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Modeling a magnifier


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From:  Antonio C. M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Sunday, March 08, 1998 12:30 AM
To:  Tesla List
Subject:  Re: Modeling a magnifier

John H. Couture wrote:

>   Tesla also said that the secondary was acting in the transformation mode.
> This means it was not in resonance and the pri/sec voltage was the same as
> the turns ratio of the windings.   JC

Correct, but this happens only while the gap is conducting. After the opening
of the gap, the secondary is just a normal coil.

>   Could you explain the above in more detail. I'm confused about the energy
> oscillating after the gap is quenched.  JC

Consider the circuit formed by the secondary coil, the third coil, and their
self-capacitances. Ignore resistive losses:

+-----+--L3-+
|     |     |
C2    L2    C3
|     |     |
+-----+-----+

C2 includes the self-capacitance of the second coil L2, of the interconnections,
and the input capacitance of L3. C3 includes the self-capacitance of the third coil
L3 and the top capacitance.
This circuit has two oscillatory modes, and if L2*C2=(L2+L3)*C3 it oscillates
exactly as a two-coil Tesla coil, with the same beating waveforms, that periodically
concentrate all the energy in C2 or in C3. (This can be demonstrated by using the
equivalence between a transformer to a T circuit of inductors.)
Actually, you can build a Tesla coil variation exactly in this way.
This is a model for the magnifier circuit after the spark gap is quenched. While
there is energy in the system, the double oscillation occurs.

Today I made some experiments at low power using the secondary of a Tesla coil
that I am building for L3-C3, another smaller coil for L2 and a variable capacitor
for C2. I charged the system by switching a high-impedance current source across
L2. I could observe clearly the beating waveforms and the energy oscillation when
C2 was set according to the equation above, exactly as in simulations using this model. 
I will prepare a full report about the experiment.

Antonio Carlos M. de Queiroz
http://www.coe.ufrj.br/~acmq