TC Output Impedance Matching (fwd)

---------- Forwarded message ----------
Date: Sat, 11 Jul 1998 06:29:04 -0600
From: terryf-at-verinet-dot-com
To: tesla-at-pupman-dot-com
Subject: TC Output Impedance Matching

Hi All,
	My recent work with TC output and arc impedances has suggested some new
equations.  I would like to define them and request any comments.

In the following:

Rl = The equivalent impedance of the load on the output of the Tesla coil.
pi = 3.14159...

Ls = The inductance of the secondary.

Cs = The total secondary capacitance.

Vo = Secondary peak voltage.

Vi = Input peak voltage.

Vm = Maximum theoretical secondary peak voltage.

The first equation is:

"Unity Load Point" equation

Rl = 1/4 x SQRT(Ls/Cs)	where  Vo=Vi	

	This equation is for the point at which the load is so great that the coil
is heavily damped and the output voltage is equal to the input voltage.
There is no voltage amplification.  This equation may prove to be wrong.  It
doesn't appear to take into account the primary to secondary turns ratio.

The second equation is:

"Power Quench Point" equation.

Rl = pi x SQRT(Ls/Cs)	

	This equation is for the point at which the load is so great that all the
energy is expended in the first burst.  There are no follow-up bursts of
voltage.  This equation appears to be quite valid.

The third equation is:

"Load Match Point" equation.

Rl = 2 x pi x SQRT(Ls/Cs)	where  Vo=1/2 x Vm  

	This equation is for the point at which the load is at the level where the
output voltage is at 1/2 the theoretical maximum value.  this would imply
that the source and load are equal and maximum energy transfer is taking place.

The fourth equation is:

"Half Power Point" equation

Rl = 4 x pi x SQRT(Ls/Cs)	where  Vo=1/SQRT(2) x Vm

	This equation is for the point at which the load is at the level where the
output voltage is at 1/SQRT(2) the theoretical maximum value.

The fifth equation is:

"No Load Point" equation

Rl >= 1000 x SQRT(Ls/Cs)		Where  Vo=Vm

This equation defines the point where the load impedance is so high that it
has no real effect on the output voltage of the coil.

	The last equation is more of a definition.
I would propose that the "Tesla Point" equation be defined as the load
impedance that a particular coil is being designed to drive.  At this time I
believe this is same as the "Load Match Point".

The sixth equation is:

"Tesla Point" equation

Rl = 2 x pi x SQRT(Ls/Cs)	Vo=1/2 x Vm

Further study may show that the best impedance to design a coil for is
different than this equation.  However, this is my "best guess" at this time.  

	These equations where arrived at by useing load studies and computer
modeling.  They are not derived mathematically at this time.  I believe the
term is "Empirical" :-).  They may or may not prove to be useful or valid.
The equations are not exact because of losses and exact peak values but they
appear to be very close in real situations.  I wanted to present them now
for any comments.  I just made the names and such up so if anyone has any
suggestions, additions, etc. please feel free.

	I will eventually write all this up but I just wanted to see what everyone
thought of these equations.  This is a first try at trying to define a way
to match a given coil's design to a given load condition (output arc).  I
haven't seen much information in this area before.

	Terry Fritz