Below is most of a post I made on this topic on another board. Thought it might be useful here as well. /Rich
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Below is most of a post I made on this topic on another board. Thought it might be useful here as well. /Rich
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Radiating 11.4 nanowatts from a linear, 1/2-wave dipole produce the maximum Part 15 FM field in free space -- both in theory and practice.
But if the antenna is not located in free space, then reflections of its radiation together with the direct signal could produce fields 3 meters away from it that are above the compliant level.
Even if the antenna is vertically polarized, and mounted essentially in free space such as on a pole on top of a building, and met the Part 15 FM limit at 3 meters, it should be noted that the FCC typically measures Part 15 FM systems from several hundred meters away. This again means that reflections of the originally compliant radiated signal can add to the direct signal to show non-compliance at the location where the FCC measures it.
The peak gain of a 1/4-wave whip working against a perfect r-f ground is the same as that of a 1/2-wave dipole. The r-f ground seen by a whip attached to a Part 15 FM transmitter consists of whatever conductors comprise the r-f ground on the circuit board, along with whatever un-decoupled conductors lead away from the transmitter (program input cable, power source, etc), and their physical orientations. Such an r-f ground is far from perfect.
So the true gain and pattern of this whip + other conductors probably never is known. But to make a conservative guess, if this whip antenna system had only 1/1,000th of the peak gain of a 1/2-wave dipole, that would mean that the highest transmitter output power possible without exceeding Part 15 FM (not counting reflections) would be 1,000 X 11.4 nanowatts, or 11.4 microwatts -- which is 1/877th of the output power rating of a 10 mW transmitter.
Typically there is no means for Part 15 FM operators to accurately measure power levels or radiated fields in these ranges. Neil (radio8z) has addressed this by shortening the whip to the height where the system can't be heard on a typical receiver much beyond 200 feet, which is the range the FCC expects for it per their OET Bulletin 63. Reducing radiation this way is the result of the poor impedance match of that shortened whip and r-f ground to the impedance the transmitter is designed to drive efficiently. Neil's pragmatic approach probably has a good chance of keeping Part 15 FM operators away from FCC problems.
For FCC compliance, almost all of the output power of a typical Part 15 FM transmitter needs to be absorbed by system losses, rather than being radiated either by a dipole or a whip.
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A 100% efficient 1/4 wave vertical monopole over a perfect ground plane has 3 dB more peak gain than a 100% efficient 1/2 wavelength dipole in free space.
A 100% efficient 1/4 wave vertical monopole over a perfect ground plane has 3 dB more peak gain than a 100% efficient 1/2 wavelength dipole in free space.
The intrinsic gain is the same. The 3 dB difference results from the fact that all of the radiation from the 1/4-wave monopole over a perfect ground plane is confined to one hemisphere.
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The intrinsic gain is the same. The 3 dB difference results from the fact that all of the radiation from the 1/4-wave monopole over a perfect ground plane is confined to one hemisphere.
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The gain of an antenna is the ratio of the maxiumum field strength produced by the antenna at a given distance compared to a 100% efficient reference antenna with the same power input. The gain is the directivity of the antenna multiplied by its efficiency. If the efficiency is 1, or 100%, the gain is the same as the directivity.
The 3 dB difference noted in the previous two posts (which, as Rich correctly says, results from the fact that all of the radiation from the 1/4 wave monopole over a perfect ground plane is confined to one hemisphere) is the difference in the gains of the two types of antennas. Because of the 3 dB difference, the gains cannot be the same. The 3 dB difference is a difference in gain of 3 dB. It does not matter what the reason for this 3 dB difference is for there to be a gain difference.
The reference antenna is usually accepted to be the isotropic radiator, which is postulated to have completely uniform radiation in all space directions. Its gain is 0 dBi, by definition. The field strength at 1 km for 1 kW of radiated power is about 173.2 mV/m.
The half-wave dipole has a particular doughnut-shaped radiation pattern and has a gain of about 2.15 dBi. The field strength at 1 km for 1 kW of radiated power is about 221.5 mV/m.
The quarter-wave monopole above a perfect ground plane has a radiation pattern shaped the same as for the half-wave dipole, except that the dougnut-shape is cut in half. Its gain is about 5.15 dBi. The field strength at 1 km for 1 kW of radiated power is about 313.2 mV/m
The editions of Kraus (1950) and Jasik (1961) that I have both give the definition of gain I give here.
The gain of an antenna is the ratio of the maxiumum field strength produced by the antenna at a given distance compared to a 100% efficient reference antenna with the same power input. The gain is the directivity of the antenna multiplied by its efficiency. If the efficiency is 1, or 100%, the gain is the same as the directivity.
The 3 dB difference noted in the previous two posts (which, as Rich correctly says, results from the fact that all of the radiation from the 1/4 wave monopole over a perfect ground plane is confined to one hemisphere) is the difference in the gains of the two types of antennas. Because of the 3 dB difference, the gains cannot be the same. The 3 dB difference is a difference in gain of 3 dB. It does not matter what the reason for this 3 dB difference is for there to be a gain difference.
The reference antenna is usually accepted to be the isotropic radiator, which is postulated to have completely uniform radiation in all space directions. Its gain is 0 dBi, by definition. The field strength at 1 km for 1 kW of radiated power is about 173.2 mV/m.
The half-wave dipole has a particular doughnut-shaped radiation pattern and has a gain of about 2.15 dBi. The field strength at 1 km for 1 kW of radiated power is about 221.5 mV/m.
The quarter-wave monopole above a perfect ground plane has a radiation pattern shaped the same as for the half-wave dipole, except that the dougnut-shape is cut in half. Its gain is about 5.15 dBi. The field strength at 1 km for 1 kW of radiated power is about 313.2 mV/m
The editions of Kraus (1950) and Jasik (1961) that I have both give the definition of gain I give here.
Ermi Roos wrote; The 3 dB difference noted in the previous two posts (which, as Rich correctly says, results from the fact that all of the radiation from the 1/4 wave monopole over a perfect ground plane is confined to one hemisphere) is the difference in the gains of the two types of antennas. Because of the 3 dB difference, the gains cannot be the same. The 3 dB difference is a difference in gain of 3 dB.
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Differentiation is required between the intrinsic gain of a monopole radiator, and the effect of the propagation environment on that gain in specific directions.
All antennas have a far-field radiation pattern/gain subject to modification by reflections and obstructions in the propagation environment.
In the case of a perfect 1/4-wave monopole over a perfect ground plane (not that either can be a physical reality), the ground reflection contributes 3.0103.. dB to the intrinsic radiation of that monopole in the horizontal plane.
But it is NOT true that a 1/4-wave, ground-mounted vertical monopole itself has ~3 dB more intrinsic gain than a 1/2-wave dipole in free space.
RF
Ermi Roos wrote; The 3 dB difference noted in the previous two posts (which, as Rich correctly says, results from the fact that all of the radiation from the 1/4 wave monopole over a perfect ground plane is confined to one hemisphere) is the difference in the gains of the two types of antennas. Because of the 3 dB difference, the gains cannot be the same. The 3 dB difference is a difference in gain of 3 dB.
______________
Differentiation is required between the intrinsic gain of a monopole radiator, and the effect of the propagation environment on that gain in specific directions.
All antennas have a far-field radiation pattern/gain subject to modification by reflections and obstructions in the propagation environment.
In the case of a perfect 1/4-wave monopole over a perfect ground plane (not that either can be a physical reality), the ground reflection contributes 3.0103.. dB to the intrinsic radiation of that monopole in the horizontal plane.
But it is NOT true that a 1/4-wave, ground-mounted vertical monopole itself has ~3 dB more intrinsic gain than a 1/2-wave dipole in free space.
RF
Rich,
I will admit that I had some difficulty understanding the point in your last post because your argument seems to me to be rather abstract.
I will try to reduce your argument into its elements to understand it better. You seem to, first of all, call for a separation between the antenna and its propagation environment. For the case of the half-wave dipole, this is conceptually easy. There is the dipole (the thing in itself) with its characteristic, or inherent (intrinsic) properties. It is contained in empty, three-dimensional, space extending in all directions to infinity.
It's a little difficult to similarly separate the "thing in itself" and its operational environment (because they appear inseparable) if one is talking about the vertical monopole above an ideal ground plane. The ground plane, which extends to infinity, is an integral component of the antenna. Without the ground plane, the antenna would not exist. The operational environment is semi-infinite free space with a boundary at the ground plane.
You also speak of "obstructions" on the operational environment, as if they should be considered separately from the antenna. Suppose the obstructions are warious other vertical monopoles on the ground plane. Such monopoles, if close enough to the powered monopole (and big emough) would affect the gain in some directions. These monopoles are actually not separate from the "antenna," but parts of a larger composite antenna.
In the situation discussed here, there are no pesky obstructions to complicate the problem, but only a simple, infinite, ground plane. The ground plane itself is the "obstruction" you speak of. You say that reflections from the ground plane add 3 dB to the "intrinsic" radiation from the monopole. Without the ground plane and its reflections, however, there would only be an end-fed 1/4 wave monopole with a voltage source with no return path for the displacement current from the monopole. In other words, in the absence of the ground plane, there would be no radiating antenna at all.
For this reason, Rich, I consider your argument about an "intrinsic gain" to be unpersuasive.
The theoretical and experimental fact is that the gain of the quarter-wave monopole above an ideal ground plane is 3 dB greater than the gain of the half-wave dipole.
Rich,
I will admit that I had some difficulty understanding the point in your last post because your argument seems to me to be rather abstract.
I will try to reduce your argument into its elements to understand it better. You seem to, first of all, call for a separation between the antenna and its propagation environment. For the case of the half-wave dipole, this is conceptually easy. There is the dipole (the thing in itself) with its characteristic, or inherent (intrinsic) properties. It is contained in empty, three-dimensional, space extending in all directions to infinity.
It's a little difficult to similarly separate the "thing in itself" and its operational environment (because they appear inseparable) if one is talking about the vertical monopole above an ideal ground plane. The ground plane, which extends to infinity, is an integral component of the antenna. Without the ground plane, the antenna would not exist. The operational environment is semi-infinite free space with a boundary at the ground plane.
You also speak of "obstructions" on the operational environment, as if they should be considered separately from the antenna. Suppose the obstructions are warious other vertical monopoles on the ground plane. Such monopoles, if close enough to the powered monopole (and big emough) would affect the gain in some directions. These monopoles are actually not separate from the "antenna," but parts of a larger composite antenna.
In the situation discussed here, there are no pesky obstructions to complicate the problem, but only a simple, infinite, ground plane. The ground plane itself is the "obstruction" you speak of. You say that reflections from the ground plane add 3 dB to the "intrinsic" radiation from the monopole. Without the ground plane and its reflections, however, there would only be an end-fed 1/4 wave monopole with a voltage source with no return path for the displacement current from the monopole. In other words, in the absence of the ground plane, there would be no radiating antenna at all.
For this reason, Rich, I consider your argument about an "intrinsic gain" to be unpersuasive.
The theoretical and experimental fact is that the gain of the quarter-wave monopole above an ideal ground plane is 3 dB greater than the gain of the half-wave dipole.
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.
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.
Ermi wrote: 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.
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Sorry, but this concept is not supported in antenna engineering texts such those of Johnson & Jasik, Balanis, Kraus and Terman.
The shape of the elevation pattern of a perfect monopole over a perfect, flat, infinite ground plane is the same whether it is used to transmit or receive. Therefore its receive gain for the groundwave (at zero degrees elevation) is the same as its transmit gain.
The groundwave gain of a resonant, 1/4-wave monopole for these conditions will be the 2.15 dBi gain of a 1/2-wave dipole in free space plus 3 dB due to the perfect ground reflection, which is 5.15 dBi in total. Maximum elevation gain for monopoles up to 5/8 wavelength in height over a perfect ground plane always occurs in the horizontal plane. These statements are easily confirmed by simple NEC models.
The loss of intrinsic receive gain suggested in the quote above may be an interpretation of monopole elevation patterns published for an ~ infinite distance, over other than a perfect, flat, infinite ground plane. In such cases the ground reflection results in an apparently zero field from the monopole in the horizontal plane, at that distance. Also in the real world the groundwave is traveling over a spherical surface (the earth), so at great distances there are obstruction and diffraction losses, as well as those related to the imperfect conductivity of the earth.
Note that these published patterns are not the result of the loss of the ground reflection, as may be inferred from the -0.86 dBi groundwave gain quoted above. And even if was, that would reduce the 1/4-wave monopole groundwave gain of 5.15 dBi by 3 dB -- which is 2.15 dBi, not -0.86 dBi.
A monopole over an imperfect, spherical ground plane will have less relative field in the groundwave than it has at some elevation angles above the horizontal plane, as a function of the distance between the monopole and the constant radial length where that field is measured. But that relative loss in the groundwave is the result of propagation conditions, and not because the relative field of the monopole was intrinsically less for groundwave fields. And such field loss will be the same for a real-world (and theoretical) monopole whether in transmit or receive mode.
A further consideration here is that the maximum amount of power that can be extracted from a radiated EM wave by a perfectly matched receiving antenna is only 1/2 of the power in the wave received by that antenna. This is related to the fact that the r-f current induced in the receiving antenna also produces radiation from that antenna, and therefore is not delivered to its output terminals. But whatever that loss is, it applies equally to waves arriving from all directions, and does not cause a 3 dB relative loss for groundwave signals as compared to skywave signals.
Probably you and I are the only ones reading this thread at this point, Ermi. So if you want to continue it, maybe we should do so off-forum.
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Ermi wrote: 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.
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Sorry, but this concept is not supported in antenna engineering texts such those of Johnson & Jasik, Balanis, Kraus and Terman.
The shape of the elevation pattern of a perfect monopole over a perfect, flat, infinite ground plane is the same whether it is used to transmit or receive. Therefore its receive gain for the groundwave (at zero degrees elevation) is the same as its transmit gain.
The groundwave gain of a resonant, 1/4-wave monopole for these conditions will be the 2.15 dBi gain of a 1/2-wave dipole in free space plus 3 dB due to the perfect ground reflection, which is 5.15 dBi in total. Maximum elevation gain for monopoles up to 5/8 wavelength in height over a perfect ground plane always occurs in the horizontal plane. These statements are easily confirmed by simple NEC models.
The loss of intrinsic receive gain suggested in the quote above may be an interpretation of monopole elevation patterns published for an ~ infinite distance, over other than a perfect, flat, infinite ground plane. In such cases the ground reflection results in an apparently zero field from the monopole in the horizontal plane, at that distance. Also in the real world the groundwave is traveling over a spherical surface (the earth), so at great distances there are obstruction and diffraction losses, as well as those related to the imperfect conductivity of the earth.
Note that these published patterns are not the result of the loss of the ground reflection, as may be inferred from the -0.86 dBi groundwave gain quoted above. And even if was, that would reduce the 1/4-wave monopole groundwave gain of 5.15 dBi by 3 dB -- which is 2.15 dBi, not -0.86 dBi.
A monopole over an imperfect, spherical ground plane will have less relative field in the groundwave than it has at some elevation angles above the horizontal plane, as a function of the distance between the monopole and the constant radial length where that field is measured. But that relative loss in the groundwave is the result of propagation conditions, and not because the relative field of the monopole was intrinsically less for groundwave fields. And such field loss will be the same for a real-world (and theoretical) monopole whether in transmit or receive mode.
A further consideration here is that the maximum amount of power that can be extracted from a radiated EM wave by a perfectly matched receiving antenna is only 1/2 of the power in the wave received by that antenna. This is related to the fact that the r-f current induced in the receiving antenna also produces radiation from that antenna, and therefore is not delivered to its output terminals. But whatever that loss is, it applies equally to waves arriving from all directions, and does not cause a 3 dB relative loss for groundwave signals as compared to skywave signals.
Probably you and I are the only ones reading this thread at this point, Ermi. So if you want to continue it, maybe we should do so off-forum.
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