Re: Bandsplitting?

From: 	Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: 	Thursday, December 04, 1997 9:53 PM
To: 	Tesla List
Subject: 	Re: Bandsplitting?

Hello Greg,

> From:   ghunter-at-mail.enterprise-dot-net[SMTP:ghunter-at-mail.enterprise-dot-net]
> Sent:   Thursday, December 04, 1997 3:55 PM
> To:     Tesla List
> Subject:    Bandsplitting?
> Hi All,
> I read a posting awhile back to the effect that over-coupled Tesla
> coils were subject to "bandsplitting".  Does that mean breaking up
> into harmonics, or what?  I've been employed in comm/nav electronics
> for many years, plus I've dabbled in amateur radio for 10 years 
> (N5QMR), but the term is unfamiliar to me.

Basically, if you magnetically couple two tuned circuits to a 
sufficient degree, a spectral analysis of the waveform produced shows 
there are two frequencies present *simultaneously*. The waveform 
looks like a DSBSC modulation envelope. The degree of coupling 
required for this to happen is defined by k > kc and this can can be 
expressed in terms of circuit values by:

       M.SQRT(Qs.Qp) > SQRT(Ls.Lp)    where M is mutual inductance.

This relationship is derived from: k = M/SQRT(Ls.Lp)  and a 
dimensionless factor, kc = 1/SQRT(Qs.Qp).  For a given set of 
inductances mounted in fixed proximity, k is fixed. kc however is
dependent on the Q's of the two circuits and that changes with 

If Kc = k, the circuits have attained critical coupling. If k > kc,
the circuits are overcoupled and the DSB envelope is the result. You 
can see that for high Q circuits, kc can be exceedingly small, far 
smaller than the typical k's of 0.1 - 0.3 that we run two coil 
systems at. All two coil systems designed to produce sparks *must* be 
overcoupled or they cannot deliver all primary energy to the 
secondary in a small and finite time (at kc = k, transfer time 
becomes infinite).
    The two frequencies can be expressed as sinusoidal functions of k.
However, what one sees in the frequency domain does *not* tell you 
what is really happening in the time domain (i.e. Voltage with 
respect to time). That is important because we are concerned with 
what voltages our coils are oscillating up to. In the time domain 
(oscilloscope as opposed to spectrum analyser), what you see 
happening is the primary ringing down as the secondary rings up. You 
see the energy transfer taking place and it is clearly taking place 
at the resonant frequency of the system. To produce the amplitude 
varying waveform you see on the scope, two quite disparate 
frequencies with the right amplitude and phase relationships must be 
present at the same time - i.e. you can synthesize the resultant 
waveform from two separate frequencies such as is done in a modulator. 

   > The same posting implied that Tesla magnifiers were immune to 
> bandsplitting.  Why is that?

The resonator isn't magnetically coupled to the primary. Instead, it 
is run by feeding a voltage into the base. In effect it is a single 
coil transformer. 

> What difference does it make if the 
> resonator is over driven by magnetic coupling or by a transmission 
> line?

The resonator can be viewed *as* a transmission line that is 
electrically 1/4 wavelength long at its resonant frequency, and up 
until sparks are produced, tied to a low impedance at one end and a 
very high impedance at the other. 

Refer to 1/4 wave transformers and coupled double-tuned circuits in a 
good radio reference book.