From: "Terrell W. Fritz"
Date: Sat, 25 Nov 2000 21:04:25 -0700
Subject: Re: [TSSP] E-Tesla6.11
Hi Paul
At 04:43 PM 11/24/2000 +0000, you wrote:
snip...
>
>Terry, you recall I expressed some doubts about the method applied in
>E-Tesla6 - I felt that it might not be representing the energy stored
>in the internal capacitance. Computers here have been churning through
>telescope data, so I've had time to sit back and work through the math
>and I'm quite certain now that your method is correct, providing that
>is, you calculate Fres by resonating your C with the right inductance.
>The required inductance is the equivalent series inductance (Les),
>formed by integrating the EMF induced along the coil,
Oh good! The capacitance should have been right. You had me worried ;-))
>
> Les = integral{ x,y = base to top, M(x,y) * I(y) * dx * dy}/Ibase.
>
>or, simplifying by replacing the mutual inductance profile M(x,y)
>with a uniformly distributed self inductance Ldc,
>
> Les = Ldc/h * integral{ x = 0 to h, I(x) * dx}/Ibase;
>
>where h is the coil length. Normalising the position variable to the
>range 0..1, and the base current Ibase to 1.0, we have
>
> Les = Lfac * Ldc,
>
>where
>
> Lfac = integral{ x = 0 to 1, In(x) * dx}
>
>in which In(x) is the normalised current profile. This is the origin
>of the factors I sent you a while ago.
>
>Terry wrote (in another thread):
>> Obviously, this would be sort of a messy development since it
>> changes some fundamental ideas that we use to calculate coil
>> values.
>
>It's this Lfac that's the origin of your concern, and also the
>solution to my misgivings about your method. In fact, although the
>internal capacitance is not accounted for explicitly in your
>capacitance determination, it does creep in through the current
>profile required to calculate Lfac. Consequently, although the good
>news is that your shunt capacitance determination is correct and can
>be used for Fres, you are effectively having to guess the internal
>capacitance contribution when you select a normalised current profile
>or Lfac factor.
>
>I guess what you need for E-Tesla7 is a magic formula for Lfac as a
>function of h/d.
Yes, I tried some things but they did not work out. May have been a math
error on my part too... It appears that Lfac is indeed very important!
>
>One thing to note is that the equivalent shunt capacitance as
>calculated by E-Tesla6 can be used to obtain the transimpedance of
>the resonator, since the total external flux relates directly to
>Ibase, and thus Ibase can be related to the Vtop assumed by the
>program.
>
>Another point. The equivalent shunt capacitance cannot be used to
>calculate the top voltage on the basis of voltage gain through energy
>storage, Vtop = Vpri * sqrt( Cpri/Csec). The Csec that is required for
>this calculation is the equivalent energy capacitance which has
>a different definition and a different value.
Very interesting!!
>
>While we're on the subject of self capacitance, I'm starting a
>campaign to deprecate the use of the term Cself. Offhand I can think
>of six different definitions of what might be called the self or
>equivalent capacitance. Each has a different value, they are all
>equally correct but each must be applied appropriately. I've trawled
>through many a discussion on the pupman archives in which arguments
>are at cross purposes through participants being vague about the
>capacitance terms they are using. Its really not safe to form any
>firm conclusions from hand-waved arguments involving the terms like
>Cself, Csec, Cintrinsic, Cdis, etc. It's easy in lumped land - all
>these values converge to a single C which can be used casually. In a
>distributed world, where different parts of the system are at different
>potentials, when you want to quantify the effect of charge or energy
>distribution in some respect, you're going to have to summarise the
>distributed capacitance in some appropriate way in order to describe
>its effect by referring it to a point of interest. I'll endeavour to
>produce a document which defines all these 'equivalent self
>capacitances' and shows how each is related to the physical
>capacitance distribution, and to each other. I'll try to show how each
>can be used, eg for Fres and Vtop calculations, and also which can be
>measured and how.
That would be great! All these definitions are certainly getting cloudy
these days and I don't think any two people have the same set of ideas as
to what they all mean. A set document of their meaning would really help
keep things straight.
Cheers,
Terry
>
>That's all for now - I'll go catch up on a backlog of emails,
>
>Regards All,
>--
>Paul Nicholson,
>Manchester, UK.
>--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.