Now, How does a coil really work??

Hi All,

	The subject of resonance is a bit complex.  Having all the engineers and
experts on the list talking back and forth can be pretty confusing to many
since we assume some things are well known and we sometimes use terms
loosely.  It would also be more clear if we happened to agree too :-)  I
will give my explanation on all this.  Be aware that some will disagree
with me on certain points so realize that I too may be wrong and certain
areas are not fully understood yet.   Also I am leaving a LOT of details
out.  This could really fill a thick book.

	Is there resonance in a Tesla coil? - Of course there is.  There are all
kinds of things resonating in Tesla coils.  However, there are really
different processes or details at work. Some of which are more significant
than others.  Let me go through the ones that affect us.

	LC resonant circuits.  If you have a capacitor and inductor in series or
parallel, there will be a certain single frequency in which the components
are said to resonant.  At this frequency, the AC impedance of the
components will be equal but opposite and they will cancel each other.  In
this condition, voltages and/or currents can become very high since the
circuit may appear as a short or open circuit depending on how things are
hooked up.  It is this resonance that allows the components to oscillate
with low loss.  The only thing limiting the voltages and currents is the
power the driving circuit can deliver and the small resistances that are
inevitable in the circuit.  The primary and secondary circuits in our coils
are "tuned" to this frequency so that very high voltages are created and
oscillation can be maintained.  Because of the pulsed nature of Tesla
coils, you can tune to harmonics also but the power will be very reduced
from what it could be.  People that have found a sweet spot but only get a
very small arc are probably running on one of these harmonics instead of
the real frequency they should be tuned to.  It is very important to
realize that when you feed a tuned circuit with just the right frequency it
takes a considerable amount of time for the voltages and currents to build
up to high levels.  The tuning effect happens very quickly but the real
energy build up takes a lot of time.  Too long in our case.
	1/4 wave resonance.  This is a fun one!!  Tesla originally based his giant
coil on this.  The legacy has been with us ever since.  This is also my
favorite theory to pick on!:-)  If you take a long wire and feed it with an
ac signal that happens to be the frequency were electricity will travel 1/4
of the wavelength along the length of the wire, you will get a standing
wave.  You can also get a variety of other harmonic standing waves too.
The front of the wire will be the voltage of the signal generator but the
end of the wire will have very high voltages and low currents.  This is the
principle most radio antennas use to couple the output of the transmitter
to the impedance of the air to deliver RF power to the air (free space).
It acts much like a transformer.  Obviously, this principle appears to be
very applicable to Tesla coil operation and Tesla's Colorado Springs
experiments were based on this theory.  This is also were the idea that a
coil's wire length should be 1/4 of the wavelength of the coil came from.
However, there is a problem.  The long wire will have a 90 degree phase
shift from the beginning to the end.  This is governed by the time it takes
for electricity to travel the length of the wire at the speed of light
(actually, it is the propagation delay time which is somewhat less but...).
 Tesla coils are coils, not a length of straight wire.  When we wind them
in a coil, the individual sections of wire become magnetically coupled.
Now the currents at the base of the coil do not need to travel through the
whole length of the wire to affect the other end.  The currents at the
bottom can magnetically couple to the top of the coil which is only a few
feet away.  The time delay in that case is only a few nanoseconds (that's
REAL fast!).  If the current at the top and bottom of the coil were out of
phase, the magnetic fields would crash and cancel and have all kinds of
problems.  The simple fact is (realize, others disagree with me on this)
that the top and bottom phases of a Tesla coil's current are locked
together in phase by the magnetic fields.  This is a nice theory (1/4 wave
transmission line) and the powerful engineering equations can predict the
behavior.  However, they are overkill for what is really going on.
Understandably, the Corums, who spent an incredible amount of time
developing this theory to a very high level, are not quick to give it up!
I suspect many were so impressed with their work they assumed they had to
be right (there were many others long before the Corums who held this
theory too).  The math is basically correct (but the empirical equations
they suggest are not accurate) but the real end results say you should have
just used lumped component theory and saved yourself a whole lot of
trouble.  The secondary inductor of a Tesla coil really does act like a
simple inductor without phase shift.  My past papers and experiments show
this.  This also explains why all the simple equations work just fine for
predicting Tesla coil operation.  I would also submit that the fact that
the secondary self capacitance is distributed along the secondary coil
really doesn't make any difference in the total operation of the secondary
system.  If the capacitance were a discrete part between the top of the
coil and ground, the results would all be the same for our purposes.  One
difference is that harmonics can be found in the distributed capacitance
case but the currents are still in phase (that is NOT a well known
phenomena and many will choke on that :-)).  Just consider a series of
separate LC sections end to end.  Is phase shift necessary for harmonic
resonances to exist??  For a resonance (at the fundamental or a harmonic)
to be set up in a coil with distributed capacitance and no top load, 90
degree phase shift (or any phase shift) is NOT a requirement.  I submit it
is impossible to have significant phase shift in a tight wound coil in such
a system.  There are little effects going on but they are of no practical
significance.  A delay line would be a case where such a phase shift is
observed.  However, these devices have a very long skinny coil to isolate
the magnetic fields and have large discrete capacitors along the length.
The capacitance and energy stored in the area around the coil is also
locked in phase in a similar way the magnetic fields are.  The Corums
equations do predict all this but you have to use the correct constants
which their empirical equations fail to provide accurately enough.  Simply
change the numbers 10% and the results can shift dramatically.  When you
figure out the accurate constants (NOT easy) the phase shift is very small
along the coil.  Computer models (transmission line models) can do this
easily.  However, the results show you are back to the lumped case for any
practical purpose.   They also show reflections from the higher order
harmonic resonances in a pulsed coil, which is kind of neat, but they too
are in phase!  Also look at Antonio's neat little pendulum set up.  No
phase shift along the length of the pendulum.  What more proof does one
need :-))  Of course, the good Dr Resonance just posted a note that says
the direct opposite of all this - so take your pick :-)))))

	Resonant rise.  There is another resonant issue too.  If you take a Tesla
coil and feed it a one volt signal with a sine generator, you will generate
much higher voltages at the top at the resonant frequency (or a harmonic).
In my case I will get 160 volts at the top of my coil when feed it with a 1
volt signal.  By no accident, the Q of my coil is also 160.  So one may
quickly think that if I have 20000 volts ac at the base I will get 20000 x
160 or 3200000 volts!  Nope!  There is a problem with that too.  It takes a
considerable amount of time and energy to build up the voltage.  Long
before my coil will reach 3 MV, the primary circuit energy will run dry.
The principles of conservation of energy take over and limit my coil at
about 450kV (375kV with losses).  Also, the time needed to build up the
voltage is far too long for the primary circuit to supply energy.  Many
have tried to play with the component values to take advantage of this but
they are fighting quite a battle.  The physics just keeps working against
you.  This effect (resonant rise) can be seen in real waveforms if you know
just were to look but the effect it has is tiny.  Tube and other continuous
wave coils do use this principle but this system is very sensitive to loss.
 A small loss can quickly lower the Q and limit the voltage dramatically.
I think tube coils should be designed for very low loss at high voltage but
I am no expert on these coils...

	Sooo...  how do the things work?  By resonance :-))  Let's be more
specific.  Resonance is used to support oscillation for a period of time
and transfer energy from the primary tuned circuit to the secondary tuned
circuit.  The oscillating currents can store and transfer the energy in the
way we need.  The primary's tuned point is such that the voltage is say
20000 volts and the current is 300 amps.  However, the secondary's tuned
point is 400000 volts at 15 amps.  Inductive coupling (and to a degree,
capacitive coupling) is used to connect the two circuits.  The resonant
nature of the system will automatically try to transfer the all energy from
the primary to the secondary system.  It works pretty well.  The energy in
the primary is transferred to the secondary but the different inductances
and capacitances in the secondary support much higher voltages and much
lower currents.  The total energy is the same but the ratio of voltage to
current is much higher.  Thus, we now have very high voltages being
produced and sparks fly.  If all the energy is not dissipated right away in
the secondary, the system will transfer the energy back into the primary
again.  The energy there will try once again to transfer back to the
secondary a second time and this will continue until the losses dissipate
the systems energy.  This back and forth energy transfer is where all the
talk of quenching comes in.  We want to open the gap just as all the energy
is trapped in the secondary.  More easily said than done.  The back and
forth energy transfer wastes energy like mad.  There are many details with
that.  Some suggest that you are better off letting the energy transfer
back and forth rather than using a good quenching but super lossy gap that
eats all the energy up anyway.  It really depends.  I think rotary gaps
(low loss) are best with third or forth notch quenching but fixed gap (high
loss) systems seems to like first notch quenching...

	When an arc hits a grounded target, the coil system is shocked by the
sudden discharge of energy.  However, the principles that apply there are
concerned with impulse response theory rather than resonance.  You won't
find a lot of people who know about that subject and Tesla Coils :-))

	The streamers seem to grow larger over time due to the streamer's heating
up and establishing a nice hot arc channel.  There is no real build up of
voltage or energy in the coil over this long time frame.

	There are many many details in all this I left out and there are losses
and other issues at work.  Only computers can really come close to
simulating all this.  With the right inputs, they are extremely accurate.
There are general equations but they really are pretty far off or can't be
used do to the complexity.  One problem the Corum's equations have is that
they use continuous case equations for our transient case coils.  This got
them into trouble with their ill fated "coherence" theory.  Many of the old
theories have been around for almost 100 years so they are going to die
hard.  However, we really do have a very good idea how Tesla coils work and
we are learned more all the time.  Many of the theories are based off
Tesla's 1899 work and do not take into account that even Tesla realized in
later years some of the principles he though were correct then were really
flawed in retrospect.  However, by then he was not making great efforts in
the area and the 1899 ideas stuck.  

	Hopefully, this will help in understanding this complex subject.  It
really is not simple and all the conflicting theories that are coming and
going make it even harder to understand.  You won't find any books that
tell of all this because things are changing so fast these days.  Of
course, all this bleeding edge stuff is what makes it so much fun!

You may want to see my latest paper at:


"Modeled and Actual Voltages and Currents within a Tesla Coil"

This shows all the voltages and currents in my coil.  Both the actual and
computer predicted versions.  If any theory disagrees with these results,
there is a problem with the theory!!  :-)