There always seems to be a lot of confusion concerning the effect of radials on vertical antennas, so I've gathered some notes here to (hopefully) clear up a few things. For purposes of discussion, I'll use a typical vertical antenna for 2 meters (146 MHz), constructed of #14 aluminum wire. To see the effect of ground, a height of 10 feet (120 in) will be used with average ground conditions.

For reference, 1/4 wavelength is about 20.2 inches, but for wires it would be slightly less depending on the wire diameter. Using the models, we can then look at such things as the effect of the radial length and the angle of the radials on antenna performance and input impedance. The antenna models referred to in this note were constructed using MultiNEC. The EZNEC software was also useful for visualizing antenna currents and checking the adequacy of the models.

Common wisdom dictates that the length of radials in a ground plane antenna should be about 5% longer than 1/4 wavelength, while the vertical element is 1/4 wavelength. To test this idea, models were constructed with a vertical element and 4 horizontal radial elements of equal length and the antenna characteristics were computed for radials varying from 2 to 40 inches. To determine the equivalent wire length, a model was constructed with the length of the vertical and radial elements equal. At resonance, the length was found to be 20.05 inches.

First let's see what happens when we cut the vertical element to 1/4 wavelength and then vary the length of the radials. The results of calculating the performance over real ground for a complete range of radial lengths are shown in the following table. Note that the performance is similar in free space.

 Freq (MHz) Vert Len (in) Radial Len (in) R (ohm) X (ohm) SWR(50) Max Gain @ El (deg) 146.0 20.05 2 16.63 -549.65 366.641 3.85 7 146.0 20.05 4 17.99 -282.28 91.732 3.84 7 146.0 20.05 6 18.96 -182.92 38.293 3.82 7 146.0 20.05 8 19.72 -128.73 19.686 3.80 7 146.0 20.05 10 20.38 -93.33 11.323 3.79 7 146.0 20.05 12 20.98 -67.49 7.002 3.76 7 146.0 20.05 14 21.58 -47.06 4.583 3.73 7 146.0 20.05 16 22.20 -29.85 3.185 3.69 7 146.0 20.05 18 22.88 -14.57 2.414 3.65 7 146.0 20.05 20 23.66 -0.34 2.113 3.58 7 146.0 20.05 22 24.60 13.52 2.224 3.50 7 146.0 20.05 24 25.77 27.64 2.674 3.39 7 146.0 20.05 26 27.31 42.69 3.418 3.25 7 146.0 20.05 28 29.44 59.51 4.469 3.04 7 146.0 20.05 30 32.57 79.36 5.885 2.89 37 146.0 20.05 32 37.52 104.33 7.756 2.99 36 146.0 20.05 34 46.23 138.28 10.180 3.08 36 146.0 20.05 36 64.09 189.54 13.197 3.40 59 146.0 20.05 38 110.91 278.72 16.618 4.27 59 146.0 20.05 40 302.55 453.19 19.742 5.00 58

As can be seen, the antenna resonates when the radials are also the same length as the vertical element and the antenna gain shows little variation for radials between 2 and 28 inches long. Note that when the radials are longer than 30 inches, the take off angle changes dramatically, since the radials now dominate the antenna performance.

Next, we will evaluate the performance when the vertical element is adjusted for resonance for each of the same set of radial lengths. The results of this model over real ground are shown in the following table. Once again, the results in free space are similar.

 Freq (MHz) Vert Len (in) Radial Len (in) R (ohm) X (ohm) SWR(50) Max Gain @ El (deg) 146.000 35.17364 2 400.97 0.09 8.019 4.28 7 146.000 30.10602 4 102.03 0.03 2.041 4.11 7 146.000 27.07822 6 58.99 0.02 1.180 4.01 7 146.000 25.07156 8 43.44 0.01 1.151 3.93 7 146.000 23.66342 10 35.70 0.00 1.401 3.88 7 146.000 22.6272 12 31.24 0.00 1.600 3.83 7 146.000 21.81568 14 28.31 -0.01 1.766 3.78 7 146.000 21.15283 16 26.33 0.01 1.899 3.72 7 146.000 20.57759 18 24.80 0.00 2.016 3.67 7 146.000 20.06225 20 23.71 0.00 2.109 3.58 7 146.000 19.57939 22 22.83 0.00 2.190 3.49 7 146.000 19.10864 24 22.28 0.04 2.244 3.36 7 146.000 18.63038 26 21.92 0.00 2.281 3.19 7 146.000 18.12065 28 21.96 0.00 2.276 2.94 7 146.000 17.56111 30 22.46 0.00 2.226 2.94 37 146.000 16.90945 32 23.84 0.00 2.097 3.05 36 146.000 16.09191 34 27.08 0.01 1.846 3.10 36 146.000 15.02228 36 34.52 0.02 1.448 3.90 59 146.000 13.51005 38 54.53 0.00 1.091 4.71 58 146.000 11.2677 40 131.48 0.00 2.630 5.22 58

As can be seen, the resonant length of the vertical element varies inversely to the radial length in all cases. Once again, when the radials are longer than about 30 inches, the take-off angle changes abruptly. Interestingly it appears that there is a design of optimum impedance with a vertical length of about 26 inches and radials of about 7 inches which would yield a low take-off angle and also match 50 ohms. The typical design criteria with the radials about 5% longer than the vertical element can be viewed in both cases.

From the results we would have to conclude that there is no real advantage to making the radials slightly longer or slightly shorter than the vertical element. In fact, there may be a good reason to make the vertical element about 26 inches long and the radials about 7 inches long for ease of matching. It would still be a ground plane antenna, but not a ¼ wavelength. In fact, 26 inches is nearly equivalent to 1/3 wavelength.

Common wisdom also indicates that bending the radials downward at about a 45 degree angle improves antenna performance and matching. To check this hypothesis, the above model with a 20.05 inch vertical element was modeled, but the angle on the radials was varied from 60 degrees above the horizontal to 60 degrees below the horizontal. For each case, the length was adjusted to resonance, but the radial and vertical lengths were kept equal. (Note that for more acute angles, the modeling results may not be reliable due to limitations in the NEC software.)

 Freq (MHz) Vert Len (in) Rad Ang (deg) R (ohm) X (ohm) SWR(50) Max Gain @ El (deg) 146.000 18.75922 -60 54.36 0.00 1.087 4.62 8 146.000 18.955 -50 51.29 0.00 1.026 4.37 7 146.000 19.05364 -45 49.20 0.00 1.016 4.26 7 146.000 19.15477 -40 46.87 0.00 1.067 4.16 7 146.000 19.36388 -30 41.60 0.09 1.202 3.98 7 146.000 19.57782 -20 35.75 0.05 1.399 3.82 7 146.000 19.68933 -15 32.71 0.03 1.528 3.75 7 146.000 19.80473 -10 29.66 0.01 1.686 3.69 7 146.000 20.05 0 23.64 0.03 2.115 3.59 7 146.000 20.31474 10 17.93 0.00 2.789 3.54 7 146.000 20.45588 15 15.28 0.00 3.273 3.52 7 146.000 20.60259 20 12.80 0.00 3.907 3.53 7 146.000 20.91174 30 8.46 -0.08 5.913 3.56 7 146.000 21.25143 40 5.09 0.00 9.825 3.63 7 146.000 21.43162 45 3.77 0.00 13.259 3.68 7 146.000 21.62098 50 2.70 0.00 18.507 3.72 7 146.000 22.03908 60 1.26 0.01 39.620 3.62 7

As can be seen, the antenna performance and characteristics seems to improve when the radials are dropped (negative angles) and the impedance drops dramatically as the radials are raised above the horizontal. Indeed, radials sloping downward at about 45 degrees do seem to provide a nice match to 50 ohms and perhaps slightly more gain than horizontal radials.

To check what happens if the radials are sloped, but maintained 5% longer than the vertical element the following calculations were performed.

 Freq (MHz) Vert Len (in) Rad Ang (deg) R (ohm) X (ohm) SWR(50) Max Gain @ El (deg) 146.000 18.54821 -60 56.05 0.00 1.121 4.62 8 146.000 18.75227 -50 52.68 0.00 1.054 4.37 7 146.000 18.85471 -45 50.44 0.00 1.009 4.26 7 146.000 18.9573 -40 47.91 0.00 1.044 4.15 7 146.000 19.16425 -30 42.22 0.00 1.184 3.96 7 146.000 19.38005 -20 36.01 0.00 1.389 3.79 7 146.000 19.49248 -15 32.81 0.00 1.524 3.72 7 146.000 19.60877 -10 29.59 0.00 1.690 3.66 7 146.000 19.85489 0 23.26 0.00 2.150 3.56 7 146.000 20.12181 10 17.34 0.00 2.883 3.49 7 146.000 20.26407 15 14.60 0.00 3.425 3.48 7 146.000 20.41245 20 12.05 0.00 4.148 3.48 7 146.000 20.72777 30 7.65 0.00 6.532 3.52 7 146.000 21.06889 40 4.32 0.00 11.575 3.58 7 146.000 21.25081 45 3.06 0.00 16.347 3.61 7 146.000 21.44184 50 2.07 0.00 24.162 3.62 7 146.000 21.86202 60 0.83 0.00 59.893 3.18 7

Once again, we see that at 45 degrees downward, the impedance is nearly exactly 50 ohms. Compared to the case with equal sized vertical and radial elements, there appears to be no real advantage. The vertical element length differs by only 0.15 inches, the difference in impedance is about 1 ohm, while the gain is identical.

We therefore conclude that sloping the radials downward, indeed has a positive effect on ground plane antenna performance and that angles of about 45 degrees appear to be optimum, just as hypothesized. However, there appears to be no advantage to making the radials 5% longer than the vertical element. The very slight affect on the impedance can be obtained with equal length radials by sloping them downward by a few extra degrees, which is well within the precision of amateur construction techniques.

Questions are often asked about radials for a 5/8 wavelength antenna. Should they be the same size as for a ¼ wavelength antenna? Should they be 5/8 wavelengths long?

Before modeling, let’s explain a few things about 5/8 wavelength antennas. First, they are not resonant, so adjusting for resonance doesn’t enter into the picture at all. Second, the purpose of such an antenna design is to raise the current maximum higher up the antenna, thereby yielding a lower angle of radiation. This also has the effect of making the current at the antenna base much less, and therefore the radials have much less current flow than the ¼ wavelength case. In a ¼ wave ground plane, the current maximum is right at the base of the antenna and is also equalized by current flow in the radials. We therefore expect that the radials would be much less important in a 5/8 wave antenna than in a ¼ wave antenna.

The results of modeling a 5/8 wave vertical for various radial lengths are shown in the following table. In all cases the vertical element was set at 49.75 inches, which is a typical length used in amateur mobile installations. Note that normally a matching method is used, since the characteristic impedance of such an antenna is capacitive and the resistive component is greater than 50 ohms. Normally a tapped coil is used to feed the antenna with coax, thereby canceling the capacitance and providing an impedance transformation to 50 ohms. The matching network was not modeled in this investigation.

 Freq (MHz) Radial Len (in) R (ohm) X (ohm) SWR(50) Max Gain @ El (deg) 146.000 5 75.33 -489.75 65.835 4.07 6 146.000 10 82.88 -391.06 39.138 4.12 6 146.000 15 87.05 -358.94 31.885 4.19 6 146.000 20 89.54 -342.20 28.470 4.28 6 146.000 25 91.02 -330.37 26.314 4.40 6 146.000 30 91.78 -318.54 24.451 4.59 6 146.000 35 92.13 -300.38 21.928 4.93 6 146.000 40 101.93 -237.00 13.476 5.62 6 146.000 45 163.73 -432.22 26.362 4.54 54 146.000 50 111.91 -362.97 26.192 2.99 32 146.000 55 106.78 -345.33 24.900 3.13 6 146.000 60 105.64 -335.90 23.905 3.43 6

It is interesting to note that for radial lengths between about 10 and 36 inches, neither the gain nor the take-off angle vary significantly, but the impedance tends to have a higher resistive component and a smaller capacitive component as the length increases. For matching purposes, i.e. smaller coils and higher efficiency, there may be a slight reason to use radials in the range of 35 to 40 inches. For practical purposes, however, the differences are slight and would probably not be noticed in practice.

Therefore, as suspected due to considering the current distribution in the radials, it appears that nearly any radial length can be used. When the radials get to be on the order of 5/8 wavelength, though, they tend to also have a higher current distribution and the take-off angle becomes much higher.

73,

Walt, W5ALT

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