antenna-theory.com

[johnm]

Can someone give me, or point me to, a propagation path loss model or algorithm
(1) that includes refractivity (curvature of the wave back toward the earth as it goes thru the atmosphere due to dry air high up and moist air near the earth's surface), diffraction (the wave wrapping around an edge like a mountain ridge), ground bounce, and surface roughness,
(2) that's good for ground to air communications in the HF (0.5-50MHz) frequency range and if necessary, another one for above 50 MHz, and
(3) where an antenna height can be above 10km

For example:
Let ground in the neighborhood of the antenna parameters be
conductivity = s
relative dielectric constant = er
relative permeability = ur

Let wavelength = L
Let Tx height = Ht
Let Rx height = Hr
Let Tx power = Pt
Let the Rx antenna's effective aperture area = Ae
Let the radius of the earth = Re

I have three Tx antenna/polarization situations
(A) 1/4 wave monopole on the ground with idealized dense 1/4 wave radials a few inches above the ground (so Ht=0)
(B) 1/2 wave vertical dipole with it's center Ht/L wavelengths above the ground
(C) 1/2 wave horizontal dipole Ht/L wavelengths above the ground

Assume 1 watt (or Pt) is going into the antenna's feed point and all the power is radiated (nothing is absorbed by the antenna metal or lost due to a mismatch reflection).

My receiver antenna is far away at a ground range of Rg, and at 10km height.

I'd like a function for vertical polarization for the first two Tx antennas, and a function for horizontal polarization for the third Tx antenna, that gives the received power Pr, given,
Pt, Ht, Hr, Ae, s, ur, er, Re, Rg

Start with a smooth earth and good to Hr = 10 k feet.

Then what's added to get to Hr = 10 km height or more? In other words, since 4/3 earth radius that is typically used to account for refraction is only good to about 10 k feet, how does one correctly model a receive antenna higher up, like at 10 km height?

And then can you give me, or point me to a model that accounts diffraction and reduced ground bounce due to diffuse scattering and shadowing caused by the surface roughness? For example, where there are parameters in the model to account for the variance of the slope of the ground, and the variance in the height of the ground between the Tx and Rx. Or maybe just broad categories like coastal/plains vs Appalachian mountains vs rocky mountains, etc.

If possible, could you also point me to any references where measurement results at HF (0.5-30MHz) frequencies are given for different terrains that confirm the validity and usage of the model, or where the theory for the model is explained?

Right now, I'd just love to have a script in matlab or python or mathcad or even a spreadsheet. I'd settle for a solid reference that was complete and clear enough for me to write a script too!

Thanks!!!

[R. Fry]

[johnm]

R. Fry --- Thank you very much for responding. Longely-Rice is a good stab. That said, I was specifically looking for (1) high altitude (10km) aircraft-to-ground paths, which is quite different from terrestrial paths, (2) 0.5-30 MHz (lower frequencies, Longley Rice was made for terrestrial VHF/UHF broadcasting), and (3) equations and if possible downloadable commented python/matlab/mathcad code directed accurately addressing (1) and (2).

Regarding #1,
(a) the paths to aircraft can be much longer,
(b) a much greater percent of the path is free space and not affected by terrain,
(3) the wave does not bend as much in the dryer air above 3km,
(4) the grazing angles can cover a huge range -- all the way from near zero to 90 degrees, and
(5) the direct and ground bounce paths can arrive at the receive antenna from very different directions--e.g. 90 degrees when the grazing angle is 45 degrees--i.e. on the main-beam for one, while a null for the other.

Regarding the use of the vertical polarized reflection coefficient versus grazing angle equation over the full 0-to-90 degree grazing range for example, I have not seen an equation that correctly sums the direct and ground bounce paths--i.e. correctly accounting for the fact that the the refection coefficient equation is derived such that at a grazing angle of zero, the Tx and Rx V-pol antenna E-field=plus directions are aligned, while at 45 degrees grazing they are orthogonal, and at 90 degrees grazing their E-field=plus directions are inverted--so the phase of the standard reflection coefficient equation is effectively 180 degrees wrong at 90 degrees grazing, but correct at 0 degrees grazing.

Perhaps someone could post some equations aimed at these points, or point me to a reference, or point me to another applicable forum for this.
Thanks again.