Re: Frequency Splitting

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi All,

Many varied interpretations being presented here...

Dan wrote:
> If you had two identical tank circuits and coupled them
> together, there would be no beat frequency.

That bit's wrong.  Perfect symmetry is no problem: the dual
resonance behaviour is just fine when both LC units are identical.
This is a common misunderstanding,

>  the fres of one goes up, and the fres of one goes down,

That's the source of the error.  It's incorrect to assign one
frequency to one coil and the other frequency to the other coil.
The important thing is that both of these modes involve a joint
resonance of both coils.  Hence there's no need for the symmetry
breaking requirement which Dan suggested above.

Having said that, if one coil has its uncoupled Fres different
to the other, there will be a difference in amplitudes of the
two modes in each coil.  The low frequency coil will have a
higher proportion of V,I in the lower mode, and vice versa.
The result under these conditions is incomplete instantaneous
amplitude cancellation at the notches, resulting in incomplete
energy transfer and difficult or impossible quenching - the
system is 'out of tune'.

> When two resonant circuits are coupled together, the frequency
> response contains two distinct peaks at two different
> frequencies.

Two different frequencies, yes, but only distinct on a 'sweep' if
k is greater than about 1/Q.

D.C. wrote:
> Maybe frequency splitting isn't the best term

There are some grounds for arguing that.  In bringing up another
resonator to the first, a second 'degree of freedom' is being
introduced.   It only appears as a 'splitting' of the previous
single mode when the new resonator has its uncoupled Fres close
to that of the first.   It sure looks like a splitting when
you watch the sweep as the coupling is increased, but it doesn't
look at all like a splitting if you start with overcoupled k
but with one coil tuned to a very low Fres.   As you raise the
Fres of that coil towards the other, the sweep will show the
lower resonance peak appearing to 'push' the other resonance
away.

> two separate resonant freqs occur with overcoupling which
> produces two separate points along the coil when potential
> peaks occur.

That's not quite right.  For both modes, the potential peaks
are at the secondary top.

> these two pure freqs start "beating" against each other and
> standing waves occur.

Seen in the time domain, they beat together to produce the
desired beat envelope and notches.

But...standing waves always occur, regardless of k, so long as
Q is greater than about 6.  We *want* the standing waves - they
are just another name for a resonance or 'mode'.  It's incorrect
to suggest that standing waves only occur during overcoupling
and are undesirable.

(Of course, standing waves - resonances - higher than the two
 which make up the beat *are* likely to be undesirable because
 they do create additional voltage maxima within the secondary.)

--
Paul Nicholson
Manchester, UK.
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