Re: Mode Splitting

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Original poster: "Bob (R.A.) Jones" <a1accounting-at-bellsouth-dot-net> 


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From: "Tesla list" <tesla-at-pupman-dot-com>
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Sent: Thursday, August 19, 2004 5:28 PM
Subject: Re: Mode Splitting


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

 >
 > Better to say: With k=0 the primary and the secondary systems resonate
 > (oscillate) at the same frequency. When the coils become coupled, this
 > single frequency splits in two, one above and the other below the
 > original
 > frequency, and both systems oscillate at both frequencies
 > simultaneously.

Perhaps very clumsily I was trying state that the two modes are independent.
Yes its true that in the usual impulsive system they are excited
simultaneously but in a master oscillator SSTC or using a signal generator
either mode can be driven
independently to the extent of their Q and separation.
It has been incorrectly stated that mode splitting does not occur in an SSTC
as if
some how its a property of the drive signal as opposed to a property of the
system.

 >  > That probably needs expansion. The
 >  > reflected impedance of the primary is either inductive or capacitive
hence
 >  > the wave of one mode is shortened and the other is lengthened.  The
 >  > shortened one will have the same polarity at both end while the
lengthened
 >  > one will have the opposite polarity at its ends with one null near the
 >  > primary end. Of cause the real effect is distributed along the coil
with
 >  > the distributed inductive coupling from the primary.  Incedently I
don't
 >  > think the higher order modes of the secondary split because at those
higher
 >  > frequencies the reflected impedance of primary is always inductive so
they
 >  > are just shifted. In the case of a top load coil all modes are
truncated at
 >  > the top.
 >
 > I don't see much use in considering steady state impedances in this
 > case,
 > where there are two frequencies involved and the waveforms are all
 > transient.

I think we would agree that the system is linear  (assuming a closed spark
gap) just a collection of Ls Cs and Rs so it can be completely characterized
by it complex impedances which I
assume you refer to as steady state impedances. Hence in the usual complex
circuit analysis whether we get a transient
or not is a function of the excitation signal.

 >From the perspective of the secondary we can replace coupled primary circuit
with a parallel tuned circuit in series with primary end of the secondary
using the relationship ((Lm.s)^2)/Zp were Lm is the mutual
inductance and Zp is the series impedance of the primary. Similar to the way
you eliminate the coupling in several of your papers.
The referred impedance is equivalent to a parallel tuned circuit
which is high impedance (assuming both are at the same frequency) at the
frequency of the 1/4 wave mode of the secondary.
But that mode requires a low impedance so even though the
impedance is real (something that's bugged me for a long time) the mode can
not be supported.
Either side of the 1/4 wave frequency the impedance is low and either
inductive or capacitive hence it can support a 1/4 plus a bit or a
truncated 1/4 wave mode.

Using this description its also easy to visualize what happens if you vary
the primary and secondary frequencies.  As the separation frequency increase
one mode move down the resonance curve of the referred primary and one moves
up to the peak. At the peak the impedance is too high to support that mode
and it disappears leaving only the other mode  and the uncoupled resonance
of the primary that has very little feed thru to the secondary.
Well easy for me to visualize.
Apart from finding the roots of the transfer function.  I have not read any
explanation of the mode splitting that even come close to holding water.


One surprise, for me anyway, was that one of the split modes has null.   But
in fact that's the only way the two orthogonal modes can sum to a maximum at
the primary while summing to zero at the top end and be almost zero along
the secondary.
Then (if the frequencies and phase are right) after a time interval sum to
zero at the
primary and a max at the top of the coil.  There was  minor problem because
two orthogonal modes or for that matter three or any finite number can not
initially sum to zero over the length of secondary. To do that you need you
need a contribution from all the higher order modes.

An other intersting point is that the closer the two spilt modes are in
frequency the better they cancel along the secondary so less contribution is
required from the higher order modes.
Putting this an other way. In an impulsive system the tighter the coupling
the more energy is wasted in the higher order modes.
This ignores the distributed effects of the coupling so it may only be
partially true.
In any case I do not mean to suggest that the wasted energy is necessarily
significant relative to other losses only that its inevitable.

Bob