Resonance --- It's not a myth

To: Tesla List

It appears there is some strong confusion on the list regarding whether a
TC resonates --- yes, it does!

There are essentially two or three major types of resonators (sec coils) in
this discussion and I think that's where the confusion arises.  A loosely
coupled classic TC with a small HV terminal is called "line resonance". 
This terms comes from transmission lines which have similar properties. 
Such a machine is a 1/4 wavelength tuned inductor and has a noticeable
phase shift between the current induced into the lower area of the sec coil
and the output terminal.  The capacitance is distributed along the
secondary inductor with reference both both ground planes, other turns, and
the small HV terminal.  The capacitance of the inductor is usually greater
than the capacitance of the terminal.  Standing waves do travel up and down
this type of inductor and build both nodes of constructive and destructive
interference.  Beat frequencies occur and several resonance are noticeable
when this type of setup is scoped or examined by a spectrum analyzer.  This
type of inductor can hit potential peaks at several points between
different areas in the uppermost section of the coil and that is a very
important reason why this type of system can't be pushed very hard without
a large topload.

The second type of resonator, which is similar in design features to most
modern systems, is called "lumped resonance", ie, the energy is transferred
through a large inductance into a large capacitive resevoir -- the large
toroid type HV terminal.  The inductance is working in series resonance
with the capacitor (topload) and the large lumped capacitor itself is
working in parallel with 4 important capacitances: (1) distributed or
inter-turn capacitance of the wire which is relatively small with regard to
the other capacitive elements, (2) the capacitance of the HV toroid itself,
(3) the capacitance of the corona load, and (4) the capacitance of each of
these elements to the ground plane.  Most of these elements of capacitance
are in parallel with the ground plane.  This does vary as the arc actually
strikes the ground plane --- then it quickly switches to a series resonance
for short periods of time.  

All of these elements of series and parallel capacitance being pumped by a
series inductor form a very, very dynamic circuit which is why Tesla
oscillators are not simple to understand --- and most modern designs as
pointed out by Terry Fritz, Rich Hull, and others, become both difficult to
analyze and explain in simple terms of a classic TC oscillator operating in
a classic 1/4 wavelength form.  Form a conclusion for one set of dynamic
variables, and then the arc strikes a ground --- a whole new set of
variables with series capacitances forming in the arc channel that now act
in series and parallel with the inter-turn capacitance, ground plane, and
terminal capacitance.  Now you can see why the analysis becomes similar to
eddy vortices in a stream or hydrodynamic systems analysis --- fractal
analysis is required to form a complete picture --- and this math is
certainly beyond most experimenters who just want to make a nice spark to
educate and entertain.

The third type of resonator doesn't show up very often in TC work but also
operates on true resonance --- the pulse transformer.  This type of
resonator is characterized by a very tight coeff. of coupling --- usually
around 0.6 to 0.7.  A pulse transformer usually consists of only primary
and secondary very tightly coupled and does not have an extra or magnifier
coil involved. 

Pulse transformer systems (commonly called "drivers") can be used to drive
a third or resonator inductor which Tesla called his "extra" or "magnifier"
inductor.  This magnifier inductor resonates and develops very high
potentials driven as a series resonator with a very high current driving
source at its base.  

Resonance does occur in each of these types of resonators.  It does vary by
degree depending on which type of system you are operating --- a classic
TC, a large topload TC (most modern designs with 0.18 to 0.2 coeff.
coupling), or a pulse transformer type. 

Since most modern coil builders are using large topload capacitances as
compared to the distributed capacitance of the series driving inductor, we
should limit or analysis to the second type of resonator --- the type most
of us are using with a large toroid or sphere on top.  The first type of
resonator gets into some very heavy math regarding transmission line and
blum (or bleim) line theory. If you are truly interested, there are several
classic college electrical engineering text books filled with 2nd order
differentials regarding the complete theory of transmission lines and
resonant rise in these devices.  

I hope this data helps put things into better perspective --- imagine if
you are new to the list and just trying to learn the fundamentals of TC
operation --- we probably scared off more than a few high schoolers who
just want to build a coil and have some fun.