TSSP: List Archives

From: Paul
Date: Sat, 23 Dec 2000 16:03:33 +0000
Subject: Re: [TSSP] Final solution...great chance for it

I wrote:

> > Yes, that's the time taken to solve the network for
> > AC steady state conditions at a single frequency.

boris petkovic wrote: 

> > > -----
> I guessed you would say that.
> What about (computing time), simulating 100 turn coil
> response when step function applied ,say at  pentium
> processor?
> -----

Funny you should say that. I have a time domain simulator
which just happens to have 100 elements...its a while since
I've used it, and it doesn't do the longitudinal coupling
stuff. I don't have any timings for it, but its *very* slow,
I seem to recall an hour or more to get a solution for a
transient.

boris petkovic wrote:
 
> The purpose of his technical paper was not just to
> predict current and voltage waveforms over winding but
> to emphasize difference between standard (our),well
> known approach with the chain of coupled  qudruples
> and his method.

> Physical background of the process is better explained
> in his case.

Understood. I'd like to see more - will look forward to
the post arriving.

> Once,you re intersted in predicting Q of secondaries
> ,right?
> Now,I will ask you quite a diffucult question.
> What do you think could be the highest possible Q of
> the structure like Tesla's 100 turn 100"*100'' extra
> coil from CS?
> Imagine  there is perfect ,loseless isolation,super
> conducting winding and enviroment,and the only
> losess comes becouse of radiating.
> I don't expect concrete number ,but try to guess the
> ballpark.
> ------

OK, the only loss is due to radiation. I worked this out
once, a long time ago. Can't find my figures so I'll do
it again...

Consider the lossless TC resonating in free space with angular
freq w and stored energy E. The Q factor is then

 Q = wE/P

where P is the radiated power. From a sufficient distance away
it resembles a Herztian dipole with a dipole moment qh where
q is the displaced charge and h the coil length. 
Since V = sqrt(2E/Cee) then q = CesV = Ces sqrt(2E/Cee).

The total power radiated from a Herztian dipole is obtained
by integrating the Poynting power density over the surface
of a large bounding sphere. I'll spare the details and say

P = (1/12pi) * z * w^4 * q^2 * h^2 / c^2
  = (1/6pi) * z * w^4 * Ces^2 * h^2 * E/Cee/c^2  Watts

where c = 300 * 10^6 metre/sec, z = 377 ohms.
 
Thus 

Q = wE/P = 6pi * c^2 * Cee / (z * w^3 * Ces^2 * h^2)

Say Cee = Ces = 30pF;  w = 2.pi.10^5 rad/sec;  h = 1 metre.

Then Q is approx 6 * 10^8, pretty high.

Now is that in the right ballpark? Are we safe to ignore 
radiation? I get the feeling you're going to tell me I'm
missing something :)

Cheers,
--
Paul Nicholson,
Manchester, UK.
--


Maintainer Paul Nicholson, paul@abelian.demon.co.uk.