Velocity Factor and resonant frequency
Cecil Moore wrote:
Tom Donaly wrote:
When are you guys going to do your own experiments and
measurements.
I've already done them and reported them here, Tom. Here's
the procedure again.
1. Take a sample coil and measure the 1/4WL self resonant
frequency over my GMC pickup ground plane.
2. Keeping everything else the same, cut off half of the
above coil.
3. Add enough straight wire as a stinger to bring the
antenna system back to resonance at the previous self-
resonant frequency.
4. The delay through half the coil at the self resonant
frequency of the whole coil, is known to be 45 degrees.
The stinger is 11 degrees long. The impedance discontinuity
between the coil and the stinger provides the other 34
degrees of phase shift.
Both sides of the argument assumed only two phase shifts
were involved. Both sides were wrong. The third phase
shift is obvious once you know it exists and is perfectly
visible on a Smith Chart. When the impedance at Z01 is
1.0 on the Smith Chart and transforms to 9.0 on the Smith
Chart for Z02, that's obviously a large phase shift.
Two years ago, both sides agreed that the stinger was
about 11 degrees of the antenna.
1. Side 1 said that the base loading coil acted as a
purely lumped inductance providing 79 degrees of phase
shift essentially at a point.
2. Side 2 said that the base loading coil provided a
79 degree delay like the delay in a transmission line,
which was the source of the 79 degree phase shift.
At that time, both sides were unaware of the phase
shift occuring at the impedance discontinuity point.
Now we know that both sides were partially right and
partially wrong. As side 1 said, there is an abrupt
phase shift at a point. As side 2 said, there is a
delay through the coil. The truth seems to be just
about in the middle of the two previous arguments
which should make both sides happy.
There are tens of degrees of delay through the coil.
There are tens of degrees of abrupt phase shift at
the coil to stinger impedance discontinuity.
Both sides were equally right and equally wrong. Who
won? Both sides. Who lost? Both sides. This is the
invariable result when both sides are forced off the
rails by reality.
The only problem with that, Cecil, is that in neither the
coil nor the inductor do you have a uniform Z0. Since the
capacitance per unit length is a variable, so is Z0 which
is dependant on it. You've been sucked into Reg's
practice of assuming an average Z0 in order to do
calculations, but in your case it won't work because
you have to posit two distinct Z0s to have your impedance
boundary. In actuality, there's a constant change in Z0 up
and down both the stinger and the coil so your idea is a
bust. By the way, if you or the Corum boys really want a
transmission line resonator for your antenna/Teslacoils
you should switch to a helical resonator, the kind ensconced
in a can. Of course, the sparks will be disappointing, but the
theory will work better.
73,
Tom Donaly, KA6RUH
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