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Re: transmission line theory and secondary resonance
Hi Gavin,
Yes you have it right. But note that med C and a lump equation does
produces reasonable answers for f (10% error for the average H/D ratio
coil) for the reasons I have already posted. A fortuitous bit of luck for
Teslaphiles. It want however produce the correct voltage (this may be a very
controversial view)
Note also that the TM equation should be using the mutual inductance per
unit length but again more luck. In the average coil this is equal to the
inductance divided by the length of coil. The full equation with all
effects will be posted at some point.
I and others have failed to find a formula for the intrinsic C of an
isolated hollow cylinder but I have not given up hope. If you find one I
would appreciate you posting it immediately.
There is a special version of Wintesla that calculates intrinsic C and gave
an answer within a few % of one measured coil. The regular one calculates a
voltage weighted C that may be similar to med C. I direct you to Terry
Fritz for either the special one or an explanation for the voltage weighted
one.
What does isotropic mean with in the context of your reply?
Regards Bob
-----Original Message-----
From: Tesla List <tesla-at-pupman-dot-com>
To: tesla-at-pupman-dot-com <tesla-at-pupman-dot-com>
Date: Thursday, May 25, 2000 10:55 PM
Subject: transmission line theory and secondary resonance
>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.
>
>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.
>
>
>
>
>
>