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Re: Determination of the propagation parameters of a helical coil
Hi all,
I have completed it and I have reached my goal.
I started of with the view that the lumped equation using Medhurst C could
not possibly produce the correct frequency. This was due to my belief (and
others) that Medhurst C was the true self C of the coil.
Now the true self C of the coil is between 2 and 3 times Medhurst C
(approx. 3 for short coils and 2 for very long coils, autotransformer
analysis). So a quick bit of lumped approximation shows that the lumped
equation using Medhurst C would work which it does so circuit laws are
right.
If you then use the true self C in a transmission line type equation you
get a good answer. Which was what I originally thought. But now I know
that the standard transmission line equations don't apply because of the
mutual coupling between turns. So why such a close answer?? Perhaps the
circuit laws are wrong.
The correct parameter that must be used in the transmission line equation is
the mutual inductance per unit length and is a function of frequency. But
for coils greater than 5 diameters long this has the same numerical value
(<0.1% error) as the total inductance divided by the length of the coil (for
wavelengths at least 4x the coil length). Hence the equation works and the
circuit laws are correct. i.e. measure the true L and C of your coil and the
frequency is the reciprocal of four times the squareroot of the product of
the L and C measured in H and F respectively. Strictly this only true for
long coils and does necessarily include accurate "end effects" which I
believe will make the coils appears electrically longer. This effect will be
doubled for isolated coil compared to a coil on a ground plain. It also does
not include the effects of internal C. For one coil I compared the results
with, it produces an answer closer to the measured frequency than Medhurst.
This may have just been lucky as I estimated the self C and did not include
end effects.
The same reason that makes the velocity equation valid also makes the wave
impedance equation valid again accurate only for long coils and wavelengths.
I dont know what effect the end effects will have on the impedance.
Revelation is a wonderful feeling.
It is interesting to speculate whether a simple addition law for top C
drops out of the equations. Are the circuit laws going to be that kind
to us?
Regards Bob (a waveophile or more accurately a circuitlawophile )