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Author Topic:   Comparing Gain from Antenna Height Increase to Loss in Transmission Line
jimh posted 02-10-2013 02:31 PM ET (US)   Profile for jimh   Send Email to jimh  
Comparing Gain from Antenna Height Increase to Loss in Transmission Line

In a previous article, the relationship between the distance to the radio horizon and the antenna height was found to be related by the 0.5-exponent. To double the distance to the radio horizon required the antenna height to increase by a factor of four. In general, an increase in the radio horizon is desired because it tends to reduce the path loss by making the path become a line-of-sight (LOS) path as contrasted with an over-the-horizon path. We might say that in an LOS path the path loss will tend to be more like a factor of 20log(d) (the free space theoretical loss), whereas on a non-LOS path the path loss will tend to be more like 40log(d) (a factor sometimes used to model real-world path loss). This are a bit simplistic assumptions, but I think they are reasonable approximations.

In order to assess the benefit of having a higher antenna, we must determine what increase in signal it might deliver. For a path which was already in the line-of-sight distance, that is, a path already within the radio horizon of the initial antenna height, increasing antenna height does not tend to produce much improvement. There may be some effect attributed to locating the antenna more in the clear, and thus reducing ground reflections. (This effect is called "height gain".) We will ignore that influence for this simple analysis. For paths which were formerly beyond the radio horizon, we can consider the improvement in those paths that will result from raising the antenna. We can characterize the difference in path loss as follows:

--for a LOS path the loss is proportional to 20log(d)
--for a non-LOS path the loss is proportional to 40log(d)

This means the path loss is cut in half, or a gain of 3-dB has occurred. This is a reasonable assumption. If we increase the antenna height by a factor of four, we may expect the signal for some station on the fringe of the range to increase by a factor of two. We could say we get a doubling of the radio range with a four-fold height increase.

To increase the antenna height usually requires an increase in the transmission line, with subsequent increase in transmission line loss. Line loss occurs in direct proportion to line length. Therefore increasing the antenna height by a factor of four also increases the loss by a factor of four. Clearly at some point the benefit of increased height will be overcome by the liability of increased transmission line loss.

Consider for a moment that we might have a transmission line with very low loss, perhaps no loss at all. With such a transmission line there would never be any penalty incurred as antenna height was raised. Unfortunately, no such loss-less transmission lines exits. Therefore we must consider that the transmission line will have some loss. We know that if a transmission line of a certain loss has its length increased four times, the loss will increase by four times. What we must determine is how much loss will occur. As long as the total loss resulting from the four-fold increase in transmission line is not greater than 3-dB (the gain we got from the height increase) it will be advantageous to increase antenna height. In order for a quadrupling of line length to cause a loss of 3-dB, the original length would have to have shown one-fourth that loss, or 0.75-dB.

The natural conclusion of these factors is to suggest that an increase in range that occurs by quadrupling antenna height can be accomplished as long as the original feed line loss was less than 0.75-dB for the original length. (We should consider only the vertical distance. We can say that any horizontal length of transmission line would be the same no matter what the antenna height.)

In the case of a VHF Marine Band antenna on a small boat, we can estimate that the vertical portion of the tranzmission line on a typical installation will probably be no more than 10-feet. The typical transmission line used if RG-58C/U. This has a loss characteristic at 150-Mhz of 0.66-dB for 10-feet. If we increase the length to 40-feet the loss will be 2.5-dB. This is less loss than the gain we will get from raising the antenna. This means that raising the antenna to 40-feet from 10-feet will still tend to improve the radio range, even with the fourfold increase in transmission line loss.

Of course, it would be better to change to a transmission line with less loss, and in that way we could recover more of the gain obtained from the longer radio horizon. A lower-loss transmission line might not be entirely practical in some situations. Or the expense might not be tolerable.

In general, a good rule of thumb is to hold transmission line loss to less than 1-dB.

jimh posted 02-10-2013 02:37 PM ET (US)     Profile for jimh  Send Email to jimh     
Consider the case mentioned above: the antenna is increased to 40-feet in height from 10-feet. If we want to hold the transmission line loss to be the same as the original case, we must upgrade the transmission line to a low-loss line.

For 40-feet of length at 150-MHz, we can use LMR-400; it will have a loss of about 0.67-dB. This is comparable to the original installation. Changing the transmission line to LMR-400 from RG-58C/U will keep the line loss the same as the original situation, and this allows all of the benefit of the higher antenna to be realized.

jimh posted 02-11-2013 11:49 AM ET (US)     Profile for jimh  Send Email to jimh     
Influence of transmission line loss on radio communication

A transmission line is typically necessary to make connection between a radio transmitter or receiver and the antenna being used. Transmission lines are not inherently lossless, so some signal will be lost in the transmission line. How much power loss can be tolerated? I have suggested that as a general rule the transmission line loss ought to be limited to about 1-dB.

The decibel expresses a ratio of power levels. A loss in power level of 1-dB is a change by a factor 0.7943. In the case of a radio transmitter producing 25-watts of power, a loss of 1-dB in the transmission line means a reduction in power to 19.85-watts. We have lost about 20-percent of our power.

If we allow transmission line loss to increase to 2-dB, the change in power is a factor of 0.63. We would lose about 37-percent of our power. A loss of 3-dB is a factor of 0.50--we would lose half our power in the transmission line.

Power loss in a transmission line is directly proportional to the length of the transmission line. Transmission line loss varies with the quality of the transmission line and the size. A physically larger transmission line will generally have lower loss. By using the best possible materials and construction methods, a transmission line can minimize loss. This also means that transmission line loss varies with the transmission line cost. The less loss, the greater the cost, as well as usually greater size.

It would be best to reduce all transmission line loss as much as possible, but factors of size and cost tend to limit the process. To improve loss characteristics, some transmission lines are made to be semi-rigid. They have specific minimum bend radius, and can be difficult to fit into small spaces or conform to certain bends required. For all of these reasons, transmission line loss has to be balanced against the practical aspects of its installation and cost. Experience has shown that in many situations, reducing transmission line loss can become expensive and awkward. For many situations, a practical range for transmission line loss is to allow up to 1-dB of loss.

A typical small boat radio installation for the VHF Marine Band will require a transmission line length of 15-feet. The transmission line is typically RG-58C/U coaxial cable. At 150-MHz, 15-feet of RG-58C/U transmission line will have a loss of 0.93-dB. Let us suppose that in a particular installation there was five feet of excess cable. How much transmission line loss will be eliminated if five feet of cable is removed? Only 0.31-dB of loss will be eliminated. There is an old rule in electrical wiring that says, "Any cable cut to length will be too short." It may be more useful to tolerate that extra 0.3-dB of loss than to have a cable that becomes too short.

jharrell posted 02-12-2013 01:03 AM ET (US)     Profile for jharrell    
Of course if you wanted to eliminate feed line losses you could use an LNA correct?:
jimh posted 02-12-2013 10:11 AM ET (US)     Profile for jimh  Send Email to jimh     
In my opinion there is no value in an LNA for a VHF Marine Band receiver on a small boat.

Overcoming transmission line loss on receive can be done with a pre-amplifier mounted at the antenna. This actually will likely create more loss on transmit, as the pre-amplifier must be switched out of the circuit for transmit. The switching circuit will likely have insertion loss.

At the VHF Marine Band it is extremely unlikely that receiver sensitivity is being significantly reduced by loss occurring in the transmission line. The calculation of the influence of transmission line loss on the ultimate sensitivity of the receiver is a complex problem. While an interesting problem, I think exploration of it in detail is beyond the scope or intention of this discussion.

It is more likely that ultimate receiver sensitivity on a small boat for a VHF Marine Band receiver will be limited by local noise sources. Locating an antenna close to an engine using spark ignition is typically not a good environment for obtaining an extremely low noise environment.

Loss of transmitted signal due to transmission line loss is probably of more concern. The only way to overcome transmission line loss is to locate the transmitter closer to the antenna. This could be done by using a black-box radio. On boats with a structure that was high enough and strong enough to put the antenna 40-feet above the water, the size and weight of a black-box radio would likely allow it to be installed near the antenna. Weather protection and 12-Volt power would have to be provided to the elevated installation location. The remote control head would need a long extension. This approach would eliminate most transmission line loss. The cost of such a method should be compared to the cost of just using a lower-loss transmission line and conventional mounting.

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