The conceit that goes with random wire antennas is that they amount to taking a random chunk of wire, stringing it up in the air, and using it as an antenna. In my mind, this is a pretty serious misuse of the term ‘random’. To be usable with any sensible antenna tuner, the wire must be non-resonant at the frequencies you care about. So, for an antenna that you want to use on every band, 10m-40m, the wire must not be resonant on any frequency in any of those bands. This is ‘random length’ in the sense that the length is very, very carefully chosen. In other words, entirely non-random.
The trick, here, is that the very high impedance of a non-resonant wire that is fed at the end is handled with an unun, often with the ratio of 9:1, that transforms it down reasonably close to 50 ohms, so that a modest built-in antenna tuner in a transceiver can handle it.
Building such an unun is a topic I’ll deal with another time. Today I want to talk about how we go about choosing a wire length that is not resonant on any frequency in any band we care about.
So, for an antenna we intend to be used as an NVIS antenna, those bands might be 30m, 40m, 60m, 80m, 160m, because those are the bands where NVIS style operation makes sense. We can safely ignore 6m, 10m, 12m, 15m, 17m, 20m.
When will a wire be resonant for a given frequency? Obviously, when the length of the wire is a half wavelength for that frequency. But also, every integer multiple of that length.
A useful in-depth explanation is here. A somewhat less useful explanation on which that is founded is here
All well and good, then. We write a bit of software, give it the bands we care about, and out pops a set of suitable lengths. Cut your wire to one of those lengths, throw in your 9:1 unun, and the proverbial Robert is your parent’s sibling.
(pun intended) Let’s look at the calculated possible ranges for an end fed non resonant antenna intended for use on 10m, 12m, 15m, 17m, 20m. Such an antenna might be useful for POTA deployment in the current state of the solar cycle, where high bands are very useful and band agility is desired.
My software calculates:
| Length | Resonant F | Range |
|---|---|---|
| 7.88 ± 7.88 | 59.400002 MHz | [0.00 - 15.76] |
| 17.72 ± 1.01 | 26.409512 MHz | [16.71 - 18.73] |
| 20.31 ± 1.51 | 23.042316 MHz | [18.80 - 21.82] |
| 24.02 ± 1.74 | 19.481615 MHz | [22.29 - 25.76] |
| 28.71 ± 2.81 | 16.301708 MHz | [25.90 - 31.52] |
| 35.44 ± 2.01 | 13.204756 MHz | [33.43 - 37.45] |
| 40.62 ± 3.02 | 11.521158 MHz | [37.61 - 43.64] |
| 45.34 ± 0.77 | 10.322033 MHz | [44.57 - 46.11] |
| 46.80 ± 0.47 | 9.999001 MHz | [46.34 - 47.27] |
| 50.83 ± 0.69 | 9.206979 MHz | [50.14 - 51.52] |
| 53.99 ± 2.19 | 8.667729 MHz | [51.80 - 56.18] |
| 59.72 ± 3.31 | 7.836669 MHz | [56.41 - 63.03] |
| 70.88 ± 4.03 | 6.602377 MHz | [66.86 - 74.91] |
| 76.24 ± 1.03 | 6.138121 MHz | [75.21 - 77.28] |
| 78.25 ± 0.54 | 5.981048 MHz | [77.71 - 78.79] |
| 85.42 ± 1.85 | 5.478678 MHz | [83.57 - 87.27] |
| 90.68 ± 1.54 | 5.161016 MHz | [89.14 - 92.22] |
| 93.16 ± 0.48 | 5.023865 MHz | [92.67 - 93.64] |
| 94.28 ± 0.27 | 4.963961 MHz | [94.01 - 94.55] |
| 101.66 ± 1.38 | 4.603489 MHz | [100.29 - 103.04] |
| 106.35 ± 2.74 | 4.400575 MHz | [103.61 - 109.09] |
| 121.53 ± 4.53 | 3.850892 MHz | [117.00 - 126.06] |
| 136.02 ± 2.31 | 3.440678 MHz | [133.71 - 138.33] |
| 140.41 ± 1.40 | 3.333000 MHz | [139.01 - 141.82] |
| 151.58 ± 1.15 | 3.087521 MHz | [150.43 - 152.73] |
| 156.79 ± 0.79 | 2.984925 MHz | [156.00 - 157.58] |
| 167.85 ± 0.70 | 2.788285 MHz | [167.14 - 168.55] |
| 171.28 ± 2.05 | 2.732385 MHz | [169.22 - 173.33] |
| 184.15 ± 0.29 | 2.541471 MHz | [183.86 - 184.43] |
| 186.31 ± 0.96 | 2.511933 MHz | [185.35 - 187.27] |
| 188.56 ± 0.53 | 2.481980 MHz | [188.03 - 189.09] |
| 202.71 ± 2.14 | 2.308717 MHz | [200.57 - 204.85] |
| 217.73 ± 0.45 | 2.149414 MHz | [217.29 - 218.18] |
| 235.18 ± 1.18 | 1.989950 MHz | [234.00 - 236.36] |
| 251.42 ± 0.70 | 1.861444 MHz | [250.71 - 252.12] |
| 267.65 ± 0.23 | 1.748528 MHz | [267.43 - 267.88] |
You’ll observe that there are a bunch of lengths which are not resonant on any frequency in a desired band, but are impractical for one of two reasons:
while not actually resonant on a desired frequency, the length is so very close to a band edge that it might be difficult to get a limited range tuner to tune on at frequencies close to that edge.
As a practical matter, cutting the wire to the right length would be a fussy affair. For example, cutting a wire to 184.15 feet to within 4 inches is certainly possible, but much harder than hitting 40.62 feet to within 3 feet. The former will require care, the latter you can probably hit just by pacing off the distance on the ground.
Each band has a lower band limit and an upper band limit, and a bandwidth which is the difference between the two. As you progress up the multiples of the half wavelengths, the difference between the two grows. Eventually this means that the range of lengths for one multiple overlaps the range for the next multiple. Beyond this point, the ranges will always overlap in this way, so this sets an upper limit on a non-resonant length for that band.
Obviously, for a multi-band non-resonant antenna, the maximum length will be the shortest maximum length of the included bands.
Those maximum lengths are:
| band | λ/2 multiple | len(ft) |
|---|---|---|
| 2m | 36 | 117.000 |
| 6m | 13 | 121.333 |
| 10m | 17 | 283.636 |
| 12m | 249 | 4681.873 |
| 15m | 47 | 1047.273 |
| 17m | 181 | 4688.243 |
| 20m | 40 | 1337.143 |
| 30m | 202 | 9360.000 |
| 40m | 24 | 1602.740 |
| 60m | 67 | 5882.440 |
| 80m | 8 | 1053.000 |
| 160m | 9 | 2340.000 |
| 630m | 68 | 67415.445 |
| 2200m | 65 | 224150.953 |
Obviously some bands have maximum lengths that are actually longer than any practical antenna. But some bands (2m, 6m, 10m) have maximum lengths that aren’t impractical. In particular, it’s worth noting that you can’t have a non-resonant antenna that works on 6m that is longer than ~121 feet.
In any case, we don’t care about the length directly, what we care about is resonant frequencies. Different wire diameter, different wire insulation, different heights above ground, different objects in proximity to the wire, will all affect the resonant frequency(s).
A useful exploration of this is this article. Deeper exploration at this W4RNL article. What, then, are we to do?
We need to stop thinking in length and start thinking in resonant frequency. So when we select our wire length, what we really want to do is select a target resonant frequency, do some rough calculations to get an approximate length, and then trim the wire to that resonant frequency, and thus ensure it will not be resonant on any frequency we care about.
But…
Remember that the resonant frequency of our wire is going to depend on the environment in which it’s being used. Soil conductivity, proximity to objects, height above ground will all affect the resonant frequency.
So, we want to pick a length where the resonant frequency avoids being resonant on any of the frequencies on any of the bands we care about despite changes in enviroment. My best idea on how to do this is:
For POTA use with an all band radio, we probably want to be free to operate on all bands, 10m through 40m, perhaps with 6m thrown in for good measure if adding it doesn’t alter the practicalities of the length very much.
So for 10m, 12m, 15m, 17m, 20m, 30m, 40m my software tells us: [ 10m 12m 15m 17m 20m 30m 40m ]
| Length | Resonant F | Range |
|---|---|---|
| 7.88 ± 7.88 | 59.400002 MHz | [0.00 - 15.76] |
| 17.72 ± 1.01 | 26.409512 MHz | [16.71 - 18.73] |
| 20.31 ± 1.51 | 23.042316 MHz | [18.80 - 21.82] |
| 24.02 ± 1.74 | 19.481615 MHz | [22.29 - 25.76] |
| 28.71 ± 2.81 | 16.301708 MHz | [25.90 - 31.52] |
| 35.44 ± 2.01 | 13.204756 MHz | [33.43 - 37.45] |
| 40.62 ± 3.02 | 11.521158 MHz | [37.61 - 43.64] |
| 45.34 ± 0.77 | 10.322033 MHz | [44.57 - 46.11] |
| 46.80 ± 0.47 | 9.999001 MHz | [46.34 - 47.27] |
| 50.83 ± 0.69 | 9.206979 MHz | [50.14 - 51.52] |
| 53.99 ± 2.19 | 8.667729 MHz | [51.80 - 56.18] |
| 59.72 ± 3.31 | 7.836669 MHz | [56.41 - 63.03] |
| 70.88 ± 4.03 | 6.602377 MHz | [66.86 - 74.91] |
| 76.24 ± 1.03 | 6.138121 MHz | [75.21 - 77.28] |
| 78.25 ± 0.54 | 5.981048 MHz | [77.71 - 78.79] |
| 85.42 ± 1.85 | 5.478678 MHz | [83.57 - 87.27] |
| 90.68 ± 1.54 | 5.161016 MHz | [89.14 - 92.22] |
| 93.16 ± 0.48 | 5.023865 MHz | [92.67 - 93.64] |
| 94.28 ± 0.27 | 4.963961 MHz | [94.01 - 94.55] |
| 101.66 ± 1.38 | 4.603489 MHz | [100.29 - 103.04] |
| 106.35 ± 2.74 | 4.400575 MHz | [103.61 - 109.09] |
| 121.53 ± 4.53 | 3.850892 MHz | [117.00 - 126.06] |
| 136.02 ± 2.31 | 3.440678 MHz | [133.71 - 138.33] |
| 140.41 ± 1.40 | 3.333000 MHz | [139.01 - 141.82] |
| 151.58 ± 1.15 | 3.087521 MHz | [150.43 - 152.73] |
| 156.79 ± 0.79 | 2.984925 MHz | [156.00 - 157.58] |
| 167.85 ± 0.70 | 2.788285 MHz | [167.14 - 168.55] |
| 171.28 ± 2.05 | 2.732385 MHz | [169.22 - 173.33] |
| 184.15 ± 0.29 | 2.541471 MHz | [183.86 - 184.43] |
| 186.31 ± 0.96 | 2.511933 MHz | [185.35 - 187.27] |
| 188.56 ± 0.53 | 2.481980 MHz | [188.03 - 189.09] |
| 202.71 ± 2.14 | 2.308717 MHz | [200.57 - 204.85] |
| 217.73 ± 0.45 | 2.149414 MHz | [217.29 - 218.18] |
| 235.18 ± 1.18 | 1.989950 MHz | [234.00 - 236.36] |
| 251.42 ± 0.70 | 1.861444 MHz | [250.71 - 252.12] |
| 267.65 ± 0.23 | 1.748528 MHz | [267.43 - 267.88] |
Throwing in 6m does not change things substantially and so it seems to me we might as well include it:
| Length | Resonant F | Range |
|---|---|---|
| 4.33 ± 4.33 | 107.999992 MHz | [0.00 - 8.67] |
| 12.56 ± 3.20 | 37.264744 MHz | [9.36 - 15.76] |
| 17.02 ± 0.31 | 27.490910 MHz | [16.71 - 17.33] |
| 22.36 ± 3.64 | 20.930231 MHz | [18.72 - 26.00] |
| 29.80 ± 1.72 | 15.705977 MHz | [28.08 - 31.52] |
| 34.05 ± 0.62 | 13.745455 MHz | [33.43 - 34.67] |
| 40.39 ± 2.95 | 11.587983 MHz | [37.44 - 43.33] |
| 47.04 ± 0.24 | 9.949749 MHz | [46.80 - 47.27] |
| 51.07 ± 0.93 | 9.163637 MHz | [50.14 - 52.00] |
| 58.41 ± 2.25 | 8.011869 MHz | [56.16 - 60.67] |
| 68.10 ± 1.24 | 6.872727 MHz | [66.86 - 69.33] |
| 76.44 ± 1.56 | 6.122449 MHz | [74.88 - 78.00] |
| 85.45 ± 1.21 | 5.476673 MHz | [84.24 - 86.67] |
| 94.07 ± 0.47 | 4.974874 MHz | [93.60 - 94.55] |
| 103.48 ± 0.52 | 4.522613 MHz | [102.96 - 104.00] |
| 112.67 ± 0.00 | 4.153846 MHz | [112.67 - 112.67] |
| 1000.00 ± 0.00 | 0.468000 MHz | [1000.00 - 1000.00] |
For POTA use we probably don’t care about any of the lengths beyond 100 feet. To my eye, the good lengths I see are: |Length | Resonant F | Range| |:–|:–|:–| 17.72 ± 1.01 | 26.409512 MHz | [16.71 - 18.73] 20.31 ± 1.51 | 23.042316 MHz | [18.80 - 21.82] 24.02 ± 1.74 | 19.481615 MHz | [22.29 - 25.76] 28.71 ± 2.81 | 16.301708 MHz | [25.90 - 31.52] 35.44 ± 2.01 | 13.204756 MHz | [33.43 - 37.45] 40.62 ± 3.02 | 11.521158 MHz | [37.61 - 43.64] 53.99 ± 2.19 | 8.667729 MHz | [51.80 - 56.18] 59.72 ± 3.31 | 7.836669 MHz | [56.41 - 63.03] 70.88 ± 4.03 | 6.602377 MHz | [66.86 - 74.91] 76.24 ± 1.03 | 6.138121 MHz | [75.21 - 77.28] 85.42 ± 1.85 | 5.478678 MHz | [83.57 - 87.27] 90.68 ± 1.54 | 5.161016 MHz | [89.14 - 92.22] 101.66 ± 1.38 | 4.603489 MHz | [100.29 - 103.04] 106.35 ± 2.74 | 4.400575 MHz | [103.61 - 109.09] 121.53 ± 4.53 | 3.850892 MHz | [117.00 - 126.06]
17.72’ and 20.31’ are handy because you can get them entirely vertical on a 21 foot SOTABEAMS carbon-6 telescoping carbon fiber mast. (17.72’ is a little iffy on 6m but probably fine) 24.02’, 28.71’ are vertical on any of the easily available 31’ fiberglass telescoping mast. 40.62’, 53.99’, 70.88’ are all nice slopers or inverted Vs on a 31’ mast, or pulled up on a line in a tall tree.
[ 20m 30m 40m ]
| Length | Resonant F | Range |
|---|---|---|
| 16.31 ± 16.31 | 28.700001 MHz | [0.00 - 32.61] |
| 39.77 ± 6.34 | 11.768117 MHz | [33.43 - 46.11] |
| 55.22 ± 8.89 | 8.474712 MHz | [46.34 - 64.11] |
| 79.54 ± 12.68 | 5.884058 MHz | [66.86 - 92.22] |
| 95.26 ± 2.58 | 4.913051 MHz | [92.67 - 97.84] |
| 114.25 ± 13.97 | 4.096192 MHz | [100.29 - 128.22] |
16.31’ is probably too short to be useful on 40m. 39.77’, 55.22’ seem like good lengths for a SOTA deployment, perhaps with a 21’ mast to make an inverted V or a sloper. 79.54’ seems pretty long, as does 95.26’ and 114.25’
[ 30m 40m 60m 80m 160m ]
| Length | Resonant F | Range |
|---|---|---|
| 23.05 ± 23.05 | 20.299999 MHz | [0.00 - 46.11] |
| 55.22 ± 8.89 | 8.474712 MHz | [46.34 - 64.11] |
| 76.68 ± 9.82 | 6.103142 MHz | [66.86 - 86.51] |
| 90.01 ± 2.21 | 5.199375 MHz | [87.80 - 92.22] |
| 104.84 ± 12.16 | 4.464088 MHz | [92.67 - 117.00] |
| 136.02 ± 2.31 | 3.440678 MHz | [133.71 - 138.33] |
| 156.01 ± 17.00 | 2.999780 MHz | [139.01 - 173.01] |
| 180.02 ± 4.41 | 2.599688 MHz | [175.61 - 184.43] |
| 188.84 ± 3.49 | 2.478319 MHz | [185.35 - 192.33] |
| 215.56 ± 14.99 | 2.171123 MHz | [200.57 - 230.54] |
| 232.84 ± 1.16 | 2.009950 MHz | [231.68 - 234.00] |
| 272.04 ± 4.61 | 1.720339 MHz | [267.43 - 276.65] |
| 299.28 ± 21.26 | 1.563733 MHz | [278.02 - 320.55] |
55.22’ might work. 76.68 is probably long enough for 80m to work well. 90.01’ looks like a handy length, as does 104.84. Beyond that my favorites would be 156.01’ and 215.56’ but all the listed lengths would probably be fine.
In the light of all that it’s interesting to look at the lengths of radiating wires used in various commercially available EFRW/non-resonant antennas.
Tufteln: 41’, 58’, 71’, 84’ KM4CFT: 29’, 35.5’, 41’, 58’, 71’ Palomar: 71’, 155’, 173’ chameleon: 71’ ko4fsz: 84’ Sotabeams: 42’
It’s a little hard to know exactly what resonant frequencies are for these lengths, as much depends on wire, insulation, and the deployment.
But all of those lengths fall in (or very close to) the length ranges I calculate. The 155’ and 173’ Palomar lengths seem curious to me, as they fall close to but not in any calculated range. It may be that the quoted length includes the feedpoint assembly, or something, and not the actual radiator length.
Clearly it’s time for building some antennas and experimenting. So there will be more on this subject in the future, I expect.