RE: Series resonance/Was: Waveguide TC

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "John H. Couture by way of Terry Fritz <twftesla-at-qwest-dot-net>" <couturejh-at-mgte-dot-com>


Paul -

Tesla said his system did not use Hertzian waves. I take that to mean he was
going to use currents instead of wave radiation. Aren't these two different
methods of transferring electrical energy?
The energy via current has to have a return conductive circuit.
The energy via radiation can take off (antenna) into space and never return.
Maxwell provided two equations to show this difference. Something like this

Magnetic field   fHl dl = dx/dt+Ic

Electric field   fEl dl = -dw/dt

The Tesla coil is a combination of these two systems?
I must confess I don't use these two equations to design my Tesla coils!!

John Couture

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-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Sunday, December 15, 2002 3:43 PM
To: tesla-at-pupman-dot-com
Subject: Re: Series resonance/Was: Waveguide TC


Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<paul-at-abelian.demon.co.uk>

dwp wrote:

  > My recollection is that Kirchoffs law applies to _circuits.

Yes, but Kirchhoff's current law is really just an expression of
charge conservation:  The net charge flow (ie current) into a point
must equal the rate of increase of charge stored at that point.

The above statement can be rephrased by saying: The total current
into a node (including displacement current entering from the node's
self capacitance) sums to zero.

BTW, it makes little sense to look at a TC secondary and declare
it a series resonant or parallel resonant circuit.  This series or
parallel property only makes sense when you
a) specify a port into the resonantor through which you will view
    its impedance or drive the thing.
b) specify a resonant mode of the coil, 1/4 wave, 1/2 wave, etc.

For example, if you break into the base circuit of a 1/4 wave coil
it looks like a series LC circuit, whereas if you connect across
the coil itself, it looks like a parallel LC circuit.

  > When sparking, the top terminal is not open
  > and the resonance may not be strong.

If the resonator has a lossy load at the end, the reflection
coefficient no longer has magnitude unity, the reflected wave is
weaker than the forward wave, and real power moves up the coil to
exit at the top.  Under these conditions you will see a phase change
of the current along the coil, since you now have a real travelling
wave resulting from the incomplete cancellation of the two
components of the standing wave.  But you'll have to be quick with
your measurement because if the phase change is large, so is the rate
of energy loss!

To answer some of Jolyon's original questions,

  > A lumped series-resonant circuit can be visualised as an inductor L
  > and a capacitor C in series with a signal source or "generator".

Ok, you specified a port by saying the generator is in series with
the LC, so then the lowest resonant mode of the coil looks like a
series resonance.

  > Surely there is a 90 degree phase shift between current at the
  > driven end and the current at the "terminal" end i.e. current
  > flowing "through" the capacitor?

No, not necessarily.  The essential 90 phase difference of any
resonator, any mode, occurs between the circulating current and the
induced voltage across the reactances.   Generally, current sampled
at any point has the same phase as any other.  Likewise the voltage
sampled across any reactance will have the same phase as that across
any other reactance.

Make careful distinction between the circulating current of the
resonator, and the load current.  The circulating current is 90
degrees from the induced voltages, so that when you hook up a
resistive load across one of those voltages, the load current is
in phase with the voltage and thus 90 degrees from the circulating
current.  Therefore the answer to the question is that there is
no phase shift between in the input current and the circulating
current (since the input port is a series port) but there is a 90
degree shift between input and output current (since the output is
a parallel port).

  > Is the "series-resonant secondary" like the quarterwave resonant
  > theory incorrect

They are both correct.
--
Paul Nicholson,
Manchester, UK
--