[Elecraft] Matching resonant antennas

[Jim Brown]

On 7/16/2020 9:57 PM, Ken WA8JXM wrote:
> So pruning a horizontal dipole will never provide a 1:1 SWR except at 0.18
> wavelength above ground (the ONLY elevation where the radiation resistance
> is 50 ohms)?  About 97 ft for 160m, 24 ft for 40m, 6 ft for 10m?  A dipole
> a half wave above ground has a 70 ohm radiation resistance and therefore a
> 1.4:1 SWR is the absolute best?

No, it's FAR more complex than that. Horizontal antennas see the 
reflection from the earth as a parasitic element, which adds a complex 
impedance to the equivalent circuit. The reflection, and thus the 
parasitic impedance, will depend on height above ground, the skin depth 
of the earth, and the electrical qualities of the soil.

The ON4UN book, "Low Band DXing," includes a set of very interesting 
plots of antenna impedance as a function of height and soil quality. In 
general, the feedpoint Z of low dipoles oscillates as height varies, 
with the average near 50 ohms, while high dipoles oscillate around 70-80 
ohms. It's easy to see this in the very simple NEC model of a center-fed 
dipole (the model is a wire with a generator in the center of it) by 
varying the height and the soil parameters.

My dipoles for 40 and 80M are up about 125 ft in tall trees, and I have 
lousy soil. The model predicts Z at resonance in the range of 85 ohms, 
and I've measured 88 ohms. I feed them with RG11. Some years ago, I was 
planning antennas for a CQP county expedition in a spot that has scrub 
trees (max rigging height ~40 ft) and lousy soil, but is on a small 
knoll, so the takeoff angle is great. NEC predicted 75 ohms for one of 
them and 50 ohms for the other, so we carried RG8 for one and RG11 for 
the other. When we measured them, they turned out as the NEC model 
predicted.

There are computational tools and instrumentation that one can learn a 
lot from if we use them to study stuff like this. NEC is one of them.

73, Jim K9YC