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>


----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Sunday, December 15, 2002 9:02 AM
Subject: Re: Series resonance/Was: Waveguide TC


 > Original poster: "davep by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<davep-at-quik-dot-com>
 >
 >
 >
 > >  > Original poster: "Jolyon Vater Cox by way of Terry Fritz
 > ><twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>
 >
 > >  > Jim,
 > >  > From what I understand an open-ended 1/4 wave transmission
 >
 > >>line is series-resonant circuit; series resonant tuned
 >
 > >>circuit have 90 degree phase shift between current at
 > >  > the driven end (low impedance) and current at the terminal
 >
 > >>end (high impedance).
 > >Except that by Kirchoffs Current Law, the current in and out
 >
 > >of the terminals must sum to zero.
 >
 >          My recollection is that Kirchoffs law applies to
 >          _circuits.  Closed entities, or things in them.

Yep.. but consider, with a two terminal device, the current in on terminal 1
MUST be the same as the current out on terminal 2.  Kirchoff's current law
says, in effect, that the currents in all the paths to a given node must sum
to zero. We place a "virtual node" inside the "box" and there are only two
paths, so the sum must be zero.


 >          By observation:
 >                  Antenna circuits need not be closed (some are).
 >                  1/4 wave antennas DO have a current peak at the
 >                  base.
 >          (other 'series resonant' circuits may not....)

Consider the "two terminals" for the antenna (i.e. the feed point).  Pretty
clearly, the current "in" on one terminal has to match the current "out" on
the other.   A resistor is a two terminal device which follows the rules as
well.  (i.e. KCL doesn't say anything about power dissipation.).

That 1/4 antenna is a substantial fraction of a wavelength in size, unlike a
TC secondary. When the propagation speed of the EM field from one part of
the structure to another is a significant factor, then my statement about
the equality of the phase/magnitudecurrents at the two terminals in a series
circuit becomes less valid. (i.e. the lumped approximation isn't valid).

 > >Therefore the current at the bottom of the secondary has to
 >
 > >be equal to the current at the top of the secondary.
 >

Tesla coil secondaries are nowhere near a wavelength (say, hundreds of
meters) long.

 >          Also:
 >
 > >EXCEPT.. there is some parasitic capacitance (not insignificant) from the
 > >secondary winding to "ground", and some current flows through that
 > >capacitance.  But, a number of folks have made measurements of the
current
 > >at top and bottom and find they are only a few degrees apart.
 >          Sparking or not?

Don't know off hand, but I'll bet it doesn't make a heck of a lot of
difference..  The spark (or not)  is "outside" the secondary inductor

 >
 >
 >
 > >  > A lumped series-resonant circuit can be visualised as an inductor L
and a
 > >  > capacitor C
 > >  > in series with a signal source or "generator". 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?
 >
 > >Nope.. in a series circuit, the currents all have to be equal.
 >
 >          In a closed series circuit...
 >          And the use of 'series resonance' in this case is
 >          a mental model, an analogy, and need not be pushed too
 >          far.

It IS a closed series circuit... Consider the secondary inductor as one
component, the topload capacitance (to the ground) as another, and the
connection from ground to the bottom of the secondary as the thing that
"closes the loop".  A more sophisticated model would be a bunch of nested
parallel loops, to incorporate the capacitance of the secondary windings to
ground (with an occasional nonlinear resistance in parallel (the sparks),
which if taken in the limit, is much like a transmission line.  However, if
you try and consider the TC secondary as a transmission line connected to a
capactive/resistive load, you'll find that it doesn't behave much like a
classical line.  It doesn't have uniform impedance along the line, for one
thing. It also has significant coupling from one part of the secondary to
another.  It is MUCH more like that familar component the lumped inductor
(i.e. the inductance varies not as length (as a transmission line would) but
as the square of length (assuming constant turns/inch).