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Before posting my previous comments about the comparison between the half-wave dipole in empty space and the quarter-wave monopole over a ground plane, I tried to find out if anyone else had expressed a viewpoint in print that was similar to what Rich stated in his posts. Not finding any such source, I did the best I could in answering Rich.
Since posting, I have found in an article by John W. Ames and William A. Edson in the Nov./Dec. 1983 and Jan./Feb. 1984 issues of R.F. Design that a debate similar to the one between Rich and myself has happened before. The name of the article is “Gain, Capture Area, and Transmission Loss for Grounded Monopoles and Elevated Dipoles.” The article criticizes “artificial constructs” such as “gain calculated as though the antenna were in free space.” Emphasis was given to the words, “as though.” Unfortunately, the authors did not cite any sources of where these supposed “artificial constructs” were expressed.
I think that some authors had felt the need to equate the the half-wave dipole in empty space and the quarter wave monopole over a perfect ground plane because there are certain theoretical difficulties with the quarter wave monopole over ground. These difficulties are distracting when one is trying to teach the very complicated subject of antenna theory, and it makes pedagogical sense to simplify the subject by equating the two types of antennas.
One difficulty with the quarter-wave monopole above ground is that the reciprocity theorem does not hold exactly. The reciprocity theorem states that the receiver gain of an antenna is the same as the transmitter gain. For the monopole above ground, the two gains are the same only if the source of the received signal is a skywave. If the source of the received signal is a groundwave, the receiver gain is only -.86 dBi. A quarter-wave monopole above ground generates groundwaves, but it is a poor receiver of groundwaves.
Another difficulty with the monopole above ground is that two monopoles above ground (one a transmitting antenna and the other a receiving antenna) cannot be properly thought of as two separate antennas because the infinite ground plane, and the distance between the antennas, are components of both antennas.
Still another difficulty with the monopole above ground is that an isotropic source is defined as being in free space, but, to generate a grounwave, an isotropic source should be above the ground plane. This is a difficult situation conceptually, because an isotropic source is already a fiction, and to redefine this fiction as another kind of fiction is simply hopeless. Nobody has been able to clearly define what is meant by an isotropic source above ground. Ames and Edson have characterized the idea of an isotropic source above ground as another “artificial construct.”
The situation would certainly be simpler if we looked at the monopole above ground as being equivalent to a dipole in free space, but this notion is not consistent with physical reality. “Nature is what it is, not what we would want it to be.” E.T. Whittaker. I think that it is best to simply use the definitions of receiver gain and transmitter gain and accept the results that are obtained by measurement (or, for the ideal case, by calculation.) The tramsmitter gain for the quarter-wave monopole above ground is 3 dB higher than the transmitter gain of a half-wave dipole in free space. The receiver gain of a quarter-wave monopole above ground is the same as the transmitter gain when receiving a skywave, and -.86 dBi when receiving a groundwave.