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 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.

 > ...
 > Incidently the complex frequency plane is very similar to a 2D coulomb flux
 > plane. The poles and zeros have similar properties to positive and negative
 > point charges.  The response at any point in the complex frequency plane is
 > the sum of the reciprical of the distance to each poles and zero, positive
 > for poles and negative for zeros (from memory) with an overall scaling
 > factor.

This also shows the the effect of poles and zeros decays with the
distance
(in frequency) to them.

Antonio Carlos M. de Queiroz