Topband: Low-angle radiation from vertical antennas

[Dan Maguire via Topband]

This is somewhat related to the "vertical on a beach" thread but I figured if I put that in the subject line I might get lynched.

In the past there have been questions about the accuracy of NEC far field calculations at low take-off angles for vertical antennas since the far field does not include the ground wave.  To help resolve the issue I modeled a λ/4 vertical with and without the ground wave at multiple slant (radial) distances and plotted the results.

This is for the 160m band at 10°, 1°, and 0.1° take-off angles with slant (radial) distances varying from 100 m to 100 km:

http://ac6la.com/adhoc/VertFlds9.png

And this is for 40m:

http://ac6la.com/adhoc/VertFlds10.png

As expected, the far field values decay at a "1/r" rate.  With log-log scales that's a one decade decrease for every one decade increase in radial distance.  At close-in distances the far field does indeed under-estimate the total field which includes ground wave.  However, for typical sky wave propagation the difference has vanished (plot lines converged) long before the ionosphere has been reached.

For each of the 3 take-off angles, calculations were done at 100 different distances in order to get smooth curves.  Obviously I didn't do those one at a time; I used AutoEZ with 100 test cases.  Each test case generated an EZNEC "Setups > Near Field" like this.

http://ac6la.com/adhoc/VertFlds5.png

Near Field calculations report the total field, including the ground wave, and are valid at any distance from the antenna.  For the Far Field, also done for each test case, AutoEZ can convert the dBi values produced by EZNEC to the corresponding mV/m field strengths.

Dan, AC6LA
http://ac6la.com