From: Paul
Date: Fri, 24 Nov 2000 16:43:04 +0000
Subject: Re: [TSSP] E-Tesla6.11
Terrell W. Fritz wrote:
> I think my other post today address this. I think the top of the
> coil is rather dead aside from capacitive effects.
Comparatively, but not completely dead. Recall the bathtub shape of
the external capacitance profile. That extra capacitance at the top
helps keeps the coil alive, right up to the top turn. Plus, the
internal capacitance is receiving its maximum exitation at the ends
of the coil, so its displacement current needs to be added in also.
You'll see from your voltage profiles that the voltage continues to
rise all the way up to the top. If you look at the bare coil current
profile, eg example 1 in
http://www.abelian.demon.co.uk/tssp/pn1710/
you'll see that the current is still significant in the top part of
the coil, only plunging steeply to zero at the very top.
> >
> >#2 - is your calculated Cself the Medhurst value or the DC value?
>
> I simply calculate the capacitance of a cylinder shaped object in
> the given room. I guess that would be Cself but perhaps the
> definitions are a bit in disarray at the moment.
Terry is placing a prototype voltage profile onto the coil and then
calculating the total external flux leaving the resonator. This, when
divided by Vtop, leads to the total equivalent shunt capacitance,
which would be the DC capacitance if Terry replaced the tesla-like V
profile with a uniform voltage.
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,
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.
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.
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'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.