Sorry Jim, you're mistaken on many counts.
An antenna does not have VF, but the wire we use for it does. VF of an
infinitely thin bare wire in free space is 1. Surrounding it with a
dielectric (insulation) makes it longer electrically, usually by a few
percent. So does making the wire fatter. These differences are usually
described using VF.
Placing a conductor close to earth (within a few inches) causes it to
couple to the earth, which also makes it electrically longer. We could
also describe this using VF.
VF is NOT constant with frequency, whether in a transmission line or in
wire. VF of all transmission lines starts out quite small at audio
frequencies, rises quickly through the audio spectrum, eventually
reaching a near constant value at mid-VHF. It is this near-constant
value that is computed by the simple equation that doesn't include
frequency. For most lines, VF has reached about 98% of its final value
at 2 MHz.
Likewise, Zo is not constant with frequency, nor is it a pure
resistance. It starts out quite high at low audio frequencies and is
dominated by capacitance. Zo falls rapidly in the audio spectrum, and is
quite close to its final value at 2 MHz, but is still capacitive,
typically 1-2 ohms.
This can be clearly seen in N6BV's TLW software that comes on the CD
with the ARRL Antenna Book. Choose your favorite coax, set the frequency
to 2 MHz, make the line 300-400 ft long, and terminate it in a pure
resistance. TLW will tell you Zo. Now select Volt/Current next to the
Graph button (lower right corner) and you'll see that there are
standing waves on the line (the graphs are not a straight line). Now set
the Load to the R and X values for Zo and hit Graph again. Now the V and
I lines are nearly straight, indicating quite low SWR. They would lay
exactly on top of each other, but the R and X values for Zo are rounded
off.
The fact that Zo, VF, and attenuation vary with frequency is clearly
predicted by the full transmission line equations. There's a brief
discussion of this in
http://k9yc.com/Coax-Stubs.pdf
which also shows how VF and attenuation can be computed and plotted vs
frequency by making two measurements of a sample with a vector analyzer
like the AIM, SARK, and VNWA analyzers. The two measurements are then
exported to AC6LA's excellent freeware Excel spreadsheet called ZPlots.
There's a longer discussion of this, specifically written for audio
people, but obviously important for radio, in
http://k9yc.com/TransLines-LowFreq.pdf
73, Jim K9YC
On Fri,12/30/2016 11:12 AM, Jim Allen wrote:
but “velocity factor” is a characteristic of transmission lines. Interestingly, it is
independent of frequency (up to the limit of the dielectric). It depends on the
geometry of the line and the dielectric material. > > Antennas don’t have a
velocity factor. The shortened elements are caused by capacitive loading against (RF)
ground. There is a percentage of the free-space electrical length due to capacitive
loading, but it is not a velocity factor.
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