Re: Magnifer vs. Tesla Coil

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: "Robert Jones" <alwynj48-at-earthlink-dot-net>

 > I was curious about how the poles moved so I looked back at my analysis.
 > Unfortuatly there is a bug in my sofware and it crashes after a short time.
 > However from inspection. I believe the following is true similar to you
 > statement

How did you simulate the system? Paul Nicholson tssp programs can make
an accurate simulation. For more qualitative results it's possible to
simulate a discrete version with several LC sections, after estimating
proper values. A simpler model is an uniform transmission line loaded
by a capacitor.

 > As top load is  added the poles pairs shift to a lower frequency by
 > approximatly the same amount (ignoring dispersion) were as from at least one
 > perspective the zeros do not move.

I imagine that you are looking at the impedance seen at the output of
the system. In an analysis of a single coil (modelled as a transmission
line or anything else) loaded by a capacitor, the zeros of the output
impedance really don't move if the load capacitance is changed. This
must be in this way, because at the frequencies of the zeros the load
capacitor is short-circuited, and so its value doesn't affect the
zeros.
The low-frequency poles can be moved to arbitrarily low frequencies by
adding larger terminal capacitance, but the other poles move by
approximately the same amount, never crossing the zeros. The second
lowest
resonance never crosses about twice the frequency of the lowest
resonance
in the unloaded case.

 > As more top load is added the higher
 > order poles at approximatly 3, 5, 7 etc of the self fresonant frquency
 > progrssevily move to wards the fixed zeros at approximatly 2,4,6 etc. Hence
 > for very large(say 1/10 self res or 100 times self C) toploades the higher
 > order poles will be very near  to the zeros and hence cancell each other.
 > Because of this cancelleation effect a second order model will accuretly
 > (say 1%) model a coil with a large(1/10 self res or 100 times self C) top
 > load up to say 1.9 times resonance and possibly even beyond assuming good
 > cancellation.

Interesting observation.
Note that a coil loaded by a huge terminal capacitance is effectively
grounded at both ends, and so operating in "1/2 wave" mode. Additional
resonances are expected to appear around 2, 4, 6, etc. times the
fundamental resonance frequency, but it's difficult to "excite" them
because there are zeros very close to these same frequencies.

 >   I was suprised you have not found mesured differences between your lumped
 > model and real coils. This quick and dirty calculation suggests your correct
 > with average top loades. Consider a top loaded coil such that its resonance
 > is reduced to a half,  At 3/2 of its resonance frquency  the relative
 > distances to the first poles and zeros  is approximatly 1:6  with the
 > inverse square law thats 1:36. Just  approx  3% contribution which would be
 > reduced futher to say 2% by the next pole pair. With a small top load say a
 > reduction to 0.7 of self resonance the contribution is a still only about
 > 10%. Compared to the no top load case at 3/2 its 1:1 say 30% with the
 > effects of the next poles.

With zeros close to the poles, the amplitudes of the corresponding modes
decay quickly. Add losses that grow with frequency to the system and
the modes (in the now nonlinear system) decrease even more.

I was worried bout the effect of high-order resonances on magnifiers,
because if they are designed for modes a:a+1:a+n, n large, there is
a resonance at quite high frequency, easily above the main resonance
of the unloaded system. But I didn't observe anything evidently wrong
experimentally. The cancellation may explain why.

Antonio Carlos M. de Queiroz