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Re: Series or Parallel resonant ? ( was: New pics and scope waveforms)

Tesla List wrote:

> Hope I got it right, too. It would seem to me that the induced currents on
> the secondary,similar to that on a transformer, are 180 phased as regards
> its causitive source by mutual induction. Thus the currents on the secondary
> are 180 out of phase with that primary current from the tank circuit. The
> currents on the secondary are given an increased resonant rise of voltage
> because that side of the equation is a series resonance, Not another tank
> circuit. In this way we can view both the resonant rise of amperage occuring
> on the tank circuit, simultaneous to a resonant rise of voltage on the
> secondary.

Actually, if you measure the currents in the primary and secondary
windings
you will see that they are at approximately 90 degrees. A Tesla coil
cannot be analyzed correctly with considerations that apply to simple
LC circuits in series or in parallel, driven by sinusoidal sources. 
The operation of the system is more correctly viewed as the one of a 
parallel LC circuit in parallel with a series LC circuit, both tuned to 
different frequencies, and executing a transient started by the
initial primary voltage:
(Use a constant-width font to see the ascii art)

Original circuit: Two parallel LC circuits with the inductors coupled.
The only excitation is the initial voltage in C1.

            K12
     +-----+   +-----+
 +   |     |   |     |
Vc1  C1    L1  L2    C2
 -   |     |   |     |
     +-----+   +-----+

Substituting the transformer by an equivalent with an ideal transformer:

             1:n
     +-----+     +--+-Ly--+
 +   |      )   (   |     |
Vc1  C1     )   (   Lx    C2
 -   |      )   (   |     |
     +-----+     +--+-----+

Lx=K12^2*L2; Ly=(1-K12^2)*L2; n=K12*sqrt(L2/L1)

Moving C1 to the other side and discarding the transformer:

       +-----+-Ly--+
 +     |     |     |
Vc1*n C1/n^2 Lx    C2
 -     |     |     |
       +-----+-----+

The new "primary" circuit C1/n^2, Lx continues to resonate at the 
same frequency of the original circuit C1, L1.
But the new "secondary" circuit Ly, C2 resonates at a higher
frequency. This transformerless circuit behaves exactly as a 
Tesla coil. The "double resonance" condition for this circuit is:
(C1/n^2)*Lx = (Lx+Ly)*C2.
The waveforms at the capacitors in this or in the original 
circuit are identical (with the scaling factor n), and are not 
sinusoids, but look as sinusoids that increase and decrease 
periodically in amplitude. Some relationships are interesting if 
we insist in viewing those waveforms as sinusoids:
- The current in the primary is at 90 degrees with the primary
  voltage, because both occur in C1.
- The current in the secondary is at 0 or 180 degrees from the
  primary voltage, depending on the direction of energy flow,
  from the primary to the secondary or backwards. Note that this
  would be impossible with pure sinusoids in a lossless circuit.
- The current in the secondary is so at +/-90 degrees with the
  primary current.
- The secondary voltage is at +/-90 degrees with the primary
  voltage, by the effect of the secondary current in C2.
(+/- polarities depend on the direction of the measurements,
of course.) Resistive losses don't affect these relationships
significantly.

Antonio Carlos M. de Queiroz