transmission line theory and secondary resonance

To: tesla-at-pupman-dot-com
Subject: transmission line theory and secondary resonance
From: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Thu, 25 May 2000 17:50:05 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Hi Bob,
O.K. it's finally sunk in regarding the transmission line analysis of
secondary coils and the true or intrinsic capacity involved; I think.

The Medhurst self capacity is only for when a larger capacity is added
to the coil, in the case of TCs, this is the top load or isotropic
capacity. This value can not be used to calculate the resonant frequency
of a free standing coil which has no top load.

Now for transmission lines:

The formula for a wave to propagate across a unit length of transmission
line is given by:

t = sqr (L * C)

where L is the inductance of the line per unit length and C is the
capacity per unit length.

Now, for a particular length of transmission line, the resonant
frequency is simply the frequency at which a single wave cycle sits on
the line. With this specific condition the time for propagation t is
equal to the waves periodic time, hence:

fr = 1/t

and so

fr = 1 / sqr (L * C)

For quarter wave resonance, the length of line should have sitting on it
a single wave of frequency equal to four times the resonant frequency
fr, so that

4 * fr = 1 / sqr (L * C)

and so

fr = 1 / (4 * sqr (L * C))

I would then guess, using similar logic that:

fr = 1 / (2 * sqr (L * C))

For a bipolar resonator?

But the C in the above formula is not the Medhurst value for self
capacity, but a more fundamental value called Cintrinsic.

Cintrinsic is the isotropic capacity of a cylinder having the same
dimensions as the wound helical coil being analyzed.

So for a quarter wave resonating coil having no top load and far removed
from other objects in it's vicinity, the formula applies:

fr = 1 / (4* sqr(L * C))

for long TC secondaries.

Have I got it right ??!!

If so, has anyone yet found the formula for the isotropic capacity of a
cylinder yet?

Thanks again for your help and patients Bob and Malcolm.

Kind regards,

Gavin, U.K.