An Important Post.

From: 	Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: 	Monday, August 04, 1997 7:22 PM
To: 	tesla-at-pupman-dot-com
Subject: 	An Important Post.

Dear list, 
            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 :)

Future experiments:
- 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.