|
How to measure soil constants at HF
It is fairly easy to measure soil conductivity at DC and power
frequencies. See program EARTHRES. Such measurement values apply up to a few hundred kHz. A few years back I became curious about what happens to conductivity at HF. And at what frequencies does soil permittivity begin to matter. Most amateur activity is at HF and above. Yet, without even thimking about it, we persist in plugging in power frequency values into formulae and computer programs. A volume of soil between a pair of electrodes behaves as a resistance in parallel with a capacitor. So this is what I did - 1. Obtain a 16-inch length of galvanised steel tube, 5 inches in diameter. (Mine was industrial ventilation duct) 2. Block off one end of the tube with a rigid disk of plastic insulating material. 3. Obtain a 17-inch length of copper water pipe, diameter = 0.6 inches. 4. Locate the water pipe in the centre of the tube, resting on the plastic disk at the bottom. 5. You now have a coaxial structure of accurately known dimensions. When empty, Zo = 128 ohms. 1/4-wave at 191 MHz 6. Obtain a mixed sample of soil from various places in your garden under your antenna. 7. Fill the galvanised tube in easy stages with garden soil. At each stage compress and pack-down the soil to about the same density as it was in your garden. Make sure the soil is in contact with the inside surface of the tube. 8. Cover the top of the soil in the tube with a flat disk, with a hole in the middle, to discourage evaporation of moisture and drying out of the soil. 9. You now have 16-inch length of transmission line on which you can make HF impedance measurements using instruments as simple as hand-held antenna analysers. Resistance measurements at 50 or 60 Hz can be obtained from volts/milliamps. Although connecting leads can be kept very short it is advisable to correct measurements for lead-length above 10 MHz. Measurements were made up to VHF. 10. Using classical transmission line formulae in reverse, the values of line conductance G, capacitance C and hence permittivity K of the "insulating" material, i.e., the soil, can be calculated. 11. Measurements are of input impedance of the line with the other end open cicuit. The basic equation is Zin = Zo*Coth(A + jB) where A is line attenuation and B is line phase shift. At the lower frequencies the line is very short and G and Capacitance and then K, can be calculated directly from measurements and line dimsnsions. 12. A clinical thermometer can be inserted deep in the soil. If the test cylinder is too large to fit in the domestic fridge, by leaving the test sample out of doors overnight in winter the effects of temperature can be observed as the sample slowly warms up from freezing. Soil has a high negative temperature coefficient of resistance. Resistance increases as temperature decreases. My garden soil is roughly -2 percent per degree C at 20 degrees C. 13. I have made HF measurements in other shaped containers, usually smaller and plastic, with copper sheets for electrodes. Also in the garden itself between radials and arrays of relatively short rods. Any sort of measurements are more useful than none. Some people say the only way to deternine soil characteristics is to construct a 1/4-wave vertical antenna, feed it with 50 Kwatt at 500 KHz and measure field strength at 1 mile intervals for 100 miles. And then do some calculations. Don't you believe it! ---- Reg G4FGQ |
Hi Reg,
You've presented a very interesting way of measuring soil characteristics. When I return to Florida in November I'm going to use your method of measuring the soil underneath the dipole whose impedances I measured over the frequency range 14 to 15 MHz at various heights above ground, including one set of measurements with the dipole lying on the ground. One of the reasons I offered to distribute the data from my measurements is to see whether anyone can deduce any soil characteristics from the changes in impedance with height. The changes are significant. For example, the terminal impedance with the dipole on the ground runs from 470 + j250 at 14 MHz to 570 + j132 at 15 MHz. The inductive reactance doesn't become capacitive until the dipole is 2 ft off the ground. In addition, except at zero height, the resistance component decreases with height, but for every height the resistance increases with frequency. Do you think any of the soil characteristics could be determined by such data? Would you like a copy of my data, just fer the helovit? Walt, W2DU |
Well Reg,
After years of harping on about your lack of a method, you rummage this up: On Mon, 20 Jun 2005 10:49:54 +0000 (UTC), "Reg Edwards" wrote: .... 13. I have made HF measurements in other shaped containers, usually smaller and plastic, with copper sheets for electrodes. Also in the garden itself between radials and arrays of relatively short rods. Any sort of measurements are more useful than none. I don't see you asking Walt for his data to CONFIRM your method. I don't see you doing any where near Walt's effort in building a sample matrix of your own to test against your method to CONFIRM your method. Validation seems to be an orphan in this discussion. Some people say the only way to deternine soil characteristics is to construct a 1/4-wave vertical antenna, feed it with 50 Kwatt at 500 KHz and measure field strength at 1 mile intervals for 100 miles. And then do some calculations. Don't you believe it! Bosh! Some people indeed. Your biology instruction in the British school system apparently didn't teach you the difference between people and straw-men. The veiled suggestion of a result 10. Using classical transmission line formulae in reverse, the values of line conductance G, capacitance C and hence permittivity K of the "insulating" material, i.e., the soil, can be calculated. is representative of an extremely thin veneer, ignoring the bulk that is so easily found by using the antenna in situ - the method you dismiss as unbelievable, and what is experienced every day by absolutely every Amateur on "Earth." Reg, it was a nicely scripted recipe. It contains well explained methods. It attends practical issues of measurement. However, it wholly lacks common sense when you reject what is already observable. What you offer is minutia of an old wife's tale. For method, any existing antenna's free-space characteristics is far better understood and revealed through a model than what you offer. And that antenna's free space Z characteristics compared against measured in situ Z performance yield the solution of what contribution local earth has to offer. Single point measurement of contaminated soil samples has as little chance of doing the same as trying to measure the ocean's capacity with a teaspoon. 73's Richard Clark, KB7QHC |
"Walter Maxwell" wrote in message
... Hi Reg, You've presented a very interesting way of measuring soil characteristics. When I return to Florida in November I'm going to use your method of measuring the soil underneath the dipole whose impedances I measured over the frequency range 14 to 15 MHz at various heights above ground, including one set of measurements with the dipole lying on the ground. One of the reasons I offered to distribute the data from my measurements is to see whether anyone can deduce any soil characteristics from the changes in impedance with height. The changes are significant. For example, the terminal impedance with the dipole on the ground runs from 470 + j250 at 14 MHz to 570 + j132 at 15 MHz. The inductive reactance doesn't become capacitive until the dipole is 2 ft off the ground. In addition, except at zero height, the resistance component decreases with height, but for every height the resistance increases with frequency. Do you think any of the soil characteristics could be determined by such data? Would you like a copy of my data, just fer the helovit? Walt, W2DU I was working at a company a few years ago, and they built a capacitor of two plates, about 6" on a side, and 0.25" separation. They measured the thing on a network analyzer, and then packed the dielectric with potting soil. Again measuring the results on the network analyzer they were able to deduce the conductivity and permittivity of the soil. I did not think potting soil was typical, but still an interesting experiment. Frank PS, Walt, I would very much like to receive your experimental dipole pdf. |
It is fairly easy to measure soil conductivity at DC and power
frequencies. See program EARTHRES. Such measurement values apply up to a few hundred kHz. A few years back I became curious about what happens to conductivity at HF. And at what frequencies does soil permittivity begin to matter. Most amateur activity is at HF and above. Yet, without even thimking about it, we persist in plugging in power frequency values into formulae and computer programs. A simpler method that avoids all the digging and repacking of the soil is described at http://www.antennasbyn6lf.com/2005/0...arameter_.html I've been meaning to try it at my qth this summer. Torsten N4OGW/5 |
I received a request from Frank, VE6CB, in the post directly above Richard's,
asking for a copy of my dipole impedance data. I tried unsuccessfully to send to Frank, but my server rejects his email address. Can someone help me get a msg to Frank? Walt, W2DU |
Walter Maxwell wrote:
I tried unsuccessfully to send to Frank, but my server rejects his email address. Can someone help me get a msg to Frank? Walt, did you remove the "nospam" from Frank's address before attempting to send? His address appears to be: -- 73, Cecil http://www.qsl.net/w5dxp ----== Posted via Newsfeeds.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =---- |
I have a paper showing measurements of soil conductivity made by the
accepted method of using a buried open wire line, which sounds similar to your method. The authors found that the conductivity varies considerably with frequency. Have your measurements shown this also? Roy Lewallen, W7EL Reg Edwards wrote: It is fairly easy to measure soil conductivity at DC and power frequencies. See program EARTHRES. Such measurement values apply up to a few hundred kHz. A few years back I became curious about what happens to conductivity at HF. And at what frequencies does soil permittivity begin to matter. Most amateur activity is at HF and above. Yet, without even thimking about it, we persist in plugging in power frequency values into formulae and computer programs. A volume of soil between a pair of electrodes behaves as a resistance in parallel with a capacitor. So this is what I did - . . . |
"Walter Maxwell" wrote in message
... I received a request from Frank, VE6CB, in the post directly above Richard's, asking for a copy of my dipole impedance data. I tried unsuccessfully to send to Frank, but my server rejects his email address. Can someone help me get a msg to Frank? Walt, W2DU Sorry Walt, but I put in some anti spam characters in my e-mail. My actual address is Thanks, Frank |
Although knowledge of surface ground conductivity and dielectric
constant is much better than nothing, unfortunately it's still not enough to get truly accurate results from modeling or calculation. Most grounds are stratified, as anyone can discover by digging a few feet down, with layers which can be vastly different. The skin depth at 3.5 MHz in average soil is 16 feet, and at 7 MHz and above about 13 feet(*), which means that significant current flows to depths several times these values. To make an accurate representation of the ground would require knowledge of the ground characteristics to several tens of feet. Fortunately, horizontally polarized antennas are quite insensitive to ground characteristics except at high elevation angles. So for amateur purposes, it's of interest mostly for vertical antennas and NVIS operation with horizontal antennas. To accurately predict the field strength for vertically polarized antennas, you would need to know ground characteristics typically for a few hundred feet from the antenna (depending on the height and current distribution on the antenna and the elevation angle of interest) -- the distance at which the field from the antenna strikes the ground and reflects to interfere with the direct field. This is admittedly a simplification of what really happens, but the distance where the effects occur is approximately right. You also need to know the ground characteristics in the close vicinity of the antenna to evaluate the efficiency of an antenna having a radial system. Besides the problems of stratified ground, many of us live in an urban environment where buried utilities, pipes, reinforcing bar, and houses are likely to be within the radius of interest. Finally, even if you had exact information about each layer of a stratified ground, I don't know of any readily available program which can make use of that information. NEC based programs like EZNEC can accommodate only a single ground characteristic, and assume that the ground is homogeneous to an infinite depth. I'm not convinced that there's any single value which can be substituted for a stratified ground which will behave like the stratified ground. This is the weakest point of currently available modeling programs. But even if they could model stratified ground, you'd have to know values for each ground layer. The method used in broadcasting, where the skin depth is on the order of 25 feet(*), of measuring the attenuation of a ground wave signal over a lengthy path is a much more accurate way of determing overall path loss than simple measurement of surface ground characteristics, since it automatically takes into account all the factors I've mentioned. Again, knowledge of surface ground characteristics is better than nothing, but don't be fooled into thinking that it gives you real information about the ground in which the RF current flows. Had Brown, Lewis, and Epstein measured the surface ground conductivity, it wouldn't have helped us much. (*) You might notice that the skin depths don't follow the familiar rule of decreasing as the square root of frequency. That's because the familiar rule is valid only for good conductors. Average Earth acts like a good conductor below about 7 MHz, but above that it's more like a dielectric, where the skin depth becomes independent of frequency. Consequently it's not less than 12 - 13 feet at any frequency for average soil. Roy Lewallen, W7EL |
Walter Maxwell wrote:
. . . One of the reasons I offered to distribute the data from my measurements is to see whether anyone can deduce any soil characteristics from the changes in impedance with height. The changes are significant. For example, the terminal impedance with the dipole on the ground runs from 470 + j250 at 14 MHz to 570 + j132 at 15 MHz. The inductive reactance doesn't become capacitive until the dipole is 2 ft off the ground. In addition, except at zero height, the resistance component decreases with height, but for every height the resistance increases with frequency. Do you think any of the soil characteristics could be determined by such data? . . . I haven't looked into this carefully, but one person I know who was very involved in NVIS operation (where ground characteristics are important) tried it some years ago. He concluded that it wasn't possible to set the antenna height and make measurements with sufficient accuracy to infer the ground characteristics with any confidence. Roy Lewallen, W7EL |
Roy, W7EL wrote:
I haven't looked into this carefully, but one person I know who was very involved in NVIS operation (where ground characteristics are important) tried it some years ago. He concluded that it wasn't possible to set the antenna height and make measurements with sufficient accuracy to infer the ground characteristics with any confidence. Roy Lewallen, W7EL Understood, Roy, but was this person saying that with just one height it wouldn't give sufficient accuracy, or is he saying that with impedance knowledge at many different heights there would still be no determination of any of the ground characteristics? Would you not like to see my data before concluding it couldn't reveal any ground characteristics.? Walt |
On Mon, 20 Jun 2005 16:21:58 -0400, "Walter Maxwell"
wrote: Understood, Roy, but was this person saying that with just one height it wouldn't give sufficient accuracy, or is he saying that with impedance knowledge at many different heights there would still be no determination of any of the ground characteristics? Hi Walt, And per my several critiques into this matter, all such broad proclamations lack the fundamental of drawing a validation through correlating work in the subject. Let's examine the one point offered: He concluded that it wasn't possible to set the antenna height and make measurements with sufficient accuracy to infer the ground characteristics with any confidence. This, of course, presumes that this source has any actual authoritative data. Something that is prohibitively beyond the scope of an individual to determine (when it is already rejected through correlations of antenna characteristics and measurements) in the first place suggests there is none. Roy has already pointed out the futility of a piece-wise measurement throughout the bulk of earth soaked by RF to its skin depth. I have pointed out that these several treatments offered only go to the thin veneer of soil. Some conclusions drawn were preposterous on the face of the data offered. Further, to suggest the four lead measurement be stretched to employing wavelength sized leads is fraught with error through the denial of those leads becoming what every Amateur already has, an antenna. Reg has dismissed the use of an antenna to measure the earth's contribution of loss, or to distinguish its characteristics by perturbing the known characteristic of an antenna. Such dismissal is not an argument - it is a conceit. Walt, your data is comprehensive enough to build a soil model for the band you studied. I seriously doubt anyone could challenge your results if they were internally consistent. 73's Richard Clark, KB7QHC |
Walt, your data is comprehensive enough to build a soil model for the band you studied. I seriously doubt anyone could challenge your results if they were internally consistent. 73's Richard Clark, KB7QHC Thanks Richard, you've made my day! Walt |
Dick,
PHOOEY ! 88, Punchinello |
On Mon, 20 Jun 2005 21:48:28 +0000 (UTC), "Reg Edwards"
rustling his apron wrote: Dick, PHOOEY ! Yeah, but you heard it from me first. :-0 |
Walter,
What people want to know is how soil constants change with frequency. Measurements at one frequency will tell you nothing about that. Yes please, send me a copy of your test results. But I can't guarantee receiving anything attached to an e-mail. My computer is playing games. Can you send it AS an e-mail. ---- Reg. ======================================== "Walter Maxwell" wrote in message ... Walt, your data is comprehensive enough to build a soil model for the band you studied. I seriously doubt anyone could challenge your results if they were internally consistent. 73's Richard Clark, KB7QHC Thanks Richard, you've made my day! Walt |
PHOOEY !
Yeah, but you heard it from me first. :-0 ============================ You are not so clever. You didn't detect my deliberate mistake. Ah well, I suppose I shall have to tell you. Soil constants are not constant. Wanna make a bet you don't have the last say? Punchinello |
Walter Maxwell wrote: Roy, W7EL wrote: I haven't looked into this carefully, but one person I know who was very involved in NVIS operation (where ground characteristics are important) tried it some years ago. He concluded that it wasn't possible to set the antenna height and make measurements with sufficient accuracy to infer the ground characteristics with any confidence. Roy Lewallen, W7EL Understood, Roy, but was this person saying that with just one height it wouldn't give sufficient accuracy, or is he saying that with impedance knowledge at many different heights there would still be no determination of any of the ground characteristics? I interpreted what he said as meaning that he looked into the method and determined it wasn't practical. Surely he thought of making numerous measurements. He's a very capable engineer, so I took what he said at face value. On the other hand, I don't think he's highly skilled in making precision antenna measurements, so he might have assumed that a level of accuracy wasn't achievable which in fact might be. You might spend a little while with EZNEC looking at how much a change in ground conductivity or permittivity changes the antenna input Z at various heights, and how much the height changes the Z with a given set of ground characteristics. Then consider whether you'd be able to set the height and make the impedance measurements accurately enough to infer the ground characteristics with any degree of confidence. Would you not like to see my data before concluding it couldn't reveal any ground characteristics.? I'd like to see your data, but it wouldn't be enough information to conclude whether the method would be practical or not. Roy Lewallen, W7EL |
It would be interesting to recreate the measurements at other locations. My
location has 500 feet of sand below me. It would be a great improvement just to have poor soil. "Walter Maxwell" wrote in message ... Hi Reg, You've presented a very interesting way of measuring soil characteristics. When I return to Florida in November I'm going to use your method of measuring the soil underneath the dipole whose impedances I measured over the frequency range 14 to 15 MHz at various heights above ground, including one set of measurements with the dipole lying on the ground. One of the reasons I offered to distribute the data from my measurements is to see whether anyone can deduce any soil characteristics from the changes in impedance with height. The changes are significant. For example, the terminal impedance with the dipole on the ground runs from 470 + j250 at 14 MHz to 570 + j132 at 15 MHz. The inductive reactance doesn't become capacitive until the dipole is 2 ft off the ground. In addition, except at zero height, the resistance component decreases with height, but for every height the resistance increases with frequency. Do you think any of the soil characteristics could be determined by such data? Would you like a copy of my data, just fer the helovit? Walt, W2DU |
Hi All,
Reg asked if I could send my data as an email, so I converted the file to text format to be able to present the data in full here in this msg. I checked to see that the tabular format remained intact, and it did in Outlook Express, so here it is. I hope the tabular format will remain intact in your browsers. Be sure to give your screen maximum width. If it doesn't, let me know and I'll resend in PDF format. I'd like to hear your comments. Walt, W2DU Dipole Terminal Impedance Data Obtained From Measurements at Various Heights Above Ground in the Frequency Range from 14.0 to 15.0 MHz. Measurements Made be W2DU at the W2DU site in DeLand, Florida. 081883z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 0 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 32.24 82.000 .7129 5.97 .8361 11.203 471.51 249.55 14.050 34.51 85.410 .7122 5.95 .8355 11.162 472.73 246.63 14.100 37.29 89.720 .7130 5.97 .8367 11.246 492.08 236.91 14.150 40.17 93.780 .7133 5.98 .8372 11.287 499.53 233.27 14.200 43.26 98.590 .7161 6.04 .8408 11.562 519.29 232.53 14.250 47.28 101.890 .7108 5.91 .8348 11.104 500.18 221.92 14.300 50.16 106.640 .7158 6.04 .8410 11.575 507.65 243.02 14.350 54.38 111.640 .7175 6.08 .8432 11.752 514.89 247.15 14.400 60.56 117.710 .7177 6.09 .8437 11.793 538.46 229.17 14.450 66.85 122.840 .7167 6.06 .8427 11.717 540.01 222.81 14.500 74.16 127.930 .7152 6.02 .8411 11.590 539.31 215.08 14.550 82.61 137.040 .7235 6.23 .8511 12.435 592.76 215.22 14.600 92.70 139.380 .7148 6.01 .8412 11.595 554.28 198.71 14.650 105.06 144.030 .7121 5.95 .8383 11.366 554.30 180.74 14.700 117.42 149.660 .7143 6.00 .8410 11.580 563.86 185.38 14.750 131.84 152.680 .7125 5.96 .8392 11.437 556.91 183.08 14.800 149.35 155.540 .7126 5.96 .8395 11.462 562.13 177.94 14.850 168.92 155.220 .7110 5.92 .8378 11.333 559.18 171.07 14.900 191.58 150.340 .7077 5.84 .8342 11.065 553.87 154.78 14.950 217.85 144.480 .7096 5.89 .8366 11.242 569.11 146.40 15.000 244.11 130.130 .7083 5.86 .8353 11.144 570.70 132.61 081683z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 1 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 56.65 41.790 .3540 2.10 .4152 2.420 126.17 21.64 14.050 57.78 43.490 .3640 2.14 .4270 2.490 129.06 24.11 14.100 57.89 44.820 .3732 2.19 .4380 2.559 130.13 29.60 14.150 59.43 46.140 .3794 2.22 .4453 2.606 131.77 31.51 14.200 60.56 47.750 .3883 2.27 .4560 2.676 133.64 35.13 14.250 61.80 49.260 .3963 2.31 .4655 2.742 135.02 38.76 14.300 63.45 50.770 .4036 2.35 .4741 2.803 136.53 41.73 14.350 65.20 52.400 .4115 2.40 .4836 2.873 138.13 45.04 14.400 66.95 54.380 .4215 2.46 .4955 2.964 140.14 49.29 14.450 69.53 56.120 .4292 2.50 .5046 3.037 142.41 51.88 14.500 71.89 57.380 .4344 2.54 .5109 3.089 142.99 54.70 14.550 74.37 62.060 .4581 2.69 .5389 3.338 149.79 63.78 14.600 77.77 63.840 .4652 2.74 .5475 3.420 151.82 66.84 14.650 81.37 66.420 .4764 2.82 .5608 3.554 154.95 71.86 14.700 85.49 68.030 .4830 2.87 .5687 3.637 156.79 75.00 14.750 90.33 69.490 .4895 2.92 .5765 3.723 159.23 77.78 14.800 94.97 71.080 .4970 2.98 .5856 3.826 160.68 82.03 14.850 100.94 72.460 .5047 3.04 .5948 3.936 163.76 85.54 14.900 109.18 73.830 .5146 3.12 .6066 4.084 170.44 88.74 14.950 114.33 73.580 .5179 3.15 .6107 4.137 168.91 92.16 15.000 121.54 73.330 .5240 3.20 .6180 4.236 170.74 95.74 081183z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 2 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 75.81 28.790 .2716 1.75 .3186 1.935 99.53 -18.85 14.050 74.98 28.610 .2685 1.73 .3150 1.920 100.61 -14.90 14.100 74.16 28.720 .2672 1.73 .3135 1.913 101.73 -10.81 14.150 73.85 29.050 .2684 1.73 .3150 1.920 102.94 -7.36 14.200 73.13 29.650 .2703 1.74 .3174 1.930 104.10 -2.96 14.250 72.31 30.810 .2757 1.76 .3238 1.958 105.65 2.12 14.300 72.20 31.400 .2791 1.77 .3279 1.976 106.24 5.88 14.350 72.20 32.610 .2865 1.80 .3367 2.015 107.55 10.11 14.400 73.13 34.240 .2979 1.85 .3502 2.078 110.01 13.54 14.450 74.16 35.500 .3070 1.89 .3609 2.130 111.73 16.80 14.500 74.47 37.100 .3169 1.93 .3727 2.188 112.78 21.77 14.550 75.81 38.690 .3279 1.98 .3857 2.256 114.62 25.56 14.600 77.25 39.790 .3360 2.01 .3954 2.308 115.59 28.88 14.650 79.00 41.910 .3500 2.08 .4119 2.401 117.83 33.57 14.700 80.86 42.860 .3574 2.11 .4209 2.453 118.47 36.77 14.750 83.43 44.810 .3709 2.18 .4368 2.551 120.78 41.13 14.800 86.00 46.350 .3819 2.24 .4499 2.636 122.18 45.27 14.850 88.89 47.810 .3928 2.29 .4629 2.724 123.50 49.44 14.900 92.70 48.990 .4037 2.35 .4758 2.815 125.59 53.04 14.950 96.51 50.170 .4145 2.42 .4887 2.912 127.08 57.19 15.000 100.94 51.330 .4261 2.49 .5026 3.021 128.90 61.64 082483z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 3 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 88.79 23.290 .2894 1.81 .3394 2.027 89.27 -35.58 14.050 87.65 21.710 .2794 1.78 .3278 1.975 89.92 -32.38 14.100 86.00 20.640 .2691 1.74 .3158 1.923 90.82 -28.58 14.150 84.46 20.000 .2605 1.70 .3057 1.881 91.78 -24.84 14.200 82.40 19.790 .2511 1.67 .2949 1.836 92.70 -20.22 14.250 81.37 19.930 .2474 1.66 .2906 1.819 93.89 -16.72 14.300 80.34 20.350 .2450 1.65 .2878 1.808 95.07 -12.95 14.350 79.52 20.910 .2441 1.65 .2869 1.805 96.17 -9.20 14.400 78.49 21.670 .2436 1.64 .2863 1.802 96.97 -4.90 14.450 78.28 22.700 .2477 1.66 .2912 1.822 98.34 -1.26 14.500 78.18 23.720 .2522 1.67 .2966 1.844 99.47 2.43 14.550 78.28 25.020 .2590 1.70 .3047 1.876 100.76 6.37 14.600 78.38 26.580 .2671 1.73 .3143 1.917 101.93 10.81 14.650 79.31 28.120 .2777 1.77 .3269 1.971 103.65 14.60 14.700 80.34 29.860 .2893 1.81 .3407 2.033 105.29 18.84 14.750 82.09 31.190 .3006 1.86 .3541 2.096 107.15 22.20 14.800 83.43 33.180 .3137 1.91 .3696 2.172 108.53 27.11 14.850 85.49 33.870 .3222 1.95 .3797 2.224 109.60 29.92 14.900 87.55 35.230 .3335 2.00 .3931 2.296 110.71 33.99 14.950 90.13 36.660 .3461 2.06 .4081 2.379 112.12 38.22 15.000 92.70 38.000 .3579 2.11 .4221 2.461 112.92 42.62 082483z2.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 4 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 96.61 20.140 .3102 1.90 .3638 2.143 83.63 -43.32 14.050 94.55 17.650 .2956 1.84 .3468 2.062 84.18 -39.69 14.100 92.19 16.030 .2816 1.78 .3305 1.987 85.13 -35.85 14.150 89.10 14.980 .2652 1.72 .3113 1.904 86.08 -31.09 14.200 87.04 14.370 .2541 1.68 .2984 1.851 87.01 -27.34 14.250 84.87 14.180 .2434 1.64 .2858 1.800 87.89 -23.24 14.300 82.50 14.340 .2325 1.61 .2731 1.751 88.55 -18.64 14.350 81.37 14.980 .2291 1.59 .2692 1.737 89.89 -15.13 14.400 80.24 15.830 .2267 1.59 .2665 1.727 91.10 -11.30 14.450 78.69 16.540 .2222 1.57 .2613 1.708 91.40 -6.94 14.500 78.28 17.720 .2252 1.58 .2649 1.721 92.73 -3.34 14.550 77.87 19.180 .2298 1.60 .2703 1.741 94.00 0.73 14.600 77.77 20.550 .2356 1.62 .2773 1.767 95.10 4.59 14.650 78.07 22.050 .2438 1.64 .2870 1.805 96.40 8.40 14.700 78.59 23.880 .2544 1.68 .2996 1.855 97.87 12.64 14.750 79.52 25.420 .2650 1.72 .3121 1.907 99.20 16.42 14.800 80.44 27.090 .2760 1.76 .3252 1.964 100.21 20.59 14.850 81.89 28.890 .2890 1.81 .3406 2.033 101.57 24.82 14.900 83.43 30.540 .3013 1.86 .3551 2.101 102.50 29.02 14.950 86.01 32.110 .3156 1.92 .3722 2.185 104.42 32.92 15.000 88.07 33.530 .3275 1.97 .3862 2.258 105.04 37.05 080283z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 5 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 103.00 18.640 .3316 1.99 .3889 2.273 80.23 -48.99 14.050 99.39 15.580 .3113 1.90 .3652 2.150 81.17 -44.27 14.100 96.31 12.980 .2933 1.83 .3442 2.050 81.61 -40.08 14.150 94.25 11.450 .2814 1.78 .3303 1.987 82.47 -37.03 14.200 90.13 10.560 .2605 1.70 .3058 1.881 83.25 -31.62 14.250 87.65 10.035 .2473 1.66 .2904 1.819 83.99 -27.78 14.300 85.49 10.210 .2367 1.62 .2781 1.770 85.09 -23.94 14.350 83.43 10.660 .2271 1.59 .2668 1.728 86.07 -19.93 14.400 81.37 11.460 .2184 1.56 .2567 1.691 86.91 -15.54 14.450 80.34 12.460 .2160 1.55 .2539 1.681 88.21 -11.97 14.500 78.80 13.860 .2128 1.54 .2502 1.668 89.10 -7.34 14.550 78.18 15.260 .2149 1.55 .2528 1.677 90.33 -3.47 14.600 77.77 16.640 .2185 1.56 .2571 1.692 91.37 0.37 14.650 77.46 18.290 .2241 1.58 .2638 1.717 92.36 4.58 14.700 77.56 19.930 .2319 1.60 .2731 1.751 93.38 8.61 14.750 78.04 21.660 .2418 1.64 .2848 1.796 94.54 12.63 14.800 78.80 23.310 .2524 1.68 .2974 1.846 95.59 16.54 14.850 79.83 25.260 .2653 1.72 .3126 1.909 96.74 20.89 14.900 80.86 27.110 .2774 1.77 .3270 1.972 97.36 25.27 14.950 82.92 28.760 .2915 1.82 .3437 2.047 98.86 29.13 15.000 85.18 30.530 .3063 1.88 .3612 2.131 100.20 33.36 082483z3.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 8 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 109.70 13.860 .3494 2.07 .4098 2.388 74.16 -53.16 14.050 105.60 9.890 .3286 1.98 .3854 2.254 74.80 -48.85 14.100 101.04 6.950 .3064 1.88 .3595 2.123 75.46 -44.26 14.150 97.34 5.020 .2881 1.81 .3382 2.022 76.16 -40.42 14.200 93.73 3.870 .2701 1.74 .3172 1.929 76.93 -36.50 14.250 89.25 3.750 .2474 1.66 .2905 1.819 77.81 -31.35 14.300 86.83 3.500 .2344 1.61 .2753 1.760 78.50 -28.11 14.350 84.46 4.080 .2219 1.57 .2607 1.705 79.62 -24.45 14.400 81.89 5.190 .2086 1.53 .2452 1.650 80.67 -20.09 14.450 80.03 6.370 .1997 1.50 .2348 1.614 81.72 -16.17 14.500 78.28 7.790 .1924 1.48 .2263 1.585 82.63 -11.99 14.550 77.15 9.450 .1902 1.47 .2237 1.576 83.84 -7.98 14.600 76.22 11.160 .1902 1.47 .2239 1.577 84.85 -3.91 14.650 75.71 13.040 .1943 1.48 .2287 1.593 86.02 0.18 14.700 75.71 15.170 .2028 1.51 .2388 1.627 87.53 4.36 14.750 75.71 17.080 .2111 1.54 .2487 1.662 88.46 8.49 14.800 76.22 18.990 .2221 1.57 .2617 1.709 89.60 12.46 14.850 76.74 20.610 .2319 1.60 .2732 1.752 90.18 16.20 14.900 78.07 23.020 .2484 1.66 .2928 1.828 91.79 20.78 14.950 79.31 25.150 .2630 1.71 .3101 1.899 92.65 25.21 15.000 80.86 27.330 .2785 1.77 .3284 1.978 93.42 29.76 072083z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 10 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 106.61 9.286 .3321 1.99 .3894 2.276 71.35 -49.54 14.050 102.18 5.872 .3105 1.90 .3643 2.146 71.88 -45.34 14.100 96.92 3.546 .2853 1.80 .3348 2.007 72.47 -40.43 14.150 92.70 2.544 .2643 1.72 .3103 1.900 73.40 -36.23 14.200 88.58 2.113 .2430 1.64 .2853 1.798 74.16 -31.82 14.250 84.98 2.421 .2235 1.58 .2625 1.712 75.07 -27.50 14.300 81.89 3.007 .2063 1.52 .2424 1.640 75.84 -23.36 14.350 79.10 4.390 .1914 1.47 .2249 1.580 76.99 -18.90 14.400 76.74 5.868 .1794 1.44 .2109 1.535 77.93 -14.52 14.450 75.19 7.682 .1742 1.42 .2048 1.515 79.31 -10.46 14.500 73.64 9.655 .1710 1.41 .2011 1.503 80.38 -6.01 14.550 72.20 11.821 .1712 1.41 .2014 1.505 81.21 -1.25 14.600 71.59 14.110 .1784 1.43 .2099 1.531 82.49 3.13 14.650 71.59 16.246 .1891 1.47 .2225 1.572 83.91 7.06 14.700 71.59 18.299 .2000 1.50 .2355 1.616 84.86 11.11 14.750 72.10 20.678 .2151 1.55 .2533 1.678 86.26 15.38 14.800 72.82 23.176 .2316 1.60 .2728 1.750 87.54 19.89 14.850 74.16 25.589 .2493 1.66 .2937 1.832 89.11 24.18 14.900 75.40 27.718 .2646 1.72 .3119 1.907 89.94 28.31 14.950 76.53 30.435 .2825 1.79 .3331 1.999 90.30 33.42 15.000 78.28 32.533 .2980 1.85 .3515 2.084 90.79 37.55 082883z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 12 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 117.42 12.430 .3760 2.21 .4410 2.578 70.77 -58.39 14.050 113.09 7.150 .3559 2.11 .4175 2.434 71.15 -54.32 14.100 108.15 3.300 .3345 2.01 .3925 2.292 71.74 -50.08 14.150 103.00 0.600 .3121 1.91 .3664 2.156 72.35 -45.67 14.200 98.37 -0.951 .2913 1.82 .3420 2.039 73.09 -41.55 14.250 93.94 -1.660 .2702 1.74 .3173 1.930 73.85 -37.31 14.300 90.13 -1.820 .2510 1.67 .2948 1.836 74.58 -33.32 14.350 86.52 -1.460 .2316 1.60 .2722 1.748 75.24 -29.15 14.400 83.43 -0.521 .2142 1.55 .2518 1.673 76.08 -24.99 14.450 80.65 0.450 .1979 1.49 .2327 1.607 76.58 -20.92 14.500 78.28 1.930 .1841 1.45 .2165 1.553 77.28 -16.71 14.550 76.43 3.770 .1743 1.42 .2051 1.516 78.21 -12.47 14.600 75.19 5.820 .1699 1.41 .2000 1.500 79.39 -8.34 14.650 74.16 7.710 .1681 1.40 .1979 1.493 80.22 -4.32 14.700 73.13 10.070 .1695 1.41 .1996 1.499 80.93 0.35 14.750 72.62 12.240 .1752 1.42 .2063 1.520 81.61 4.61 14.800 72.62 14.530 .1853 1.45 .2183 1.559 82.53 8.85 14.850 72.62 16.840 .1965 1.49 .2316 1.603 82.99 13.25 14.900 73.13 19.730 .2136 1.54 .2518 1.673 83.87 18.28 14.950 74.16 21.070 .2245 1.58 .2647 1.720 84.42 21.19 15.000 75.91 24.930 .2509 1.67 .2959 1.841 86.13 27.44 071983z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 14 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 112.27 14.571 .3599 2.12 .4220 2.460 73.92 -55.35 14.050 108.15 9.751 .3387 2.02 .3973 2.319 74.20 -50.96 14.100 103.52 6.489 .3168 1.93 .3717 2.183 74.86 -46.45 14.150 98.78 2.831 .2936 1.83 .3447 2.052 74.19 -41.86 14.200 94.76 2.831 .2746 1.76 .3224 1.952 76.08 -37.67 14.250 90.64 2.470 .2539 1.68 .2981 1.850 76.93 -33.10 14.300 87.55 2.587 .2377 1.62 .2792 1.775 77.87 -29.20 14.350 84.25 3.171 .2200 1.56 .2585 1.697 78.60 -24.71 14.400 81.37 4.201 .2045 1.51 .2403 1.633 79.36 -20.19 14.450 79.31 5.723 .1945 1.48 .2287 1.593 80.57 -15.94 14.500 77.25 7.379 .1856 1.46 .2182 1.558 81.39 -11.36 14.550 76.01 9.141 .1829 1.45 .2152 1.548 82.50 -7.24 14.600 74.68 11.233 .1822 1.45 .2144 1.546 83.34 -2.51 14.650 74.26 13.515 .1889 1.47 .2223 1.572 84.80 1.86 14.700 74.16 15.646 .1977 1.49 .2327 1.607 86.06 6.06 14.750 74.16 18.441 .2110 1.53 .2485 1.661 87.43 11.21 14.800 74.37 20.068 .2201 1.56 .2592 1.700 87.82 14.93 14.850 74.68 22.357 .2332 1.61 .2748 1.758 88.28 19.54 14.900 76.12 24.631 .2500 1.67 .2946 1.835 89.76 23.76 14.950 77.25 27.023 .2660 1.72 .3137 1.914 90.35 28.43 15.000 78.38 29.667 .2830 1.79 .3338 2.002 90.42 33.51 082883z2.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 16 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 118.97 16.210 .3854 2.25 .4520 2.650 72.84 -60.71 14.050 114.85 10.320 .3648 2.15 .4280 2.497 73.13 -56.36 14.100 109.70 5.500 .3417 2.04 .4010 2.339 73.36 -51.59 14.150 105.06 2.380 .3213 1.95 .3772 2.211 73.88 -47.45 14.200 100.73 0.296 .3020 1.87 .3546 2.099 74.47 -43.53 14.250 95.48 -1.095 .2776 1.77 .3260 1.967 74.73 -38.60 14.300 91.67 -1.434 .2588 1.70 .3040 1.874 75.47 -34.63 14.350 88.07 -1.150 .2399 1.63 .2820 1.785 76.24 -30.46 14.400 85.28 -0.556 .2246 1.58 .2640 1.717 77.09 -26.73 14.450 82.40 0.346 .2082 1.53 .2448 1.648 77.65 -22.58 14.500 78.80 2.170 .1874 1.46 .2204 1.566 77.90 -16.98 14.550 77.25 3.940 .1796 1.44 .2113 1.536 79.07 -13.02 14.600 75.40 6.030 .1716 1.41 .2020 1.506 79.76 -8.30 14.650 74.26 8.120 .1698 1.41 .1999 1.500 80.63 -3.97 14.675 73.95 9.270 .1715 1.41 .2019 1.506 81.25 -1.81 14.700 73.13 10.480 .1710 1.41 .2013 1.504 81.21 0.82 14.750 72.51 12.810 .1770 1.43 .2085 1.527 81.83 5.36 14.800 72.51 15.140 .1877 1.46 .2211 1.568 82.72 9.67 14.850 72.51 16.770 .1957 1.49 .2306 1.600 82.82 13.21 14.900 73.13 19.500 .2124 1.54 .2503 1.668 83.78 17.98 14.950 74.16 23.010 .2349 1.61 .2770 1.766 84.97 23.80 15.000 75.40 26.200 .2562 1.69 .3022 1.866 85.67 29.27 071783z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 22 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 123.60 23.710 .4104 2.39 .4813 2.856 75.90 -66.80 14.050 120.51 15.800 .3901 2.28 .4577 2.688 75.51 -62.12 14.100 117.42 10.990 .3747 2.20 .4397 2.570 76.32 -58.76 14.150 112.27 6.042 .3521 2.09 .4133 2.409 76.52 -53.83 14.200 108.15 2.460 .3343 2.00 .3925 2.292 76.73 -50.01 14.250 103.00 0.281 .3121 1.91 .3666 2.157 77.29 -45.27 14.300 98.37 -1.119 .2913 1.82 .3422 2.040 77.70 -40.79 14.400 90.13 -1.701 .2509 1.67 .2949 1.837 78.53 -31.85 14.500 84.98 -0.345 .2229 1.57 .2621 1.711 80.19 -24.33 14.600 80.03 2.843 .1953 1.49 .2298 1.597 81.48 -15.04 14.700 77.25 6.803 .1843 1.45 .2170 1.554 83.16 -6.11 14.750 76.22 9.966 .1865 1.46 .2196 1.563 84.39 -0.33 14.800 75.91 11.486 .1897 1.47 .2235 1.576 84.87 3.29 14.850 76.22 14.141 .2011 1.50 .2369 1.621 86.30 8.09 14.900 76.22 16.640 .2115 1.54 .2493 1.664 86.73 13.02 14.950 76.74 19.197 .2252 1.58 .2655 1.723 87.30 17.92 15.000 78.28 21.400 .2415 1.64 .2849 1.797 88.62 22.18 Dipole Terminal Impedance Data Obtained From Measurements at Various Heights Above Ground in the Frequency Range from 14.0 to 15.0 MHz. Measurements Made be W2DU at the W2DU site in DeLand, Florida. 081883z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 0 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 32.24 82.000 .7129 5.97 .8361 11.203 471.51 249.55 14.050 34.51 85.410 .7122 5.95 .8355 11.162 472.73 246.63 14.100 37.29 89.720 .7130 5.97 .8367 11.246 492.08 236.91 14.150 40.17 93.780 .7133 5.98 .8372 11.287 499.53 233.27 14.200 43.26 98.590 .7161 6.04 .8408 11.562 519.29 232.53 14.250 47.28 101.890 .7108 5.91 .8348 11.104 500.18 221.92 14.300 50.16 106.640 .7158 6.04 .8410 11.575 507.65 243.02 14.350 54.38 111.640 .7175 6.08 .8432 11.752 514.89 247.15 14.400 60.56 117.710 .7177 6.09 .8437 11.793 538.46 229.17 14.450 66.85 122.840 .7167 6.06 .8427 11.717 540.01 222.81 14.500 74.16 127.930 .7152 6.02 .8411 11.590 539.31 215.08 14.550 82.61 137.040 .7235 6.23 .8511 12.435 592.76 215.22 14.600 92.70 139.380 .7148 6.01 .8412 11.595 554.28 198.71 14.650 105.06 144.030 .7121 5.95 .8383 11.366 554.30 180.74 14.700 117.42 149.660 .7143 6.00 .8410 11.580 563.86 185.38 14.750 131.84 152.680 .7125 5.96 .8392 11.437 556.91 183.08 14.800 149.35 155.540 .7126 5.96 .8395 11.462 562.13 177.94 14.850 168.92 155.220 .7110 5.92 .8378 11.333 559.18 171.07 14.900 191.58 150.340 .7077 5.84 .8342 11.065 553.87 154.78 14.950 217.85 144.480 .7096 5.89 .8366 11.242 569.11 146.40 15.000 244.11 130.130 .7083 5.86 .8353 11.144 570.70 132.61 081683z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 1 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 56.65 41.790 .3540 2.10 .4152 2.420 126.17 21.64 14.050 57.78 43.490 .3640 2.14 .4270 2.490 129.06 24.11 14.100 57.89 44.820 .3732 2.19 .4380 2.559 130.13 29.60 14.150 59.43 46.140 .3794 2.22 .4453 2.606 131.77 31.51 14.200 60.56 47.750 .3883 2.27 .4560 2.676 133.64 35.13 14.250 61.80 49.260 .3963 2.31 .4655 2.742 135.02 38.76 14.300 63.45 50.770 .4036 2.35 .4741 2.803 136.53 41.73 14.350 65.20 52.400 .4115 2.40 .4836 2.873 138.13 45.04 14.400 66.95 54.380 .4215 2.46 .4955 2.964 140.14 49.29 14.450 69.53 56.120 .4292 2.50 .5046 3.037 142.41 51.88 14.500 71.89 57.380 .4344 2.54 .5109 3.089 142.99 54.70 14.550 74.37 62.060 .4581 2.69 .5389 3.338 149.79 63.78 14.600 77.77 63.840 .4652 2.74 .5475 3.420 151.82 66.84 14.650 81.37 66.420 .4764 2.82 .5608 3.554 154.95 71.86 14.700 85.49 68.030 .4830 2.87 .5687 3.637 156.79 75.00 14.750 90.33 69.490 .4895 2.92 .5765 3.723 159.23 77.78 14.800 94.97 71.080 .4970 2.98 .5856 3.826 160.68 82.03 14.850 100.94 72.460 .5047 3.04 .5948 3.936 163.76 85.54 14.900 109.18 73.830 .5146 3.12 .6066 4.084 170.44 88.74 14.950 114.33 73.580 .5179 3.15 .6107 4.137 168.91 92.16 15.000 121.54 73.330 .5240 3.20 .6180 4.236 170.74 95.74 081183z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 2 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 75.81 28.790 .2716 1.75 .3186 1.935 99.53 -18.85 14.050 74.98 28.610 .2685 1.73 .3150 1.920 100.61 -14.90 14.100 74.16 28.720 .2672 1.73 .3135 1.913 101.73 -10.81 14.150 73.85 29.050 .2684 1.73 .3150 1.920 102.94 -7.36 14.200 73.13 29.650 .2703 1.74 .3174 1.930 104.10 -2.96 14.250 72.31 30.810 .2757 1.76 .3238 1.958 105.65 2.12 14.300 72.20 31.400 .2791 1.77 .3279 1.976 106.24 5.88 14.350 72.20 32.610 .2865 1.80 .3367 2.015 107.55 10.11 14.400 73.13 34.240 .2979 1.85 .3502 2.078 110.01 13.54 14.450 74.16 35.500 .3070 1.89 .3609 2.130 111.73 16.80 14.500 74.47 37.100 .3169 1.93 .3727 2.188 112.78 21.77 14.550 75.81 38.690 .3279 1.98 .3857 2.256 114.62 25.56 14.600 77.25 39.790 .3360 2.01 .3954 2.308 115.59 28.88 14.650 79.00 41.910 .3500 2.08 .4119 2.401 117.83 33.57 14.700 80.86 42.860 .3574 2.11 .4209 2.453 118.47 36.77 14.750 83.43 44.810 .3709 2.18 .4368 2.551 120.78 41.13 14.800 86.00 46.350 .3819 2.24 .4499 2.636 122.18 45.27 14.850 88.89 47.810 .3928 2.29 .4629 2.724 123.50 49.44 14.900 92.70 48.990 .4037 2.35 .4758 2.815 125.59 53.04 14.950 96.51 50.170 .4145 2.42 .4887 2.912 127.08 57.19 15.000 100.94 51.330 .4261 2.49 .5026 3.021 128.90 61.64 082483z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 3 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 88.79 23.290 .2894 1.81 .3394 2.027 89.27 -35.58 14.050 87.65 21.710 .2794 1.78 .3278 1.975 89.92 -32.38 14.100 86.00 20.640 .2691 1.74 .3158 1.923 90.82 -28.58 14.150 84.46 20.000 .2605 1.70 .3057 1.881 91.78 -24.84 14.200 82.40 19.790 .2511 1.67 .2949 1.836 92.70 -20.22 14.250 81.37 19.930 .2474 1.66 .2906 1.819 93.89 -16.72 14.300 80.34 20.350 .2450 1.65 .2878 1.808 95.07 -12.95 14.350 79.52 20.910 .2441 1.65 .2869 1.805 96.17 -9.20 14.400 78.49 21.670 .2436 1.64 .2863 1.802 96.97 -4.90 14.450 78.28 22.700 .2477 1.66 .2912 1.822 98.34 -1.26 14.500 78.18 23.720 .2522 1.67 .2966 1.844 99.47 2.43 14.550 78.28 25.020 .2590 1.70 .3047 1.876 100.76 6.37 14.600 78.38 26.580 .2671 1.73 .3143 1.917 101.93 10.81 14.650 79.31 28.120 .2777 1.77 .3269 1.971 103.65 14.60 14.700 80.34 29.860 .2893 1.81 .3407 2.033 105.29 18.84 14.750 82.09 31.190 .3006 1.86 .3541 2.096 107.15 22.20 14.800 83.43 33.180 .3137 1.91 .3696 2.172 108.53 27.11 14.850 85.49 33.870 .3222 1.95 .3797 2.224 109.60 29.92 14.900 87.55 35.230 .3335 2.00 .3931 2.296 110.71 33.99 14.950 90.13 36.660 .3461 2.06 .4081 2.379 112.12 38.22 15.000 92.70 38.000 .3579 2.11 .4221 2.461 112.92 42.62 082483z2.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 4 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 96.61 20.140 .3102 1.90 .3638 2.143 83.63 -43.32 14.050 94.55 17.650 .2956 1.84 .3468 2.062 84.18 -39.69 14.100 92.19 16.030 .2816 1.78 .3305 1.987 85.13 -35.85 14.150 89.10 14.980 .2652 1.72 .3113 1.904 86.08 -31.09 14.200 87.04 14.370 .2541 1.68 .2984 1.851 87.01 -27.34 14.250 84.87 14.180 .2434 1.64 .2858 1.800 87.89 -23.24 14.300 82.50 14.340 .2325 1.61 .2731 1.751 88.55 -18.64 14.350 81.37 14.980 .2291 1.59 .2692 1.737 89.89 -15.13 14.400 80.24 15.830 .2267 1.59 .2665 1.727 91.10 -11.30 14.450 78.69 16.540 .2222 1.57 .2613 1.708 91.40 -6.94 14.500 78.28 17.720 .2252 1.58 .2649 1.721 92.73 -3.34 14.550 77.87 19.180 .2298 1.60 .2703 1.741 94.00 0.73 14.600 77.77 20.550 .2356 1.62 .2773 1.767 95.10 4.59 14.650 78.07 22.050 .2438 1.64 .2870 1.805 96.40 8.40 14.700 78.59 23.880 .2544 1.68 .2996 1.855 97.87 12.64 14.750 79.52 25.420 .2650 1.72 .3121 1.907 99.20 16.42 14.800 80.44 27.090 .2760 1.76 .3252 1.964 100.21 20.59 14.850 81.89 28.890 .2890 1.81 .3406 2.033 101.57 24.82 14.900 83.43 30.540 .3013 1.86 .3551 2.101 102.50 29.02 14.950 86.01 32.110 .3156 1.92 .3722 2.185 104.42 32.92 15.000 88.07 33.530 .3275 1.97 .3862 2.258 105.04 37.05 080283z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 5 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 103.00 18.640 .3316 1.99 .3889 2.273 80.23 -48.99 14.050 99.39 15.580 .3113 1.90 .3652 2.150 81.17 -44.27 14.100 96.31 12.980 .2933 1.83 .3442 2.050 81.61 -40.08 14.150 94.25 11.450 .2814 1.78 .3303 1.987 82.47 -37.03 14.200 90.13 10.560 .2605 1.70 .3058 1.881 83.25 -31.62 14.250 87.65 10.035 .2473 1.66 .2904 1.819 83.99 -27.78 14.300 85.49 10.210 .2367 1.62 .2781 1.770 85.09 -23.94 14.350 83.43 10.660 .2271 1.59 .2668 1.728 86.07 -19.93 14.400 81.37 11.460 .2184 1.56 .2567 1.691 86.91 -15.54 14.450 80.34 12.460 .2160 1.55 .2539 1.681 88.21 -11.97 14.500 78.80 13.860 .2128 1.54 .2502 1.668 89.10 -7.34 14.550 78.18 15.260 .2149 1.55 .2528 1.677 90.33 -3.47 14.600 77.77 16.640 .2185 1.56 .2571 1.692 91.37 0.37 14.650 77.46 18.290 .2241 1.58 .2638 1.717 92.36 4.58 14.700 77.56 19.930 .2319 1.60 .2731 1.751 93.38 8.61 14.750 78.04 21.660 .2418 1.64 .2848 1.796 94.54 12.63 14.800 78.80 23.310 .2524 1.68 .2974 1.846 95.59 16.54 14.850 79.83 25.260 .2653 1.72 .3126 1.909 96.74 20.89 14.900 80.86 27.110 .2774 1.77 .3270 1.972 97.36 25.27 14.950 82.92 28.760 .2915 1.82 .3437 2.047 98.86 29.13 15.000 85.18 30.530 .3063 1.88 .3612 2.131 100.20 33.36 082483z3.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 8 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 109.70 13.860 .3494 2.07 .4098 2.388 74.16 -53.16 14.050 105.60 9.890 .3286 1.98 .3854 2.254 74.80 -48.85 14.100 101.04 6.950 .3064 1.88 .3595 2.123 75.46 -44.26 14.150 97.34 5.020 .2881 1.81 .3382 2.022 76.16 -40.42 14.200 93.73 3.870 .2701 1.74 .3172 1.929 76.93 -36.50 14.250 89.25 3.750 .2474 1.66 .2905 1.819 77.81 -31.35 14.300 86.83 3.500 .2344 1.61 .2753 1.760 78.50 -28.11 14.350 84.46 4.080 .2219 1.57 .2607 1.705 79.62 -24.45 14.400 81.89 5.190 .2086 1.53 .2452 1.650 80.67 -20.09 14.450 80.03 6.370 .1997 1.50 .2348 1.614 81.72 -16.17 14.500 78.28 7.790 .1924 1.48 .2263 1.585 82.63 -11.99 14.550 77.15 9.450 .1902 1.47 .2237 1.576 83.84 -7.98 14.600 76.22 11.160 .1902 1.47 .2239 1.577 84.85 -3.91 14.650 75.71 13.040 .1943 1.48 .2287 1.593 86.02 0.18 14.700 75.71 15.170 .2028 1.51 .2388 1.627 87.53 4.36 14.750 75.71 17.080 .2111 1.54 .2487 1.662 88.46 8.49 14.800 76.22 18.990 .2221 1.57 .2617 1.709 89.60 12.46 14.850 76.74 20.610 .2319 1.60 .2732 1.752 90.18 16.20 14.900 78.07 23.020 .2484 1.66 .2928 1.828 91.79 20.78 14.950 79.31 25.150 .2630 1.71 .3101 1.899 92.65 25.21 15.000 80.86 27.330 .2785 1.77 .3284 1.978 93.42 29.76 072083z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 10 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 106.61 9.286 .3321 1.99 .3894 2.276 71.35 -49.54 14.050 102.18 5.872 .3105 1.90 .3643 2.146 71.88 -45.34 14.100 96.92 3.546 .2853 1.80 .3348 2.007 72.47 -40.43 14.150 92.70 2.544 .2643 1.72 .3103 1.900 73.40 -36.23 14.200 88.58 2.113 .2430 1.64 .2853 1.798 74.16 -31.82 14.250 84.98 2.421 .2235 1.58 .2625 1.712 75.07 -27.50 14.300 81.89 3.007 .2063 1.52 .2424 1.640 75.84 -23.36 14.350 79.10 4.390 .1914 1.47 .2249 1.580 76.99 -18.90 14.400 76.74 5.868 .1794 1.44 .2109 1.535 77.93 -14.52 14.450 75.19 7.682 .1742 1.42 .2048 1.515 79.31 -10.46 14.500 73.64 9.655 .1710 1.41 .2011 1.503 80.38 -6.01 14.550 72.20 11.821 .1712 1.41 .2014 1.505 81.21 -1.25 14.600 71.59 14.110 .1784 1.43 .2099 1.531 82.49 3.13 14.650 71.59 16.246 .1891 1.47 .2225 1.572 83.91 7.06 14.700 71.59 18.299 .2000 1.50 .2355 1.616 84.86 11.11 14.750 72.10 20.678 .2151 1.55 .2533 1.678 86.26 15.38 14.800 72.82 23.176 .2316 1.60 .2728 1.750 87.54 19.89 14.850 74.16 25.589 .2493 1.66 .2937 1.832 89.11 24.18 14.900 75.40 27.718 .2646 1.72 .3119 1.907 89.94 28.31 14.950 76.53 30.435 .2825 1.79 .3331 1.999 90.30 33.42 15.000 78.28 32.533 .2980 1.85 .3515 2.084 90.79 37.55 082883z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 12 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 117.42 12.430 .3760 2.21 .4410 2.578 70.77 -58.39 14.050 113.09 7.150 .3559 2.11 .4175 2.434 71.15 -54.32 14.100 108.15 3.300 .3345 2.01 .3925 2.292 71.74 -50.08 14.150 103.00 0.600 .3121 1.91 .3664 2.156 72.35 -45.67 14.200 98.37 -0.951 .2913 1.82 .3420 2.039 73.09 -41.55 14.250 93.94 -1.660 .2702 1.74 .3173 1.930 73.85 -37.31 14.300 90.13 -1.820 .2510 1.67 .2948 1.836 74.58 -33.32 14.350 86.52 -1.460 .2316 1.60 .2722 1.748 75.24 -29.15 14.400 83.43 -0.521 .2142 1.55 .2518 1.673 76.08 -24.99 14.450 80.65 0.450 .1979 1.49 .2327 1.607 76.58 -20.92 14.500 78.28 1.930 .1841 1.45 .2165 1.553 77.28 -16.71 14.550 76.43 3.770 .1743 1.42 .2051 1.516 78.21 -12.47 14.600 75.19 5.820 .1699 1.41 .2000 1.500 79.39 -8.34 14.650 74.16 7.710 .1681 1.40 .1979 1.493 80.22 -4.32 14.700 73.13 10.070 .1695 1.41 .1996 1.499 80.93 0.35 14.750 72.62 12.240 .1752 1.42 .2063 1.520 81.61 4.61 14.800 72.62 14.530 .1853 1.45 .2183 1.559 82.53 8.85 14.850 72.62 16.840 .1965 1.49 .2316 1.603 82.99 13.25 14.900 73.13 19.730 .2136 1.54 .2518 1.673 83.87 18.28 14.950 74.16 21.070 .2245 1.58 .2647 1.720 84.42 21.19 15.000 75.91 24.930 .2509 1.67 .2959 1.841 86.13 27.44 071983z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 14 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 112.27 14.571 .3599 2.12 .4220 2.460 73.92 -55.35 14.050 108.15 9.751 .3387 2.02 .3973 2.319 74.20 -50.96 14.100 103.52 6.489 .3168 1.93 .3717 2.183 74.86 -46.45 14.150 98.78 2.831 .2936 1.83 .3447 2.052 74.19 -41.86 14.200 94.76 2.831 .2746 1.76 .3224 1.952 76.08 -37.67 14.250 90.64 2.470 .2539 1.68 .2981 1.850 76.93 -33.10 14.300 87.55 2.587 .2377 1.62 .2792 1.775 77.87 -29.20 14.350 84.25 3.171 .2200 1.56 .2585 1.697 78.60 -24.71 14.400 81.37 4.201 .2045 1.51 .2403 1.633 79.36 -20.19 14.450 79.31 5.723 .1945 1.48 .2287 1.593 80.57 -15.94 14.500 77.25 7.379 .1856 1.46 .2182 1.558 81.39 -11.36 14.550 76.01 9.141 .1829 1.45 .2152 1.548 82.50 -7.24 14.600 74.68 11.233 .1822 1.45 .2144 1.546 83.34 -2.51 14.650 74.26 13.515 .1889 1.47 .2223 1.572 84.80 1.86 14.700 74.16 15.646 .1977 1.49 .2327 1.607 86.06 6.06 14.750 74.16 18.441 .2110 1.53 .2485 1.661 87.43 11.21 14.800 74.37 20.068 .2201 1.56 .2592 1.700 87.82 14.93 14.850 74.68 22.357 .2332 1.61 .2748 1.758 88.28 19.54 14.900 76.12 24.631 .2500 1.67 .2946 1.835 89.76 23.76 14.950 77.25 27.023 .2660 1.72 .3137 1.914 90.35 28.43 15.000 78.38 29.667 .2830 1.79 .3338 2.002 90.42 33.51 082883z2.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 16 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 118.97 16.210 .3854 2.25 .4520 2.650 72.84 -60.71 14.050 114.85 10.320 .3648 2.15 .4280 2.497 73.13 -56.36 14.100 109.70 5.500 .3417 2.04 .4010 2.339 73.36 -51.59 14.150 105.06 2.380 .3213 1.95 .3772 2.211 73.88 -47.45 14.200 100.73 0.296 .3020 1.87 .3546 2.099 74.47 -43.53 14.250 95.48 -1.095 .2776 1.77 .3260 1.967 74.73 -38.60 14.300 91.67 -1.434 .2588 1.70 .3040 1.874 75.47 -34.63 14.350 88.07 -1.150 .2399 1.63 .2820 1.785 76.24 -30.46 14.400 85.28 -0.556 .2246 1.58 .2640 1.717 77.09 -26.73 14.450 82.40 0.346 .2082 1.53 .2448 1.648 77.65 -22.58 14.500 78.80 2.170 .1874 1.46 .2204 1.566 77.90 -16.98 14.550 77.25 3.940 .1796 1.44 .2113 1.536 79.07 -13.02 14.600 75.40 6.030 .1716 1.41 .2020 1.506 79.76 -8.30 14.650 74.26 8.120 .1698 1.41 .1999 1.500 80.63 -3.97 14.675 73.95 9.270 .1715 1.41 .2019 1.506 81.25 -1.81 14.700 73.13 10.480 .1710 1.41 .2013 1.504 81.21 0.82 14.750 72.51 12.810 .1770 1.43 .2085 1.527 81.83 5.36 14.800 72.51 15.140 .1877 1.46 .2211 1.568 82.72 9.67 14.850 72.51 16.770 .1957 1.49 .2306 1.600 82.82 13.21 14.900 73.13 19.500 .2124 1.54 .2503 1.668 83.78 17.98 14.950 74.16 23.010 .2349 1.61 .2770 1.766 84.97 23.80 15.000 75.40 26.200 .2562 1.69 .3022 1.866 85.67 29.27 071783z1.dat 20-Meter Dipole, Length = 32.33 ft, HEIGHT = 22 ft, Calibrated Feed Line = 42.25 feet (40 feet RG-58 + balun of 2-ft RG-141 w/100 No.73 beads, RF Bridge General Radio GR-1606-A, Signal Generator Ferris Microvolter 70B, Receiver Collins 75A-4. TRANSFORMING Zi = Ri+jXi MEASURED AT LINE INPUT TO ZL = RL+jXL AT LOAD FEED LINE CALIBRATION: LINE-LENGTH IN DEGREES/MHZ, PHI = 23.72 LINE ATTENUATION IN DB/SQR(MHZ), A = .185 LINE IMPEDANCE, ZC = 54 F Ri Xi RHOi SWRi RHO L SWR L RL XL ----------------------------------------------------------------------------- 14.000 123.60 23.710 .4104 2.39 .4813 2.856 75.90 -66.80 14.050 120.51 15.800 .3901 2.28 .4577 2.688 75.51 -62.12 14.100 117.42 10.990 .3747 2.20 .4397 2.570 76.32 -58.76 14.150 112.27 6.042 .3521 2.09 .4133 2.409 76.52 -53.83 14.200 108.15 2.460 .3343 2.00 .3925 2.292 76.73 -50.01 14.250 103.00 0.281 .3121 1.91 .3666 2.157 77.29 -45.27 14.300 98.37 -1.119 .2913 1.82 .3422 2.040 77.70 -40.79 14.400 90.13 -1.701 .2509 1.67 .2949 1.837 78.53 -31.85 14.500 84.98 -0.345 .2229 1.57 .2621 1.711 80.19 -24.33 14.600 80.03 2.843 .1953 1.49 .2298 1.597 81.48 -15.04 14.700 77.25 6.803 .1843 1.45 .2170 1.554 83.16 -6.11 14.750 76.22 9.966 .1865 1.46 .2196 1.563 84.39 -0.33 14.800 75.91 11.486 .1897 1.47 .2235 1.576 84.87 3.29 14.850 76.22 14.141 .2011 1.50 .2369 1.621 86.30 8.09 14.900 76.22 16.640 .2115 1.54 .2493 1.664 86.73 13.02 14.950 76.74 19.197 .2252 1.58 .2655 1.723 87.30 17.92 15.000 78.28 21.400 .2415 1.64 .2849 1.797 88.62 22.18 |
Reg, to answer your request to put my data in a format useable in an email
without attaching a file, I found a way to convert the data to a text file. Consequently, I uploaded the entire data file in the preceding thread, Antenna Impedance Measurements. Please look for it there. Walt |
Reg, I goofed. The antenna impedance data in text format went into this thread
by mistake instead of into the Antenna Measurements thread. Unfortunately, the tabular integrity is not as good as with the PDF file. I hope you can decipher it. Walt, W2DU |
Walter Maxwell, W2DU wrote:
"Do you think any soil characteristics could be determined by such data?" Kraus has an interesting figure, No. 11-20 on page 305 of his 1950 edition of "Antennas". It is the feedpoint resistance versus height in wavelengths over perfect ground (a copper sheet?) of a resonant 1/2-wave dipole. It varies from zero ohms at zero height to a maximum of about 100 ohms at 0.35 wavelength above ground. The resistance settles down to just above 70 ohms at infinite height (free space radiation resistance value). Clean dry sand may be a very good insulator. If it were deep enough, a dipole lain on it might have a feedpoint of about 70 ohme. Better soil conductivity might shift the drivepoint of the dipole to a lower resistance as the Kraus figure indicates for perfect ground next to the dipole. Several measurements at slightly different locations and times may need to be made and averaged for reliable results. The curve in Fig. 11-20 oscillates around the free space radiation resistance so that at some altitudes feedpoint resistance goes down as altitude increases. One would need to know which part of the curve the measured resistance fell upon. Walt may be on to something with his method for determining earth constants. There are so many broadcast stations in the USA that soil conductivity has been already determined in nearly all areas. For unknown areas, one could lay out radial paths from existing stations and measure feild strengths along the radial at several places and see how much more attenuation there is versus the "unattenuated" values expected and determine average ground conductivity by the loss added by the ground. Best regards, Richard Harrison, KB5WZI |
Fred W4JLE wrote:
It would be interesting to recreate the measurements at other locations. My location has 500 feet of sand below me. It would be a great improvement just to have poor soil. Depends on your objective. For NVIS operation with a horizontal antenna, where you need the reflection, that's probably true. But for a vertical or for DX with a horizontal antenna, you're better off with the sand. Perfect ground has no loss; free space has no loss. There's an intermediate quality of ground at which the loss is maximum at a given frequency. Unfortunately, this happens to be in the range of ordinary ground characteristics in the HF range. Your ground should be very low loss. And your pattern should resemble free space, with a very strong field at very low radiation angles. Roy Lewallen, W7EL |
On Mon, 20 Jun 2005 23:02:27 +0000 (UTC), "Reg Edwards"
wrote: PHOOEY ! Yeah, but you heard it from me first. :-0 ============================ You are not so clever. You didn't detect my deliberate mistake. Ah well, I suppose I shall have to tell you. Soil constants are not constant. Wanna make a bet you don't have the last say? Punchinello Ah Punchinello! No, I am not clever at all. You can chalk that one up to charity. You are certainly entitled to the last say - "put some dirt in it and say Amen." (John Wayne in "Red River" an example of high conductance earth of the Texas panhandle country.) 73's Richard Clark, KB7QHC |
On Mon, 20 Jun 2005 23:17:40 -0400, "Walter Maxwell"
wrote: Hi All, Reg asked if I could send my data as an email, so I converted the file to text format to be able to present the data in full here in this msg. I checked to see that the tabular format remained intact, and it did in Outlook Express, so here it is. I hope the tabular format will remain intact in your browsers. Be sure to give your screen maximum width. If it doesn't, let me know and I'll resend in PDF format. I'd like to hear your comments. Hi Walt, Thanx big time for this work of dedication. I have other projects to attend to, but I am sure looking forward to close examination of this trove of data by hunkering down with Mathcad and casting up some charts. Hope to do that within the week if not sooner. 73's Richard Clark, KB7QHC |
"Richard Harrison" wrote in message ... Walter Maxwell, W2DU wrote: "Do you think any soil characteristics could be determined by such data?" Kraus has an interesting figure, No. 11-20 on page 305 of his 1950 edition of "Antennas". It is the feedpoint resistance versus height in wavelengths over perfect ground (a copper sheet?) of a resonant 1/2-wave dipole. It varies from zero ohms at zero height to a maximum of about 100 ohms at 0.35 wavelength above ground. The resistance settles down to just above 70 ohms at infinite height (free space radiation resistance value). Clean dry sand may be a very good insulator. If it were deep enough, a dipole lain on it might have a feedpoint of about 70 ohme. Better soil conductivity might shift the drivepoint of the dipole to a lower resistance as the Kraus figure indicates for perfect ground next to the dipole. Several measurements at slightly different locations and times may need to be made and averaged for reliable results. The curve in Fig. 11-20 oscillates around the free space radiation resistance so that at some altitudes feedpoint resistance goes down as altitude increases. One would need to know which part of the curve the measured resistance fell upon. Walt may be on to something with his method for determining earth constants. There are so many broadcast stations in the USA that soil conductivity has been already determined in nearly all areas. For unknown areas, one could lay out radial paths from existing stations and measure feild strengths along the radial at several places and see how much more attenuation there is versus the "unattenuated" values expected and determine average ground conductivity by the loss added by the ground. Best regards, Richard Harrison, KB5WZI Richard, your indication that the dipole input resistance of 100 ohms at 0.35 wavelength above ground is interesting, in that if you look at Kraus' graph of mutual impedance of parallel side-by-side radiators in his Fig 10-12, Page 266, you can see the reason for this. At this height above ground the the dipole is spaced 0.7 wavelengths from its image in the perfect ground plane. The mutual resistance at this spacing is -24.8 ohms, as shown in Fig 10-12 and in Table 10-1 on Page 267. Table 10-1 also shows the self resistance minus the mutual resistance at this spacing to be 97.9 ohms. There is the approximate 100 ohms shown in the graph of Fig 11-20. Note that 97.9 - 24.8 = 73.1 ohms, the nominal resistance of a thin half-wave dipole in space. Of course this data relates only to the condition of perfect ground, with total reflection and no attenuation. I would hope that the delta R and delta X values vs height taken from my measured data might shed some light on the ground conductivity and permittivity under my antenna. My soil is very sandy. Knowing that, the delta values might show some tendency to verify that condition. Walt, W2DU |
"Richard Clark" wrote in message ... On Mon, 20 Jun 2005 23:17:40 -0400, "Walter Maxwell" wrote: Hi All, Reg asked if I could send my data as an email, so I converted the file to text format to be able to present the data in full here in this msg. I checked to see that the tabular format remained intact, and it did in Outlook Express, so here it is. I hope the tabular format will remain intact in your browsers. Be sure to give your screen maximum width. If it doesn't, let me know and I'll resend in PDF format. I'd like to hear your comments. Hi Walt, Thanx big time for this work of dedication. I have other projects to attend to, but I am sure looking forward to close examination of this trove of data by hunkering down with Mathcad and casting up some charts. Hope to do that within the week if not sooner. 73's Richard Clark, KB7QHC Hi Richard, Thanx big time for considering my data worthy of your time for further examination. You've already made me anxious to see what interesting results might come from your delving into my data with Mathcad. Walt |
On Tue, 21 Jun 2005 11:37:57 -0400, "Walter Maxwell"
wrote: Thanx big time for considering my data worthy of your time for further examination. You've already made me anxious to see what interesting results might come from your delving into my data with Mathcad. Hi Walt, Even on simple examination, it proves useful. It obviously exhibits the wire wavelength altering effect of the proximity of earth. This is something Reg has harped on for years and which he curiously rejects as being incapable of demonstration in just such as your data. Perhaps this curious twist is explainable. There seems to be a new vogue of posting errant hypothesis these days so the authors can prove themselves wrong. I've seen three such admissions in just the last week. 73's Richard Clark, KB7QHC |
Walter Maxwell, W2DU wrote:
"At this height above ground (0.35 wavelength) the dipole is spaced 0.7 wavelength from its image in the perfect ground plane." I accept that, but cannot reconcile page and figure numbers. I have only the 1950 and 2003 editions of "Antennas". They are prticeless to me though I`m not as familiar with them as I am with Terman. I suggested determining ground resistance by the attenuation it adds to the ground wave. I neglected to say that the time to do so would be when sky wave propagation was small to none. Midday when using medium wave signals for signal strength measurements unless the measurement sites were close enough to the transmitter to make sky wave unimportant. I used to make medium wave broadcast station monitoring point field strength measurements within a few miles from the station, daytime, nighttime, or anytime because at this short range there is no chance of sky wave interference. You would be much more considerate of the time of day 200 miles from the station. If HF signal attenuation versus distance from the transmitter is used to determine earth resistance, for practical purposes ground wave propagation is nearly negligible, especially at the high end of the HF spectrum. I believe B, L, and E. used 3 MHz which produces some ground wave. Best regards, Richard Harrison, KB5WZI |
Anecdotally, I have noticed, I have no problem working Europe, ZS, VK, and
ZL on 75 running 90 watts. I am typically 5-9 or better in to Great Britain. My antenna is 38 feet in the center and 20 feet on both ends. Actually I have two 132 foot dipoles that are orientated 90 degrees from each other. They share a common relay box for switching in additional ladderline. That is the input to the relay box is selected by a separate relay. The unused antenna is grounded. I have tried it both grounded and ungrounded and it "seems" to be better when the unused antenna is grounded. My next set of relays will tie them both together as a big capacity hat on 160. Have not got around to doing it yet. I can push a 10 foot ground rod into the ground by hand. If I don't wet it down, I can rotate it by hand when it is 9.75 feet in the ground. If a rabbit gets in the garden, one is in dire straits trying to find a rock to throw at it. A sand pit down the road from me is over 200 feet deep and they have not hit anything other than sand in over 20 years of digging. "Roy Lewallen" wrote in message ... Fred W4JLE wrote: It would be interesting to recreate the measurements at other locations. My location has 500 feet of sand below me. It would be a great improvement just to have poor soil. Depends on your objective. For NVIS operation with a horizontal antenna, where you need the reflection, that's probably true. But for a vertical or for DX with a horizontal antenna, you're better off with the sand. Perfect ground has no loss; free space has no loss. There's an intermediate quality of ground at which the loss is maximum at a given frequency. Unfortunately, this happens to be in the range of ordinary ground characteristics in the HF range. Your ground should be very low loss. And your pattern should resemble free space, with a very strong field at very low radiation angles. Roy Lewallen, W7EL |
"Richard Harrison" wrote in message ... Walter Maxwell, W2DU wrote: "At this height above ground (0.35 wavelength) the dipole is spaced 0.7 wavelength from its image in the perfect ground plane." I accept that, but cannot reconcile page and figure numbers. I have only the 1950 and 2003 editions of "Antennas". They are prticeless to me though I`m not as familiar with them as I am with Terman. I suggested determining ground resistance by the attenuation it adds to the ground wave. I neglected to say that the time to do so would be when sky wave propagation was small to none. Midday when using medium wave signals for signal strength measurements unless the measurement sites were close enough to the transmitter to make sky wave unimportant. I used to make medium wave broadcast station monitoring point field strength measurements within a few miles from the station, daytime, nighttime, or anytime because at this short range there is no chance of sky wave interference. You would be much more considerate of the time of day 200 miles from the station. If HF signal attenuation versus distance from the transmitter is used to determine earth resistance, for practical purposes ground wave propagation is nearly negligible, especially at the high end of the HF spectrum. I believe B, L, and E. used 3 MHz which produces some ground wave. Best regards, Richard Harrison, KB5WZI Richard, I don't understand why you can't reconcile the Page numbers. I have the same editions of Kraus as you, but the edition of Kraus I'm referencing is the1950, the same as yours. Walt |
Walter, W2DU wrote:
"Richard, I don`t understamd why you can`t reconcile the page numbers." I don`t understand either, but it may be blindness and senility. Now, I`ve found everything fight where Walt said it would be! Best regards, Richard Harrison, KB5WZI |
"Richard Harrison" wrote in message ... Walter, W2DU wrote: "Richard, I don`t understamd why you can`t reconcile the page numbers." I don`t understand either, but it may be blindness and senility. Now, I`ve found everything fight where Walt said it would be! Best regards, Richard Harrison, KB5WZI Richard, that's called a 'senior moment'. Except when I do it they tell me it's my Alzheimer's Syndrome raising its ugly head. Walt |
"Richard Clark" wrote in message ... On Mon, 20 Jun 2005 23:17:40 -0400, "Walter Maxwell" wrote: Hi All, Reg asked if I could send my data as an email, so I converted the file to text format to be able to present the data in full here in this msg. I checked to see that the tabular format remained intact, and it did in Outlook Express, so here it is. I hope the tabular format will remain intact in your browsers. Be sure to give your screen maximum width. If it doesn't, let me know and I'll resend in PDF format. I'd like to hear your comments. Hi Walt, Thanx big time for this work of dedication. I have other projects to attend to, but I am sure looking forward to close examination of this trove of data by hunkering down with Mathcad and casting up some charts. Hope to do that within the week if not sooner. 73's Richard Clark, KB7QHC Hi Richard, Your mentioning Mathcad, (I have 2000i ed.) made me think of using Excel to produce some graphs of the data, however, there are two other projects that must come first. I have used Mathcad only to solve problems using the equations one can build there, and have not explored the graphing possibilities. With both Excel and Mathcad available do you think I should spend the time learning graphics with Mathcad, or stick with Excel which I already know how to use? Walt |
"Walter Maxwell" wrote You've presented a very interesting way of measuring soil characteristics. When I return to Florida in November I'm going to use your method of measuring the soil underneath the dipole ================================= Walt, would it be possible for somebody to go to B.L & E's original site and measure the soil charateristics which they completely forgot all about. Presumably, they were not aware that the type of soil had any effect on their measurments. At what time of the year did they conduct their famous experiments? Pity we shall have to wait till November for you to re-visit Florida. In view of the high temperature coefficient of soil resistivity and probability on permittivity, don't forget to take a thermometer. What was the soil temperature when you made your HF measurements versus height? Soil temperate discrepancies might be of greater order and swamp the effects of considerable changes in antenna height. But I suggest we are more interested in change of antenna impedance versus height above ground than we are in apparent change in soil characteristics versus frequency. ---- Reg, G4FGQ |
"Walter Maxwell" wrote Richard, that's called a 'senior moment'. Except when I do it they tell me it's my Alzheimer's Syndrome raising its ugly head. ===================================== I too am afflicted with Alzheimer's. I forget what I said at the beginning of a vocal sentence before I get to the end. Also I have recently had a very minor stroke which has affected the small and next fingers of my left hand. This has slowed down my keyboard dexterity. But it's quite normal for my time of life and it doesn't worry me. Least of all does KB7QHC's lying slander worry me. ---- Reg, G4FGQ |
Reg Edwards wrote:
Walt, would it be possible for somebody to go to B.L & E's original site and measure the soil charateristics which they completely forgot all about. . . But what would that tell us about the soil conditions to, say, three skin depths -- or even one? What conclusions could we draw from that information? Roy Lewallen, W7EL |
| All times are GMT +1. The time now is 11:36 PM. |
Powered by vBulletin® Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
RadioBanter.com