Home › Forums › temp › Whip Antennas for Part 15 FM Compliance › Some intuitive explanations

Total posts : 45366

My debate with Rich about the apparent reciprocity failure of monopole receiving antennas has ended on this thread, but another antenna expert (who has directed an antenna laboratory for many years) has taken up Rich’s cause, and I still continue to discuss this subject, but not (until this post) in a public forum. The level of the discussion has progressed from an offhand dismissal of my assertions to a willingness to look into the matter. I will report to this forum if a definite conclusion is reached.

The essence of the debate is that I say that, for a given separation, the ratio of the available received power to the transmitted power is the same for a pair of monopoles over a perfect (flat) ground plane as for a pair of dipoles in free space. The contrary view is that the two monopoles have 6 dB more received power than the two dipoles.

I previously made no attempt to prove this claim, and only cited Kenneth A. Norton, who, in 1959, had proved this theorem about monopoles and dipoles. What I am doing now is giving an intuitive explanation of why two monopoles have the same system power gain as two dipoles: Let us now consider two dipoles, not in free space, but a short distance above the ground plane. Unlike the situation in free space, more than one ray goes betweem the transmitting dipole and the receiving dipole. In free space, only a single ray goes between the transmitting and the receiving antennas. Near ground, there is the direct ray, and a second ray that is reflected from the ground. If the dipoles are only slightly elevated from the ground, the two rays are only slightly out of phase, and the two rays combine nearly in phase to double the field strength incident on the receiving antenna, causing a 6 dB increase in the system gain. When I say, “slightly elevated from the ground,” I don’t mean that in absolute distance, but in relative terms. That is, the elevation of the dipoles is small compared to the distance between the dipoles. This 6 dB increase in system gain is the same as is expected in the contrary view of two monopoles over a ground plane. Now, let’s look at two monopoles over a ground plane. These two monopoles over a perfect ground plane are similar to two dipoles in free space. The difference is that the two lower dipole arms are virtual, and not real, due to ground reflection. The ground reflection is used to produce the virtual dipole arms, but there is no additional ground reflection to produce the second ray which increases system gain. Therefore, the maximum system gain for two monopoles must be the same as for two dipoles in free space.

There is a corollary to the theorem above equating the system gain of two dipoles to two monopoles: If a dipole and a monopole are immersed in identical fields, the dipole will deliver to a matched load twice as much power as is available from a monopole. To explain this corollary, imagine a dipole in free space having a particular capture area. For a monopole above ground, the real dipole arm above ground receives the signal, but the virtual dipole arm below ground does not receive any signal, because the signal is only present above the ground plane. Therefore, the capture area for a monopole is half of that for a dipole, and the corollary is demonstrated.

If the angle of the incident radiation to the monopole receiving antenna were raised just a little bit above zero degrees, there would not be just the single surface wave ray applied to the antenna, but also an additional reflected ray, causing the field intensity at the antenna to be increased by 6 dB. With this additional reflected ray, the receiving gain of the monopole would be as high as the transmitting gain, instead of 6 dB below the transmitting gain.

Now, is there really a reciprocity failure if the representations of this post are true? I think that there actually is no reciprocity failure in the receiving monopole, but it is necessary to look at reciprocity not as a phenomenon of a single antenna in isolation, but of a transmitting and a receiving antenna forming a system. The principle of reciprocity is fulfilled if, for a system of two antennas, the receiving antenna can be interchanged with the transmitting antenna. For a system of two dipoles, or a system of two monopoles, it is obvious that the transmitting antenna can be interchanged for the receiving antenna. For the case of a system composed of a monopole and a vertical dipole, you also get the same system gain if you interchange the receiving antenna and the transmitting antenna. If the monopole is the transmitting antenna, and the dipole is the receiving antenna, the monopole has a gain 3 dB higher than for a dipole, and the system has a gain 3 dB higher than for two dipoles in free space. Now, if the dipole is the transmitting antenna, and the monopole is the receiving antenna, the monopole again has a gain that is 3 dB higher than for a dipole, because, since the dipole is elevated above the ground, there is a direct ray and a reflected ray going to the monopole, causing the receiving gain of the monopole to be 3 dB higher than for a dipole (instead of 3 dB lower than for a dipole). So, when the receiving and transmitting antennas are interchanged, the system gain is still 3 dB higher than for two dipoles in free space.

One of the causes of the confusion that surrounds the receiving gain of a monopole is that the authors of antenna books do not mention this subject. I’ve stated in a previous post that I thought that this omission exists for pedagogical reasons. An author of an antenna book has very limited space for explaining the entire subject of antennas. Some facts have to be omitted because it is not possible to include everything. This subject, moreover, requires a lot of nit-picking explanation, as we see in this thread, and in this post in particular. For the author who has to explain everything about antennas in one book, it is simply not worhwhile dealing with this subject.

In Chapter 2 of the first edition (1961) of Jasik’s “Antenna Engineering Handbook,” Table 2-1 gives the transmitting gain of an isotropic radiator, a very short dipole, a half-wave dipole, and a quarter-wave dipole [i.e. monopole] above a perfect ground plane. Two pages later, there is Table 2-2, which gives the receiving gain of all of these antennas, but omits the monopole above the perfect ground plane. This appears to me to be a deliberate omission. If Jasik had included the monopole, to be strictly correct, he would have had to give give two different receiving gains; one for surface wave reception, and another one for skywave reception. I think that Jasik thought that it was better to omit mention of the monopole receiving gain than to devote space to accounting for the dual gains. It looks like all of the other antenna authors have done the same thing. The result is that some experts who have devoted their lives to antennas do not know that the monopole has two different gains and insist that the dual gains do not exist. I am hoping that this subject will be studied thoroughly using both measurements and simulation so that the facts can be made clear.