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RE: Calculating secondary resonance of bipolar coils



Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <paul-at-abelian.demon.co.uk>

Ralph Zekelman wrote:

> In sweeping several of my large coils I have noticed the existence
> of the self resonant modes that are not in harmonic relationship.

That's good. Next time you're sweeping a signal generator across your
coil, especially a large one, make a note of the resonant frequencies
of each mode that you find. Do you find that beyond say the 3rd or
4th that the frequency interval between each one tends towards a
constant?

> However, one particular frequency will have the maximum amplitiude.
> Isn't this the resonant frequency? and if this is Fr, where are the
> harmonics?

The apparent 'amplitude' of the resonance will be determined by how
much power is coupled into the coil from the generator. This is likely
to appear greatest at the lowest resonant frequency, ie the usual
one for TC operation. This is because the lowest mode exhibits the
lowest input impedance for a given coil and coupling method.

I'll qualify that statement slightly. If you're picking up the coil
activity using a 'plane wave antenna' as static field pickups are
often inappropriately called, the response of such a pickup can rise
with frequency at up to 6dB per octave due to the capacitive nature of
its pickup - its a CR network, the C being the capacitance between
pickup and coil, and R the input resistance of your detector. 
A similar thing occurs with inductive loop pickups, the loop output
voltage being proportional to frequency.  With this in mind, the
higher modes may sometimes appear to have more amplitude than they
really have.

I'm not sure what you mean by asking where the harmonics are. A
resonant structure does not exhibit any special response to harmonics
of its resonant frequency (unless it's formed from some sort of time
delaying mechanism which has the same velocity at all frequencies and
no reactance at all in its end terminations, in which case the over-
tones fall into harmonic alignment, but I prefer to think of these as
separate resonances which just happen to be aligned in this special
case). So don't expect anything to happen at 2Fr, 3Fr, etc, in a TC.

Cheers
--
Paul Nicholson,
Manchester, UK.
--