Effect of Antenna Gain on Range of Communication

jimh
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Effect of Antenna Gain on Range of Communication

The effect of antenna gain on the range of communication is an often misunderstood relationship, and this is by no means limited to misunderstanding by boaters who are otherwise not expected to be acquainted with the intricacies of radio theory. But among boaters, there is a substantial groundswell for the notion that an antenna described as having 6-db gain is going to make a vast improvement in range of communication compared to using an antenna described as having 3-dB gain. The improvement in communication range is variously described as "double", "better", "much better", or "the difference between communication and no communication." Let's examine the reality, which is quite different.

In any communication system there are two fundamental power levels: the effective transmit power and the lowest power level that a receiver can receive, set by the receiver sensitivity (and by local noise, which we will ignore here). To compare, we reference these power levels in decibels to the usual standard of 0dBm, which is a power of one milliwatt (0.001-Watt) in a 50-Ohm resistance.

The typical VHF Marine Band radio transmitter will have a power output of 20-watts. (Yes, I know they are called 25-Watt radios, but power output varies with supply voltage, and production variation can result in slightly less than the rated output; we'll use 20-Watts as more realistic power.) WIth reference to 0dBm this is a power level of 10 LOG (20/.001) or +43dBm. The typical VHF Marine Band radio receiver will have a sensitivity of one microvolt at 50-Ohms. This can be shown to be a power level of -107dBm. (Most VHF Marine Band radio receivers are rated to be more sensitive, but we will use this as a conservative figure.) Since we know the two power levels, we can expect that any path loss between the receiver and transmitter cannot exceed the difference in these two levels if communication is to occur.

Transmitter power = +43dBm
Maximum path loss = -107dBm -43dBM = -150dB

If the receiver and transmitter were both operating in free space, the path loss would be according to the inverse-square-law relationship, and we could solve for distance. Path loss in decibels as a function of distance (in miles) and frequency (in Mhz) can be shown to be described by

(1) dBpathloss = -36.59 - 20 log (f) - 20 log (d)

Since the frequency factor in the above equation will be a constant of 20 log (156) = 43.8 the equation (1) above can be simplified to

(2) dBpathloss = -79.4 - 20 log (d)

Since the maximum path loss that can be tolerated is -150dB, we substitute and re-arrange to find the distance at which the path loss is -150dB:

(3) -70.6 = -20log(d)

Solving for d:

(4) d = 10^3.53 = 3388 miles

Everyone knows that you cannot expect a 25-watt VHF marine radio to communicate 3,388 miles to another boat, but, if you were in free space, that would be your range.

What should be clear from the above analysis is that propagation of radio waves on Earth does not work quite as well as it is predicted to work in free space. It should also be clear that any increase in radiated power, whether due to actual transmitter power increase or from antenna gain, will only increase the communication range by an amount that depends of how the path loss changes with distance.

Let's say we're assessing a space probe and we increase its antenna gain by 3dB; how does this affect the communication range we analyzed above? It would allow us to add 3dB to the maximum path loss, making our equations (3) and (4) above become

(5) -73.6 = -20log(d)

(6) d = 10^3.68 = 4786 miles

That is an increase of 1,398 from the initial 3388, or a factor of 1.41. That number should look familiar because it is the square root of two. We doubled the power, but the distance only increased by the square-root of two, or 1.41. This is exactly what is meant by an inverse-square-law relationship.

Getting back to boaters, claims of antenna gain, and how they will improve communication range, the suggestion that a doubling of antenna gain (3dB) will double the range is clearly impossible. Even in the absolute best environment, free space, doubling the antenna gain (3dB) would only increase the communication range by a factor of 1.41 or 41-percent. Anytime you read or hear that by going to a 6dB antenna from a 3dB antenna the communication range will double, you should recognize that this is an impossibility. It won't happen. Anyone who tells you it will is mistaken.

Since as boaters we know from experience that our communication range is not the same as in free space, we must also realize that any increase in power, which because we are limited to 25-Watt transmitters must be from antenna gain, is not going to increase the range as it would in free space propagation. Any improvement in range over Earthly paths is going to be less than in free space.

In actual analysis, the increase in path loss with distance on Earth over actual surfaces seems to obey more like a inverse-fourth-power relationship. That is to say, for example, that if the distance is doubled, the signal needed to overcome this will need a 16-times increase in power. In decibels that is 12dB. For an improvement in antenna gain to result in real-world doubling of range, the antenna gain increase would have to be to an antenna with 15dB gain from a 3db gain antenna. Again, this is not going to be possible in VHF Marine Band antennas. There just are no 15dB gain antennas out there.

Many factors combine to cause actual propagation over ground (or sea) to be higher than in free space. Signals tend to reflect off the ground (or sea). The arrival of the direct signal and ground-reflected signal occurs with almost inverted phase relationship, and signal cancellation occurs. This particularly affects a path in which both antennas are not elevated very high above ground. Significant elevation of just one antenna in the communication system to be high above ground will reduce this effect; this explains why signals from very tall towers have much improved range of communication to stations with very low antennas over more or less line-of-sight paths. Signals can also be reflected by objects in the path, causing signals to arrive at the receiver by multiple paths, called multipath propagation. Since the distances of the multipath signals are not the same as the direct path, they arrive at difference times. This also causes signal cancellation. These factors affect path loss, even when the two antennas are in line of sight of each other. In propagation over water, the height and period of wind waves also affect signal loss, as does conductivity (usually a function of salinity). All of the influences cause real-world path loss to be much higher than free space path loss.

In a separate article, I demonstrate calculation of path loss on several paths involving NOAA weather radio station signals received over long paths over freshwater, using both actual observed signals and predicted coverage maps. These calculations tend to also discover path loss at an inverse fourth-power relationship applies to these paths.

It will be instructive to calculate the improvement of a 3dB increase on range when the path loss increases at an inverse-fourth-power rate. That is easily solved by adjusting the path loss formula. Our original formula was given in equation (1). It now becomes

(7) dBpathloss = -36.59 - 20 log (f) - 40 log (d)

We can generalize the case for a 3dB change with

(8) -3 = -40 log(d)

and solve for d to find

(9) d = 10^0.75 = 1.18

That means that in real-world propagation with inverse fouth-power path loss, adding 3dB to the allowed path loss will increase the distance by a factor of about 1.18. This is a much more reasonable interpretation of the effect of changing to a 6dB gain antenna from a 3dB gain antenna: your range would increase by a factor of 1.18 in terms of distance.

There is no argument against adding antenna gain. It will always improve the communication range, and particularly because antenna gain works on both the transmit and receive signals; it increases them both by the same amount. It helps you transmit better and receive better. But higher gain is not always the best approach to antenna choice.

Antennas actually do not have any overall gain. All antennas with gain achieve that gain by a simple method: they concentrate the signal in one direction at the expense of the signal in another direction. The gain of an antenna refers only to the signal in the main lobe of the antenna compared to some other antenna, often to an idealized antenna that radiates equally well in all directions, called an isotropic radiator. Note that any practical antenna will have some sort of uneven radiation pattern and can be described as having gain if referenced to the idealized isotropic radiator. Most VHF Marine Band antennas are described in terms of their gain in reference to an isotropic radiator.

For all practical antenna, any time the main lobe of the antenna is not oriented so that the distant station is centered in the main lobe, the actual realization of antenna gain will be lower than claimed. Since it is typical for antennas with high gain to have very deep nulls in their radiation pattern, the signal strength when not in the main lobe and in one of the nulls of such an antenna will be very much lower, as much as one-hundred-times (-20dB) lower than in the main lobe. In a separate article, I discuss the typical radiation pattern of omnidirectional vertical antennas with regard to the size of their main lobe. This property of gain antennas must be clearly understood. You only get gain from them when they are carefully oriented to direct their main lobe at the other station in the communication system.

On small boats that are at sea, it is common for there to be considerable motion on the boat. Any time the bow pitches up or down, or the boat rolls to its side, the orientation of the radio antenna changes in the vertical radiation plane. The antenna becomes displaced from its normal orientation of orthogonal to the plane of the horizon. This physical displacement of the antenna causes its radiation pattern to change, directing the main lobe of the antenna away from the horizon. The result is the effective gain of the antenna is reduced when the boat is in motion in any sort of sea conditions that disrupt its stability. For this reason, on small boats it is often preferable to use an antenna with modest gain in order to enjoy the benefit of its wider main lobe radiation pattern.