[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: Magnifer vs. Tesla Coil



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


----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Thursday, November 20, 2003 6:29 AM
Subject: Re: Magnifer vs. Tesla Coil


 > 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 don't see how the two models can coincide.  It does depend on the
details
 >  > of the two models. ie the lumped model uses one set of LCR for each
coil
 >  > whereas the transmission line model presumable uses the sum of the
response
 >  > from several modes for each coil. If that is correct then the following
is
 >  > true.
 >
 > A distributed model is just slightly better than a lumped model, that is
 > an approximation that ignores higher-order natural frequencies of the
 > network. A lumped model gives you values and equations that can be used
 > in design without much complication. A complete distributed model is
 > more suitable for analysis, and maybe small adjustments. My measurements
 > of real systems designed from the lumped model show perfect qualitative
 > agreement, and just small errors easily explainable by the nonuniform
 > current in the resonator coil (affects the coupling coefficient of the
 > transformer).
 >
 >  > The lumped model can only be accurate (<10%error) for a limited region.
Two
 >  > obvious regions are below say half the self-resonant frequency, thats
what I
 >  > will call the Medhurst lumped model. In the Medhurst region you can
 >  > approximate the response of all the poles and zero with just one pair
of
 >  > poles or in your terms read modes for poles and zeros.  In the next
region
 >  > around the first pair of poles you can approximate that region with the
 >  > actual pair of poles.
 >  >
 >  > Above the resonant frquency as you approach the higher order zeros and
poles
 >  > of a real coil both of the previous lumped models will have large
errors
 >  > whereas the distributed model (if its the sum of several modes) in
theory
 >  > remains accurate.
 >
 > This would be true for a magnifier -without- a top load. The high-order
 > resonances of a coil are around three times the frequency of is first
 > resonance. When a terminal with significant capacitance is in place, the
 > main resonance is substantially reduced, but the higher order resonances
 > -remain- at high frequency (at most one of them falls to around the 1/2
 > wave
 > resonance of the bare third coil). Even the fastest possible magnifier
 > has
 > the highest resonance at a mere 3/2 of the resonance frequency of the
 > third coil+topload, so even without a topload the model predicts the
 > correct behavior. Add losses to the system, and the high-order
 > resonances disappear much more rapidly than the low-frequency ones, and
 > the lumped model works even better.
 >
 >
 > Antonio

  Hi,

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

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. 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.

  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.

Bob