters to a given coil but the actual physics
is far different that what the model would predict about the coils actual
voltage distribution along it's length.  Of course, from a total system
"lumped" perspective, such an equivalent model will still work.  However, the
equivalent coefficients of RLGC will be almost identical to a lumped inductor
and far from a transmission line of 1/4 wavelength. 

I don't mean to be super negative about their paper.  However, "I" feel it has
many major flaws.  This paper's ideas seem very out of date these days to me...

Additional reading at: