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Re: transmission line theory and secondary resonance

Hi Gavin,

On 25 May 00, at 17:50, Tesla List wrote:

> Original Poster: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net> 
> 
> 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.

Not true. If you take that value along with the secondary inductance 
and plug the values into the lumped resonance formula you will get 
consistently good results. That is NOT to say that this is a true 
indication of how the resonator works however. The Medhurst recipe 
remains just that - a recipe. 
 
> 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 ??!!

In my opinion, yes but there will be end effects such as increased 
capacitance, just as there are for a typical antenna.
 
> If so, has anyone yet found the formula for the isotropic capacity of a
> cylinder yet?

No unfortunately. Some prime old physics texts which might have 
contained the details were tossed out of the library here some time 
ago with the justification that the library needed to be kept "up to 
date" :(   Can you imagine??

      I am planning to acquire a large room here in a semester break 
to do some extensive measurements on a bundle of resonators I 
have that will prove useful in providing a benchmark for any 
developed formulae to be tested against. I can't say when and it 
might not be until the end of the year when things go quiet but given 
the right room, I can get the isolation and noise-free environment 
that is mandated for good measurements.

Regards,
Malcolm