Re: Tesla Coil RF Transmitter

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Jim wrote:

> One can have a band limited system with no standing waves. A lumped
> LC is a fine example.

Agree with your comment but not your example.  I would say a lumped
LC is a fine example of a standing wave within a (idealised) system
having a single degree of freedom.

Continuously deform a distributed resonator (eg Dan's beam or a
resonating coil) by smoothly shifting one of the reactances (say
mass or inductance) to one end, while shifting the other reactance
(elasticity or capacitance) to the other end.   You arrive at a
lumped resonator (LC circuit or mass/spring) without any
discontinuity in the mode of resonance or frequency.  The phase
relationships between displacement and velocity, or between volts
and current, remain the same.   The higher overtones of the original
resonator smoothly shift up towards infinity as the reactances
become more lumped.   There is no 'step' as the resonance 'switches'
from one physical principle to another, say.

Complete separation of the reactances can only be achieved on paper,
in the idealisation of the 'lumped' resonator (mechanical and
electrical), in which a single degree of freedom (a single pair
of dynamic variables, eg V/I or Y,Ydot) replaces the infinite
degrees of freedom of the distributed resonator.  This *is* a step
change, but it's a step change in our representation, not in the
physics.

A good example of a band limited system with no standing waves
would be a cascade of RC low pass and RC high pass filters, having
overlapping pass bands to produce a lossy bandpass filter.

Dan wrote:

> Jim:
> Any resonant system will exhibit standing waves at certain
> frequencies. I have a feeling you are of the oppinion that the
> earth has no resonant mode or frequency. Is this so, and why?

I doubt that Jim disbelieves in the Schumann resonance.  What he
is doing is reminding us that: seeing a peak in the noise spectrum
doesn't automatically imply that you have a global standing wave
resonance behind it.  Once you have detected your noise peak, you
have to perform further experiments to confirm 'global coherence'.
Otherwise, you might just have a local frequency selective effect.
(ie an effect occuring everywhere, but not involving any sort of
long-range interaction, so that each locality has its own
independent 'noise peak'.  The global resonance is confirmed by
looking at phase correlation between several very remote sites).

Also, of course, the presence of a spectrum of Schumann resonances
at the expected frequencies is strong evidence for a global standing
wave resonance.

Nobody doubts the Schumann resonances exist, nor reasonably doubts
that they have low Q factor - far too low to be of use in Tesla's
schemes.
--
Paul Nicholson
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