An Important Post.
From: Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: Monday, August 04, 1997 7:22 PM
Subject: An Important Post.
This morning I have made a breakthrough that I count as
the most important piece of research I have ever undertaken. I have
produced a model of a TC resonator using lumped components in an
artificial transmission line and measured it. The paradoxes that have
puzzled so many for so long are now explained and verified in
The Experiment: The goal was to model the resonator accurately using
real world components in such a manner as to allow *direct*
measurement of its attributes. Moreover, the model had to agree with
the formulae we use to predict frequency etc, most notably the lumped
ones (e.g. Wheeler, Medhurst). After mulling over the results of line
experiments done in the last two days, it appeared that appropriate
grading in the line was needed to get the lump calculated frequency
to agree with the measured resonant frequency and so it proved to be.
Apparatus: A seven stage line was built as follows:
1.6mH 800uH 400uH 200uH 100uH 50uH 25uH
In | | | | | | | Out
--- --- --- --- --- --- ---
--- --- --- --- --- --- ---
Gnd | | | | | | |
10pF 22pF 50pF 100pF 220pF 470pF 1000pF
Caps are silvered mica jobs. The inductors are airwound on bobbins
for the popular FX2239 potcores.
Results: Measured f = 65kHz +- 0.2kHz
Calculated f = 65kHz near as. Done by summing inductances and
capacitances and using standard 2PISQRT(LC)^-1
Most of the 90 degree phase shift along the line occurred in
the first stage as did the bulk of the voltage rise. This is
not surprising since half the total inductance appears in this stage.
Obviously the model needs to be made a lot more fine-grained to be
real close to the real thing but serves as a good indicator
Until I get a lo-Z sig gen onto it, I cannot measure Q or VSWR within
to reasonable accuracy. The line loaded the el-cheapo generator was so
heavily loaded that generator output sagged by over 75% at resonance.
With this model is shown:
- lumped frequency calc agrees with measured value despite the
distributed nature of the circuit
- grounding one end of a single layer solenoid alters it
characteristics markedly from the normal lumped behaviour but
preserves the lumped values all up. This is why we can measure L
and f and calculate C and find it agrees with well tested formulae
despite the fact that wired as a resonator, top L is almost non-
existent and appearances suggest the resonator L should be less
than the measured lumped value.
- the resonator appears to match at resonance when terminated at each
end by its calculated Zo (1.3kOhms) i.e. Vo = Vi to first order
with a 90 degree phase shift from one end to the other (second
order LP filter response at the turning point :)
- use a more finely graded line to observe gradual phase shifts
- use capacitive E transfer to measure Vo pk
- measure Q and VSWR
Some Implications of these results:
- IMHO the Corum's analysis of the two coil system as being lumped is
correct but for the wrong reasons. They claimed that because primary
flux envelopes the whole secondary with minimal time delay, the
coupled system can be treated as lumped (of course there had to be a
reason - you can't ignore measurements). However, modelling by others
in PSPICE and some elementary thinking shows this cannot be true. The
primary is heavily coupled to the bottom portion of the resonator
only. Witness the lack of effect of sticking a shorted turn (toroid)
at the top of the resonator on the primary - pretty much
unmeasureable in the primary. For that matter, it hardly affects the
resonator either :)
It is clear to me that conservation of energy must be observed in
doing output voltage calculations in the resonator. IMHO, *estimates*
of some MegaVolts output for very modest primary energy melts away
entirely.IMHO, it follows from these results that Vo for a capacitive
discharge situation should follow the rule Vo = Vi.sqrt(Cp/Cs). Many
experiments in measuring single shot sparks have suggested this for a
long time now.
It follows that a free resonator must obey the same rules except
for being free of magnetic coupling to the driving system. It follows
then that conservation of energy must also apply to a free resonator
in a pulse-driven situation because a finite amount of energy is
available to charge the distributed capacitance. Until it is measured
though, that is speculation on my part.
All for the time being. Flames, comments and refutations welcomed.