[Elecraft] Small QRP antenna

[Jim Brown]

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.