ANTENNAS FROM THE GROUND UP
We have in a past episode looked at how to construct and install parallel transmission lines. However, we have not yet looked at the questions of when we might profitably use such a line in preference to a coaxial cable. Nor have we asked which line to use among those available to be bought or built. Letþs remedy those gaps.
Here is an incomplete list of occasions on which you might want to use twinlead or open-wire parallel lines.
1. When the antenna presents an impedance that is a close match to such lines. Many terminatedd antennas, such as the rhombic or the T2FD use terminating resistors, as shown, for example, in Fig. 1. Usually, the feedpoint impedance will be a close match to the value of the resistor. Then, you have two choices for feeding the antenna. You can install impedance transformation components at the antenna terminals and run coax to the equipment. Or, you can use an open wire line that matches the antenna to a matching unit in the shack. The rhombic (8 wl long) in the figure with a 600-Ohm resistor shows under 1.3:1 SWR at 600 Ohms from 14 to 28 Mhz, a candidate for use with a 600-Ohm open-wire feedline.
2. When the losses need to be minimized on a budget. Hardline coaxial cables rival parallel lines for low losses, but they are expensive and often hard to handle. If the cable run is very long, one might wish to use a parallel line for most of it. I have heard of 50-Ohm beam installations at a long distance from the equipment that use impedance transformers at each end of the line and an open-wire feeder between. The open-wire line goes from the shack entry point to the base of the tower, with coax at either end.
3. When the impedances at the antenna terminals may show a wide range of values. This case is perhaps the most common, since it is true of almost all multi-band doublets. The typical doublet may show both resistance and reactance values running from well under 100 Ohms to well over 1000 Ohms. Because any coaxial cable would see a very high SWR on at least some of the bands, losses may well be unacceptably high on those bands. A parallel transmission line with its very low matched loss value will show much lower losses under the same conditions.
There are other reasons for using parallel lines, such as handling power levels in the 100 kW to 5 MW range, that apply to commercial operations. We can pass over them. However, we should not pass over the fact that parallel lines require special installation care to ensure that they deliver the promised low losses. Having looked at when we should use parallel lines, we can now turn to the question of which line to use. Let us use as a jumping off point a typical 135' multi-band doublet with a line to an ATU, as in Fig. 2. Which line should we use in this system.
Before we can answer this question, we must know what lines are available. The commercially available lines come in 3 general types, each with a different characteristic impedance, construction, velocity factor, and loss value.
1. 300-Ohm transmitting twinlead, sometimes flat and sometimes tubular, has a velocity factor of about 0.80 and a loss of about 0.17 dB per 100' at 3.5 Mhz. Remember that line losses increase with frequency. But RG-213 half-inch coax has double the loss of the best 300-Ohm twinlead.
2. 450-Ohm window line, a form of flat twinlead with cut-outs to minimize the vinyl between the wires, has a velocity factor of about 0.95 and a 0.1 dB loss per 100' at 3.5 Mhz, down to almost half the loss of 300-Ohm line.
3. 600-Ohm open-wire ladder line typically has a velocity factor of about 0.97 or higher and a loss of only about 0.03 dB per 100' at 3.5 Mhz. There are also commercially available ladder lines in the 400-500 Ohm range, and their VF and loss values would resemble those of the 600-Ohm line.
In looking at the loss values associated with various kinds of lines, remember that they are figures for a matched conditions, that is, a 300-Ohm resistive load with a 300-Ohm line, etc. Additional losses that result from a mismatch between the load and the line (that is, a high SWR) represent a multiplier on the basic loss value. Let's suppose that a certain SWR value creates 3 times the loss of a matched condition. The coax (RG-213) at 3.5 Mhz with a .35 dB loss per 100' will now show a loss of over 1 dB. The 600-Ohm line will show a loss of under 0.1 dB for the same SWR value.
However, there are other reasons besides line losses for selecting among the available parallel lines. Effecting a good match with the ATU in the shack requires that we have values of resistance and reactance that fall within the range of the tuner to match. Our selection of line may have a bearing on the ease and efficiency with which we can get that match.
One rough initial guide to the selection of a parallel line impedance for a muti- band antenna (or any other for which the feedpoint impedance may vary over a wide range) is the choose a line characteristic impedance (Zo) that is the geometric mean between the maximum and minimum impedances at the antenna terminals. To get a geometric mean, we simply multiply the minimum value times the maximum value and then take the square root of the result. All we need to know now is the range of values we might encounter.
Here is a list of values taken from a model of a 135' #12 AWG copper wire doublet at a height of 50' above average soil. We can use this antenna as an example.
Freq. (Mhz) Feedpoint R +/- jX 3.6 75 + j 55 7.15 4760 - j1270 10.1 95 - j 330 14.15 4270 - j1005 18.1 125 + j 5 21.15 2330 + j1435 24.95 130 - j 180 28.5 2070 + j1225
The list is representative, but not necessarily exactly what any given installation would discover. The 40-meter and 20-meter values are very high, because the antenna is very close to 1 and 2 wavelengths long at those frequencies, respectively.
The highest impedance in the table is over 4900 Ohms, while the lowest is about 93 Ohms. The geometric mean is about 677 Ohms, suggesting that a 600-Ohm parallel line would be the transmission line of initial choice.
The simple selection guide does not take into account what happens to the impedance along the line and how long the line will be for a given installation. As we have seen in past episodes, the impedance along a line undergoes continuous transformation, with changing values of both resistance and reactance. What emerges at the equipment end of the line is therefore very dependent upon the line length as well as on the impedance at the antenna terminals.
Each of the three sample lines that we looked at has a different characteristic impedance. Therefore, for any antenna terminal impedance, the transformations of impedance will be somewhat different for each of the lines. In addition, each line has a different velocity factor. Hence, for any given physical length of line, each of the three lines will be a different electrical length. The transformation of impedance is dependent on the electrical length of the line. There are programs from which we can quickly get an idea of what the equipment end conditions will be for any antenna terminal conditions. TLW, the N6BV program that comes with The ARRL Antenna Book, is one good source, and HAMCALC also has a program (Transmission Line Performance) to do the calculating task.
Representative Line Lengths and Impedances for the 135' Doublet Freq. Line Values (Zo/VF) (Mhz) 300/0.80 450/0.95 600/0.97 A. 50' Feedline 3.6 1175 - j 270 810 + j1190 765 + j1680 7.15 235 + j1030 92 + j 510 145 + j 620 10.1 40 + j 10 70 - j 180 81 - j 200 14.15 60 + j 415 45 + j 30 80 - j 10 18.1 280 + j 265 130 - j 80 140 - j 185 21.15 35 + j 175 135 - j 470 360 - j 845 24.95 90 - j 20 1460 - j 705 2800 - j 785 28.5 35 + j 100 2480 - j 905 1740 + j1335 B. 75' Feedline 3.6 140 - j 270 480 - j 960 735 - j1645 7.15 20 - j 130 175 - j 820 395 - j1235 10.1 185 - j 525 710 + j1300 1070 + j1970 14.15 30 + j 220 75 - j 370 175 - j 635 18.1 665 + j 175 135 - j 120 155 - j 295 21.15 2680 - j1200 75 - j 195 175 - j 445 24.95 710 - j 410 130 - j 170 160 - j 345 28.5 35 - j 85 75 + j 60 130 - j 110 C. 100' Feedline 3.6 75 - j 20 115 - j 325 120 - j 470 7.15 60 + j 475 40 + j 53 71 + j 15 10.1 110 + j380 60 - j 60 74 - j 85 14.15 20 + j 100 1975 - j2210 3460 + j1886 18.1 475 - j 295 145 - j165 190 - j 415 21.15 35 - j 145 65 - j 0 125 - j 200 24.95 115 + j 135 170 + j 320 140 + j 225 28.5 75 - j 345 1015 - j1305 1455 + j1355
Even though the table presents us with only a few of the nearly infinite number of values we might encounter with our own 135' doublet, it nevertheless reveals many important facts about the use of parallel feedlines. First and foremost, we can see clearly the differences that line length makes to the impedance at the equipment end of the feedline.
Second, let us consider the antenna tuner or ATU. Every tuner has limitations in both the range of resistance values that it can efficiently match--or match at all--to a 50-Ohm input. Equally, every ATU has limits to the range of reactances which it can compensate for--and the ranges may differ for capacitive and inductive reactance depending upon the tuner design. Therefore, for a wide-ranging antenna like the doublet in our example, we would be wise in arriving at equipment-end values that least tax the ATU.
We can achieve our goal in one of two ways. One way is to select a line length for our pre-chosen type of parallel line that gives us the fewest þhighþ values of resistance and reactance. We might loosely define "high" as exceeding 1500 Ohms or 1000 Ohms, but the goal would be the same. As we scan the chart under any one of the lines, we select the length that gives us the fewest high values. Where this is not possible and we already have a line in place, we still use the technique. We insert an extra length of feedline for "troublesome" bands to get an easy match there.
Of course, to arrive at an optimal line length for a particular characteristic impedance and velocity factor, we would need to calculate equipment-end impedances for numerous other line lengths. Just for this job, programs like TLW and Transmission Line Performance in HAMCALC come in handy to make short work of the task. Smith Charts can also be used for this purpose.
Wherever the line length is relatively fixed in advance, but where one has a chance to choose the characteristic impedance of the line, there is another way to minimize resistance and reactance excursions at the ATU terminals. We simply select the line impedance and velocity factor combination that gives us the smallest range of resistance and reactance at the equipment end of the line. In vinyl lines, which are commercial products, we have a limited choice. However, in open-wire or ladder lines--all of which would have velocity factors similar to the 600-Ohm line used in the example--we can construct our own lines to meet the need. Ladder lines from about 400 Ohms to 600 Ohms are available commercially, but if we need an even higher values, we can roll our own.
Remember that the doublet used in this example is only one possible multi-band antenna out of many. Changing the length of the doublet by even a foot or two might change some of the upper band impedance values considerably. Moving to a 102' or 67' doublet or to a horizontal loop would create a whole new ball game of values with which to work. However, the tools of analysis do exist in the form of antenna modeling programs and feedline calculation programs. So the task need not be merely a guessing game.
Before we close the door on the selection of parallel feedlines, let's note one final fact from the table. In each column for each line length and Zo, notice how many of the resistance values are less than 100 Ohms. In most commercial ATUs that use a network design (like the common C-L-C Tee network), it is nearly standard practice to install some sort of 4:1 transmission line transformer (often called a balun) to provide a means of converting the single-ended network into a balanced output. The "4:1" reference is to the impedance transformation in the device.
The result of having such an impedance transformer--on the dubious assumption that it performs correctly while a considerable reactive component is part of the impedance--is to transform already low impedances into still lower ones. While a match to the new very low impedances might be made by the tuner, efficiency under these conditions is very suspect. Indeed, it might be better if such units came with 1:1 broadband toroidal transformers of standard design with cores large enough not to saturate. Efficiency might well show improvement.
Updated 11-05-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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