Re: Mode Splitting

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

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

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

Some notes:

 > I wrote this description of mode (some times called frequency)  splitting
 > while exploring how an SSTC can be driven with soft switching while
 > maintaining high voltage gain (no break out). I thought it may be of
 > interest to some readers
 >
 > A naked(zero k to primary) Tesla coil secondary has oscillation modes
 > usually described as 1/4 wave, 3/4 wave etc.  all truncated if its top 
loaded.

I think about these modes as voltage profiles along the secondary coil
when the output voltage is maximum. They are not (directly) related to
the oscillation at multiple frequencies that causes the energy transfer
from the primary to the secondary circuits.

 > As the k to the primary is increased from zero the 1/4 wave mode splits in
 > two modes. One mode is higher and one mode is lower in frequency than the
 > original mode.

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.

 > They also have opposite polarity at the top of the secondary
 > for a given polarity at the primary.

They add construtively at the primary initially, while adding
destructively
at the secondary. When the energy transfer is complete, they add
construtively
at the secondary while adding destructively at the primary. The actual
polarities depend on the directions of the windings of the coils, and
how
you measure the primary voltage.

 > 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.

 > Initially the polarity of all modes including the two fundamental modes of
 > a standard coil and the three modes of a magi  are the same at the primary
 > cap and sum every where else to zero. A number of half cycles later the two
 > fundamental (or three in the magi) modes now sum to a maximum at the top
 > load and sum to zero at the primary cap.

Ok.

Antonio Carlos M. de Queiroz