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I tried to get Rich to discover the truth about the subject under discussion for himself by using his NEC program, but that did not happen. If Rich had gotten his NEC program to work correctly with the problem he had posed himself, he would have seen that, if two parallel half-wave dipoles are in free space, at the same height, operating at 1 MHz, separated by 3000 meters, with 1000 watts of radiated power from the first dipole, the maximum power available from the second dipole is about 170 mW. Values close to 170 mW were obtained by Kraus’s method and Rich’s own “other method.” My own simulation with the EZNEC demo program also gave about 170 mW. I think that if Rich were to check the setup of his NEC-2 simulation, he would get 170 mW also. If he can’t get this result, he should use another version of the NEC program.

After the simulation of the two dipoles, the next simulation to be performed with NEC is to find out how much is the maximum power available from a receiving quarter-wave monopole over a ground plane when a transmitting quarter-wave monopole over the same ground plane, separated from the receiving monopole by 3000 meters, radiates 1000 watts. I did the simulation with with my EZNEC demo program, and, as I expected, the maximum available power was about 170 mW, the same as for two half-wave dipoles in free space, separated by the same distance, and the transmitting dipole radiating 1000 watts.

I knew that two half-wave dipoles in free space would give the same maximum power transfer as two quarter-wave monopoles over a ground plane because that is a well-known theorem in antenna theory, which was proved many years ago. The earliest proof of this theorem that I know of is by Kenneth A. Norton, “System Loss in Radio Wave Propagation,” Journal of Research of the National Bureau of Standards-D, Vol. 63D, pp. 53-73, 1959.

As I explained in my previous post, if two half-wave dipoles in free space and two monopoles over a ground plane have the same power transfer ratio for the same separation distance, this proves that the receiving monopole has 6 dB less gain than the transmitting monopole. It is known that the transmitting monopole has 3 dB gain over a dipole. To make the system gain for two monopoles over a ground plane equal to the system gain of two dipoles in free space, the receiving monopole must have 6 dB less gain than the transmitting monopole.

This phenomenon has been explained as the absence of ground reflection at the receiving monopole when receiving groundwaves, which causes the effective height of the receiving monopole to be half of what it would be if skywaves were received.

I have my own intuitive explanation of the phenomenon, which I have not seen stated in print before, but it is more satisfactory to me than the “missing reflection” explanation. I hope that it also provides a convincing explanation to others:

I is well-known that the ground plane causes a quarter-wave transmitting dipole to have 3 dB more gain than a half-wave transmitting dipole in free space. This is because all of the radiated power from the transmitting monopole must be above the ground plane. Similarly, all of the radiated power intercepted by the receiving monopole must be above the ground plane. Thus, a quarter-wave monopole above ground must have only half of the capture area of a half-wave dipole in free space. So, the ground plane causes a -3 dB gain in the receiving monopole compared to a receiving dipole.

To repeat, the ground plane causes a +3 dB gain (compared to a half-wave dipole in free space) in the transmitting monopole because all of the radiated power of the monopole must be above the ground plane. At the same time, the ground plane causes a -3dB gain in the receiving monopole because it cuts off half of the incident radiation applied to it, compared to a half wave dipole. The + 3 DB gain of the transmitting monopole compared to the dipole, and the – 3dB gain of the receiving monopole compared to a dipole, combine to cause the system gain of two dipoles to have the same system gain as two monopoles. Thus, the receiving monopole gain is 6 dB less than the transmitting monopole gain when groundwaves are received.

The many thousands of field strength measurements Rich mentions of monopole antennas generating groundwaves are not relevant to this discussion because the transmitting monopole gain is not in dispute. There is only a dispute about the receiving monopole gain, and only when receiving groundwaves, and not sky waves.

It’s too bad that the antenna books mentioned do not deal with the interesting and well-established fact that reciprocity fails for receiving monopoles over ground that are intercepting groundwaves. I hope that Rich will be able to set up the dipole and monopole simulations on his NEC program so that he will be able to check out this fact for himself.