COPIED FROM ANOTHER NEWSGROUP

I see you are a follower of Medhurst.

You might like
http://www.eagleware.com/pdf/apps/20...ngSolenoid.pdf

Andy, M1EBV
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Andy,

Thanks for pointing me towards the above document.

I've never heard of Medhurst. Or anybody else who might have messed
about with an arithmetical treatment of the subject. I've never
bothered to look.

I can't understand all the details (the paper is not very well
written) but I gave the paper a couple of speedreads.

It's interesting because it treats a solenoid as a transmission line.

A few years back I evolved explicit formulae for calculating the
self-capacitance and self-resonant frequency of single-layer, solenoid
coils. Such coils are fairly common. They are used, for example, as RF
chokes and, when wound with coaxial cable, as chokes in coaxial
transmission lines. Sometimes they are just a hank of a few turns of
coaxial cable. Apart from their connecting wires they are, in effect,
isolated in space. Long solenoids also form helically wound vertical
antennas which can be top-loaded with a rod. Or horizontal, short,
continuously loaded dipoles where the resonant frequency is required
to be predictable in advance of construction.

With chokes it is required to calculate the band of frequencies over
which the impedance exceeds a fairly high given value.

My formulae are based on transmission lines with conductor length and
diameter corresponding to length and diameter of the solenoid. I
discovered this by analysis of the problem. (The author of the article
discovered it by accident when making measurements.) Provided the
number of turns is greater than 5 or 6, even with close-spaced turns,
the capacitance between turns can be ignored. Very thin wire compared
with wire spacing does decrease overall capacitance but not because
wire-to-wire capacitance is less.

As a check on the formula, if the wire is stretched out to be an
exceedingly loose helix, then the resonant frequency becomes that of a
straight length of wire - the wire is just a half-wavelength dipole
and its resonant frequency coincides with the formula.

Several of my programs use the formula which incorporates an inverse
hyperbolic function. It always struck me as being incongruous to use
such complicated functions for such a simple matter of calculating
such a very small, inconspicuous capacitance. See programs SELFRES3,
SOLNOID3, HELICAL3. There are other programs in which
self-capacitance matters but the program user is unaware of it. What
use could he make of it if values were displayed?

An Autic Antenna Analyser can be used to measure the self-resonant
frequency of a solenoid coil very accurately. Just place a 1 or 2-turn
link-coupling around the CENTRE of the coil without any other
connections. Connect the coil to the meter via an 18-inch length of
loosely-twisted pair of wires. Suspend the coil in free-space using
only the twisted pair. On the impedance magnitude range, tune the
analyser for a VERY sharp rise in impedance - and there you have it.
Maximum impedance will be several hundred ohms. Q will be very
igh - it is easy to miss resonance. So much for old-wives tales
about poor Q at self-resonance. You may notice a sharp null in the
meter reading at a very slightly higher frequency which is due to a
series-resonance in conjunction with the twisted-pair and the meter
itself. If you can't detect a null, don't worry about it.

This method works (I know of no other) with short fat loading coils,
with 160-meter helical antennas 6 feet long with 1500 turns, and with
coaxial chokes using a hank of a dozen turns, 8 inches in diameter. It
fails when the coil's resonant frequency exceeds the range of the
meter.

By the way, the self-capacitance of coils depends on their close
environment. It can jump about all over the place and change when long
connecting leads are soldered on. My formula applies to a coil in
free-space as the sensible starting point. I could derive an approxima
te formula for your toroidal coils, they are only bent transmission
lines, but at the age of 80 I don't wish to expend any further time on
the subject. smiley
----
Reg, G4FGQ.