[TowerTalk] Fwd: Change in Frequency As Antenna Height Rises

[jimlux]

On 6/1/16 1:45 PM, Hans Hammarquist via TowerTalk wrote:
>
> It seems to me that Steve's, G3TXQ and Dan's, AC6LA diagrams coincide pretty well. You find the lowest frequency at about 1/4 wave and max frequency at about 1/2 above ground. What I don't understand is how the frequency start to decrease at the high increases before it reaches 1/4 wave above ground. In my simple mind the fx should start to increase as soon as the antenna "leaves round".
>
>
> To me, and obviously I'm wrong, the capacitance to ground should affect the frequency with the result that the fx should increase when the ground capacitance decreases up to the point where speed of light start to have an effect.
>
>
> Anybody with a "simple" explanation?
>

It's basically "not simple" but what you're really looking at is the 
mutual impedance of the dipole with the "image" in the soil.  If you 
look at those graphs of mutual Z for two dipoles with variable spacing, 
you'll see a lot of similarity.

What you see as the feedpoint impedance is the combination of the 
impedance of the dipole itself in combination with the mutual impedance 
of the image antenna.

And the "other antenna" is a very lossy one.

With a fair amount of math:
Chapter 23 in Orfanidis's book http://www.ece.rutgers.edu/~orfanidi/ewa/

http://www.ece.rutgers.edu/~orfanidi/ewa/ch23.pdf   (page 1057, figure 
23.3.2)

There's a simpler plot in the ARRL Antenna book, but it's not online, 
and I don't have it handy.