Re: Series resonance/Was: Waveguide TC

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Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>


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Sent: Sunday, December 15, 2002 9:08 AM
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>
 >
 > Jim wrote:
 >
 >  > a number of folks have made measurements of the current
 >  > at top and bottom and find [current phase between top and bottom]
 >  > are only a few degrees apart.
 >
 > Yes, this is correct.  There is little or no observed phase change
 > along the coil, even if the coil is many electrical degrees long [*].
 >
 > But it is wrong to conclude, as Terry did in
 >   http://hot-streamer-dot-com/TeslaCoils/MyPapers/topsync/topsync.html
 >
 > that this invalidates the transmission line model. In this paper,
 > Terry wrote
 >
 > : The top and bottom currents in the secondary inductor are almost
 > : perfectly in phase.
 >
 > A good measurement...
 >
 > : If the 1/4 wave model of Tesla coil secondary inductors were true,
 > : these currents should be 90 degrees out of phase.
 >
 > ...but an incorrect conclusion.  Both the lumped and transmission
 > line models predict a uniform phase for standing waves.  That's why
 > they are called 'standing' waves.  This is a common enough error, as
 > Jim demonstrates,
 >
 >  > ...the phase shift between current at the top and bottom of the TC
 >  > is nowhere near 90 degrees, as it would be for a transmission line.
 >
 > This is a common source of confusion and has led to many futile
 > debates in the past. Whichever model is used, the current phase
 > is almost uniform (although of course the amplitude must vary to
 > satisfy charge conservation).  As long as the reflection coefficient
 > at each end of the coil has a magnitude close to unity, the waves
 > along the coil will be 'standing'.  Terminate the coil with its
 > characteristic impedance in order to suppress the reflected wave and
 > reveal the underlying phase change of each travelling component
 > caused by the electrical length of the coil.

Excellent point, Paul... I had been thinking travelling waves (since, in
general, I work with reasonably well matched systems) and not in terms of
standing waves (which, in general, I try to avoid).  When working with
systems with potentially large amounts of standing waves (antennas with
large reactive feed point impedances), I tend to use lumped models, more
akin to a power engineer working with reactive and active power.

 > Typically, the extra computational effort of the transmission line
 > model is not necessary for TC design, and is used only to calculate
 > the effective L and C values from which the design can proceed with
 > the lumped model.  Until recently, this has been a stumbling block
 > for coilers.  But now, thanks to Bart Anderson, you can use the
 > transmission line model to compute accurate effective LC values for
 > use in lumped models:
 >
 >   http://www.classictesla-dot-com/fantc/fantc.html
 >
 > Bear in mind that so-called lumped L and C components are in fact
 > transmission lines.  Inductors have a very high characteristic
 > impedance (large distributed L/C ratio), while capacitors have a
 > very small characteristic impedance (small distributed L/C). Thus
 > in the former, L dominates and in the latter, C is dominant. Both
 > components are normally operated well below their lowest self-
 > resonant modes, so that they approximate the ideal of a lumped
 > component.  The transmission line behaviour of ordinary L and C
 > 'lumped' components is however exposed as soon as you put them on a
 > network analyser to observe their spectrum of self-resonances.

And, I'd add that I'll bet a typical TC secondary, running over a ground
plane, has a varying L/C ratio (impedance) as you move along it, making the
transmission line analogy a bit more strained (it's a "tapered transmission
line" with a tapered propagation speed, as well)