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

---------- Forwarded message ----------
Date: Thu, 21 May 1998 08:56:11 +1200
From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Wire length,resonance, and Q

Hi Jim,
           My explanation FWIW:

> From:  bmack [SMTP:bmack-at-frontiernet-dot-net]
> Sent:  Monday, May 11, 1998 9:43 PM
> To:  tesla list
> Subject:  Wire length,resonance, and Q
> To all,
> When Dr. Tesla made initial coil designs, he often resorted to quarter
> wave length calculations as a guide.  My early impressons of this was
> that it was the upper boundry for the physical length of wire that could
> be used.  Since, however I found that this is not neccessarily the case.
> The most intriguing thing is the cases where the coil resonates at 
> frequency HIGHER than the wire length alone indicates!  Malcolm made
> a passing refence to this in one of his recent posts as well.  Preliminary
> quick experiments indicate that the coil geometry has alot to do with it's
> ultimate resonant frequency apart from the length of the wire.  Really 
> bizzare things happen when the aspect ratio is below 0.1.
> 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?
> Curious in NY
> Jim McVey

Assume one has a 1/4 wave length of wire straightened out as an aerial
(1/4 wave monopole). It has a particular distributed L and C. Now 
coil that wire up. C drops and L rises through mutual inductance 
between the turns. However, M between turns is less than 1 and Cdistr 
is dependent on wire/coil length. The only reasonable explanation I 
have been able to come up with is that due to the less than M=1 
between turns, C drops faster than L rises when the wire is coiled up 
in this way. Hence Fr is higher than for the straight wire.