Re: TC Output Impedance Matching (fwd)

---------- Forwarded message ----------
Date: Mon, 13 Jul 1998 20:34:41 -0700
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: TC Output Impedance Matching (fwd)

GL wrote:

> Ah, that's what was confusing me... if these are empirical equations,
> shouldn't they contain just terms and rational constants?
> Why do they have pi in them??  Pi hints at mathemetical derivation.

And Pi usually appears only in frequency unit conversions and 
calculations involving circular geometries.

> BTW, the non-empirical, mathematically derived equation for a
> critically damped secondary is  Rl = 2 x SQRT(Ls/Cs).

This is the relation for a resistance -in series- with Ls and Cs.
For a resistance Rl -in parallel- with an Ls, Cs parallel circuit, as
an arc in parallel with a Tesla coil secondary, the relation is:
Rl = Q x sqrt (Ls/Cs)
The critically damped situation corresponds to Q=0.5.
Q=0.707 corresponds to the no gain situation for a voltage applied
to the base of the inductor, in sinusoidal steady state.

Antonio Carlos M. de Queiroz