Re: Quarter Wavelength Frequency

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk> 

Dr. Resonance wrote:

 > 11,058 ft.
 > 1/4 lamda freq = 23 kHz w/o large toroid topload

This seems to assume a velocity factor of unity for the wound wire,
whereas we know it will be faster than that for anything in the
normal TC range of length/diameter ratios.

Ed wrote:

 > Wire length 11058 feet
 > Wire weight 56.07 pounds
 > DC resistance 70.6 ohms
 > Fr 16.779 kHz

Is that Fres for the loaded coil Ed?  If for unloaded then you'd
expect something 20% to 100% over 23kHz instead.

Malcolm wrote:

 > I have a coil which I will measure tonight and post on tomorrow
 > which has a totally outlandish H/D ratio

One problem with longer, thinner coils, is that the dielectric
properties of the coil former material begin to affect the
frequencies.   Where the thickness of the tube wall is more than a
negligible fraction of the tube radius we get a noticeable portion
of the internal capacitance E-field passing through the dielectric
instead of the air.  The mutual capacitances along the coil are
increased above the values we would calculate by any of our methods
and the actual resonant frequencies can be 5% or 10% lower than
predictions.  This problem also appears to show up at small h/d
as well as small radius.

Short of immersing the coil in a large tank of liquid dielectric
chosen to have the same permittivity as the tube material, I'm not
sure how to allow for this!

Phil LaBudde wrote:

 > So as the pitch increases, you are "stretching out" the coil back
 > into a straight wire. But doesn't space winding decrease the "Q"
 > of a coil, and therefore make it less efficient as an inductor,
 > which is what you would expect from effectively unwinding one?

We're not opening out the pitch in our models which must be why the
velocity factor is heading up to some number above 2 instead of to
around 1.  But yes, the Q would deteriorate beyond some optimum
pitch, as inductance goes down and radiation resistance increases.
If radiation resistance is suppressed by enclosing the resonator
in a cavity then the high Q factors are restored - so the low
inductance, by itself, isn't the problem.

Interesting suggestion for the use of spiral core spark plug
wire.   The unknown dielectric properties would exclude it for
quantitative measurements, but it would be fun to play with a
piece to see how it behaved at RF.  It could be looped into a
toroid and so on.  You never know, it might be a handy material for
use in radio circuits where a long-ish, perhaps tapped, resonator
is required.  It might be a worthwhile exercise to try to measure
its reactances per unit length, Q factors, etc.   I guess the
wire's pretty thin, though.

Ed wrote:
 > On reading a listing I realized I had used Wheeler's simplest
 > approximation instead of Lundin's much more exact method, but for
 > the range of L/D above the difference is less than  a percent so
 > makes no significant difference in the results.

Oh well, no matter, it doesn't affect the conclusions:  By comparing
things against measured results and against calculations drawn from
a more detailed model, we no longer need to rely on the original
calcs you used to arrive at this discovery.

 > The main error is in estimating Cd anyway.

Agreed.   Anyway, nice work Ed.  You've shed some much needed light
on the relationship between wire length and resonant frequency.
Until now all we've been able to say is that the frequency changes
in some complicated way as the wire is wound up.  You've shown that
it actually varies quite smoothly with the overall geometry  (as
opposed to being some complicated chaotic function involving turns,
pitch, etc).   As a result, coilers can now get an estimate of Fres
directly from h, d and wire length - an estimate which is probably
at least as good as using Wheeler times Medhurst.

There is one big puzzle though.  I'll write about that in another
thread.
--
Paul Nicholson
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