From: "Mark S. Rzeszotarski, Ph.D."
Date: Wed, 06 Sep 2000 12:44:38 -0500
Subject: Re: [TSSP] Low Q Values
Greetings Paul:
At 04:45 PM 09/06/2000 +0100, you wrote:
>Mark,
>
>Lets just clarify this. Your small coil, and all of Malcolm's data,
>plus your and my calculations all indicate that a decrease of Q with
>added topload is the norm. The proposal is that increase of Q with added
>topload, as exhibited by Terry's coil, is a sign of eddy current loss.
I think Terry's measurements are being affected by either the ground
plane of metal on the floor or extraneous metallic objects above his coil.
I expect to see Q fall when a topload is added, primarily because wL drops
faster than Rac as the resonant frequency drops due to the added capacitance
of the topload. Rac changes rather minimally, but w changes quite a bit.
Terry's coil is large, and I would expect that metal within two or three
coil heights could affect the results significantly. I see impedance
changes in my small 12" coil 6' from it. The addition of a toroid may
induce some eddy currents, but I think that effect is very minor. People
have sawed toroids to break the circular loop with no perceptible effect on
tesla coil output.
>Mark wrote:
>> There are several series approximations for estimating mutual
>> inductance but they work poorly with tesla coil geometries because
>> you end up subtracting terms with large values in the series.
>
>Yes, I've a lovely formula summing products of Legendre polynomials
>which suffers exactly that problem.
>
>> Can you describe the geometry you are looking to solve?
>
>That of a single turn circular loop above and parallel to
>a ground plane. I want to know the change in Q factor of the
>the loop, as a function of ground plane thickness, conductivity,
>height of loop, and of course f. Thats the ideal form to be
>fitted into the computer model of the solenoid - it can just go
>in as an adjustment to the series resistance of each turn.
>I'm happy to ignore second order effects such as coupling from a
>solenoid turn via eddy loops to other solenoid turns.
I haven't seen this one although it may be discussed in a book I
have on helical resonators. I'll look for it.
>Also, if you have a good formula for mutual inductance between
>coaxial circular current filaments, please pass it on - I'm not
>too happy with the one in use at the moment.
I have the Dover reprint of the classic text by Grover on inductance
formulas. It is essentialy a reprint of one of the NBS Circular journals
(don't remember the number). It has at least one formula there. I'll track
it down.
Regards,
Mark S. Rzeszotarski, Ph.D., MetroHealth Medical Center,Radiology
Department, Cleveland OH 44109-1998
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.