# Mode Splitting

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

Hi all,

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

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.

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

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. . Initially all the modes sum to
zero every where else but its only the first two (or three modes) that have
the correct phase to peak at the top load and sum to zero at the primary C.
Fortunately the amplitudes of the higher modes are small which is why they
can neglected in most models and analysis.

Bob

```