# Electrum output impedance (fwd)

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---------- Forwarded message ----------
Date: Sat, 11 Jul 1998 14:30:41 -0600
From: terryf-at-verinet-dot-com
To: tesla-at-pupman-dot-com
Subject: Electrum output impedance

Hi Greg Leyh and All,

I was studying the scope photos of the Electrum at:

http://www.lod-dot-org/electrum/electrumspecs.html

In another post (TC Output Impedance Matching) I propose that the
"Load Match Point" in a Tesla coil occurs when the load on the coil is equal
to the following equation:

Rl = 2 * pi * SQRT ( Ls / Cs )  =  195k ohms

For the Electrum:

Ls = 0.130 H
Cs = 135 pF
Xls = 31K ohms (the reactance of the secondary at 38kHz)

So the Load Match Point (or Tesla point) calculates out to 195k ohms.

By knowing the current to the sphere, the frequency, and the inductance of
the secondary, the voltage at the top terminal can be calculated as 1.55
million volts in the 100, 20, and 10 uS pictures.  By dividing the output
voltage by the sphere to arc current, the arc impedance can be estimated as
follows:

In all cases the 50 amps in the secondary multiplied be the reactance of 31K
ohms gives an output voltage of about 1.55M volts.

100uS           Io = 15A        Zarc = 103k ohms

20uS            Io = 5A         Zarc = 310k ohms

10uS            Io = 8A         Zarc = 194K ohms

You will notice that these numbers average out very close to the
calculated value of 195k ohms.  I suspect that the arc may begin at the
1.55M volt level but the voltage quickly reduces to ~750k volts and matches
the arc impedance.  I don't know if the coil finds this point naturally or
if the Electrum was designed to operate this way.  The close match of the
Electrum to these calculated numbers is obviously very interesting!

All the best,

Terry Fritz

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