[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> 

snip

 >
 > Many thanks for the figures from mrn6.  Things are beginning to
 > become much clearer with regard to how the lumped and distributed
 > models coincide.   And coincide they must, if they are both correctly
 > implemented (which I think they both are).
 >
snip
 >> --
 > Paul Nicholson
 > --
 >
 >

Hi Paul,

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.

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.

The practical significance of this is small for a two coil system.  However
here were talking theory and were talking about the response of coils near
higher order poles and zeros. So a lumped model and transmission line model
will diverge in theory and the divergance may be significant practicaly.
Simple put a lumped model can only be accurate at freqences well below
resonance or near one pair of the pole pairs. Accurate meaning we can in
theory make the error as small as we want by picking a lower frequency or a
frequency closer to a pole pair but only one of the pole pairs.(or zeros
with series lump)

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.

Bob