Re: Wire length,resonance, and Q (fwd)

---------- Forwarded message ----------
Date: Tue, 12 May 1998 22:49:06 -0700
From: "Antonio C. M. de Queiroz" <acmq-at-compuland-dot-com.br>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Wire length,resonance, and Q

Jim McVey wrote:
> According to conventional physics, (let me know if I missed something)
> a charge and it's attendant feilds will propagate faster  in a straight
> wire
> than in a coil. It follows that the coil should always resonate lower than
> the wire since the velocity is less than the speed of light.
> Why then, do long space wound coils resonate at a frequency higher
> than expected? This has nothing to do with the LC ratio either. I would
> expect that no matter what gain or reduction of L vs C for a given
> geometry, they should always result in a frequecy lower than that of
> a straight wire.  Whats going on here???
> Before I go and re-invent the wheel, does anyone have an explaination
> and/or experimental data on this?

The magnetic coupling transports the signal to the end of the coil faster
than the current alone would do.
If you work with the Medhurst formula for capacitance and the Wheeler
formula for inductance, you will find that for coils with significant
aspect ratio, the resonance frequency approaches twice the one predicted
by wire length only.

An experimental result:
Wire length: 318 m
Turns: 1152 
Coil length: 32 cm
Coil radius: 4.4 cm
Resonance by wire length: 236 kHz
Predicted inductance: 28 mH
Predicted capacitance: 5.6 pF
Resonance frequency by LC model: 402 kHz
Experimental resonance frequency: 385 kHz 

This first resonance is really 1/4 wave resonance, with the voltage along
the coil increasing sinusoidally. There are other resonances (3/4 wave, 5/4 wave,
etc., at higher frequencies. Do someone have data about measured frequencies
of these higher-order resonances? In my coil they do not follow the expected
frequencies 3f, 5f, etc. predicted by a TEM mode transmission line model.

Antonio Carlos M. de Queiroz