Re: Couples Therapy

Tesla List wrote:
> Original Poster: "Ruud de Graaf" <rdegraaf-at-daxis.nl>

> Searching the net I stumbled upon 'Coupling Questions & coil measurements',
> august last year on the site
> http://w4dfu.ufl.edu/listarchives/1999/August/msg00225.html. (some
> mirror???)'Magical K-values', remember Antonio? When I have more time I will
> look into this matter. The formula reminds me (probably because of the +/-
> bit) of the formula's to calculate the secondary frequencies of a coupled
> bandpass filter when k > critical:
> Flow = Fres / sqrt (1+k) and
> Fhigh = Fres / sqrt (1-k)
> and surprise surprise, these are the same as used to calculate 'the
> bandwidth' of a TC!

The circuits are similar, and the equations too.

> I don't understand which condition would require explicit resistances in the
> circuit.
> Could you explain this to me or could you give me some reference where to
> look?

A bandpass filter made with two coupled resonant circuits is a filter,
where you want a band of frequencies where the input signal is 
transferred to the output side with approximately the same gain, and 
high attenuation of signals sufficiently far from this band. This filter
is designed to exhibit a flat passband (Butterworth design), or a 
passband with two peaks and a valley between them (Chebyshev design).
In any way, there is no infinite amplification of the input signal.
If this circuit were built with ideal coils and capacitors, and excited
by an ideal sinusoidal voltage signal source, it would resonate at two 
frequencies (close to the borders of the passband), and amplify 
input signals at these frequencies without limits. This is not what we 
want in a filter, so resistors, one or two, are added to limit the Qs of 
the resonances, and produce a more or less flat passband instead of 
two sharp peaks. The most conventional circuit would be:
  o--R1--C1--+   +--+--+---o
  +          |   |  |  |   +
 Vin         L1  L2 C2 R2 Vout
  -          |   |  |  |   -
  o----------+   +--+--+---o

In a Tesla coil, what we want is lossless resonance of the circuit
when the input capacitor is charged and connected to the circuit,
to allow the transfer to the output of ideally all the energy in
the input capacitor.
This is equivalent to the repentine application of a large DC
voltage as Vin in the circuit above. The transfer takes several cycles
(b semicycles of Vout using that formula), and the resistors required 
for the filter are prejudicial, as they drain energy while the energy
transfer proccess is in the way.

Antonio Carlos m. de Queiroz