Part 3:
Planes in Space

L. B. Cebik, W4RNL (SK)

We are very comfortable modeling dipoles in free space. We use such models as the starting point for many a disquisition on dipole properties. So let us begin our journey just here.

We should note that in free space, we may model a dipole along any of the three Cartesian coordinates (or even traversing them at an angle). Free space has nothing in any direction and in every direction. Wherever the dipole broadside is, off that broadside will be maximum gain.

This reminder of free space properties is to remove any initial anxiety about modeling our dipole along the Z axis--which would be height, if we had a ground below. Since we are interested in vertical antennas relative to ground, this strategy will be handy for modeling over ground.

Let's not be too hasty in getting close to the ground. For present purposes, we shall stay 2 wavelengths above ground. At this height and above, antennas show virtually the same feedpoint impedance they show in free space, and some basic gain comparisons will be instructive as we move from full size dipoles toward monopoles with planes.

We shall retain our 2" diameter aluminum main element. If we add a plane or a hat, it will be composed of 0.25" aluminum radials. This procedure will preserve consistency throughout the exercise. Moreover, we shall continue to list gain and feedpoint values to 2 decimal places. Although this level of reporting the modeling program output has little if any practical antenna building significance, it occasionally reveals some numerical trends that might be obscured by rounding the numbers to a construction level.

Building a full size dipole in free space means nothing more than doubling the full size monopole over perfect ground. NEC does the same thing for us with the monopole as it constructs an image during calculations. The only difference shows up in the feedpoint impedance: values will be twice those reported for the monopole. Let's compare the monopole and the dipole. Gain figures list the monopole over perfect ground and the dipole in free space. They are not significant here, but will become so later.

Antenna        Length         Feed Z              Gain
(ft) (R +/- jX ohms) (dBi)

Monopole 33.25 35.97 - 0.06 5.14
Dipole 66.50 71.92 - 0.27 2.13

As shown in Figure 1, we may place hats at the ends of a dipole in a manner identical to placing one at the top of a vertical monopole. Moreover, we may construct a hatted dipole in the same way we constructed the dipole: simply by joining two monopoles with hats in the center and keeping the main elements in a line. Once more, we may expect the dipole feedpoint impedance to be twice that of the monopole. "Gain loss" is referenced to the gain of the corresponding full size antenna above. The hats on each end of dipoles consist of 4 wires of the same lengths used for the monopoles: 70%: 5.57' each; 50%: 9.90' each; and 20%: 20.7' each.

Antenna        Length         Feed Z              Gain      Gain loss
(ft) (R +/- jX ohms) (dBi) (dB)

70% Full-size
Monopole 23.275 29.08 - 0.71 5.02 -0.12
Dipole 46.550 58.15 - 1.50 2.01 -0.12

50% Full-size
Monopole 16.625 18.81 + 0.66 4.88 -0.26
Dipole 33.250 37.63 + 1.39 1.87 -0.26

20% Full-size
Monopole 6.650 3.67 - 0.61 4.59 -0.55
Dipole 13.300 7.34 - 1.41 1.58 -0.55

The relatively precise feedpoint impedance doubling is obvious. Now here is where the gain figures acquire some importance. The differences in gain of each shortened monopole relative to the full size monopole are exactly reflected in the differences in gain of each shortened dipole relative to the full size dipole. A hatted dipole (or monopole) 20% of full size, relative to a full size dipole, loses only 0.55 dB of gain--or about 1/10 of an S-unit as such measures are loosely reckoned.

Similar results accrue over ground. Since we are limiting ourselves to approaching only 2 wavelengths from ground, let's set the feedpoints of the vertical dipoles at 280' up and see what happens.

Antenna        Length         Feed Z              Gain      Gain loss
               (ft)           (R +/- jX ohms)     (dBi)     (dB)

Dipole         66.50          71.83 - 0.79        4.44

70% Full-size
Dipole         46.550         58.02 - 1.43        4.34      -0.10

50% Full-size
Dipole         33.250         37.53 + 1.45        4.21      -0.23

20% Full-size
Dipole         13.300          7.32 - 1.13        3.94      -0.50

Again, the dipole only 20% of full size loses only a half dB relative to a full size dipole, as do equivalently shrunken monopoles. If we can handle the low feedpoint impedances involved, these antennas can be useful.

The shortest of the hatted antennas has hat radials far longer than the main element itself. However, the radiation from these hats fully cancels so that all radiation in the far field pattern is vertically polarized. Moreover, the hats do not interact, as evidenced by the fact that the shortest dipole reflects the same feedpoint impedance doubling and gain reduction amount as the monopole over perfect ground. Each hat is the antenna current completion path for each of the monopoles forming the dipole.

The symmetrical hat at right angles to the main element does not radiate. However, if the radials of the hat are angled, significant radiation does occur. In general, if the antenna is vertical, and we construct a so- called sloping ground plane of wires, horizontally polarized radiation from the plane wires does cancel while vertically polarized radiation adds to the radiation of the antenna. In essence, as we split one monopole into 4 wires, leaving the other as a single element, we can bend the wires through the arc of 90 degrees and end up with a monopole and plane, as shown in Figure 2

Modeling this progression requires a caution: The wires resulting from splitting the main element yield a fatter wire than the former end of the one-wire dipole. This fatter 4-part wire carries slightly higher currents closer to the feedpoint, which raises the overall gain of the antenna in a near-dipole configuration. This shows up as a shorter length for the 4- part wire than for the 1-wire upper end. With this in mind, we can construct some models of the transition using angles of 5, 45, and 90 degrees, in order to look at both the gain and the pattern of the antenna. In all case, the upper end is 33.25' of 2" aluminum, while the lower part is 4 0.25" wires of the length given in the table.

Antenna             Radial Length       Feedpoint Z         Gain
                    (feet)              (R +/- jX ohms)     (dBi)

Simulated dipole:  5-deg from vertical
Free space          27.5                57.27 - 0.79        2.58
2 wl up                                 57.16 - 0.71        4.91/7 deg

Sloping plane:  45-deg from vertical
Free space          29.5                48.33 + 0.51        2.08
2 wl up                                 48.26 + 0.62        4.47/7 deg

"Ground" plane:  90-deg from vertical
Free space          38.7                21.38 - 0.66        1.32
2 wl up                                 21.42 - 0.59        3.85/6 deg

We can look at the gain figures in two ways. First, we can view the sloping plane antenna as reduced in gain by about 0.5 dB from a true vertical dipole of similar materials. Second, we can view the sloping plane antenna as providing about 2/3 dB gain over a similarly situated monopole with a level plane. Although the gain may not be much, it is real. However, we often throw it away by being careless with the placement of sloping radials or by not attending to the matter of resonating the entire antenna, including the sloping radials. We shall discuss the importance of resonance in a later episode. By way of preview, the importance lies not in any special property of resonance itself, but instead by what it indicates with respect to the high current position on the entire antenna, where antenna includes both the main element and the radials.

In free space, we cannot accurately model only half the antenna. The model consists of both the main element and the radials, whether those radials are pointed straight down, sloped at an angle, or placed at right angles to the main element to form a plane. Adding the term "ground" to the expression "plane" adds nothing to the model. With respect to free space modeling, the plane is simply the other half of the dipole so constructed as not to add to the overall radiation. In fact the plane does not even bend or distort the free space radiation pattern of the antenna in any way, as the elevation pattern in Figure 3 indicates. The plane acts just like a hat--or a hat acts just like a plane. In free space, the only distinction seems to be this: we use the term "hat" when the structure replaces some of the main element length, and we use the term "plane" when the structure replaces all or virtually all of the main element length, where "length" is referred to each monopole making up a dipole. electrically, there is no difference: hat and plane differences are functions of the variables we discussed in the last episode: main element diameter, main element length, radial diameter, and number of radials.

Moreover, as indicated in Figure 4, there is no rule that prevents the construction of asymmetrical hatted/planed antennas. Indeed, many short verticals for the lowest HF bands are precisely such constructions: hatted, planed vertical antennas.

Before we return to earth to muddy up the situation a bit, let's look at a problem attached to modeling dipoles that consist of one linear monopole and a plane. NEC has a limitation in that it will not permit placement of a split feedpoint at a multiple wire junction. The standard view of a vertical antenna and its plane seems to require precisely this move. One temptation is to move the feedpoint to the wire segment immediately adjacent to the junction with the radials. This can lead to problematical results, as shown in the next table. All main elements are 33.25' long.

Antenna        Radial length       Gain           Feedpoint Z
(feet) (dBi) (R +/- jX ohms)
Free space 38.7 1.32 21.38 - 0.66
2 wl up 3.85/6 deg 21.42 - 0.59

Free space 40.4 1.24 21.90 - 0.22
2 wl up 3.79/6 deg 21.95 - 0.30

Free space 41.3 1.18 22.30 - 0.50
2 wl up 3.74/6 deg 22.36 - 0.43

Free space 42.2 1.11 22.73 - 0.26
2 wl up 3.69/6 deg 22.80 - 0.19

The descending gain and increasing feedpoint impedance indicate that the antenna is being feed increasingly off center. With a dipole whose halves are identical, the physical center is also the electrical center. With an antenna whose two halves are of different construction, the electrical center may well be elsewhere. The electrical center of the antenna (dipole) is the point of highest current. As we add more radials, we increase the working diameter of the monopole we call the plane. The point of highest current moves further out away from the junction, calling for more wire on the other side of the electrical center, namely, in the radials, to return the system to resonance.

Moving the region of highest current further into the plane moves it also into the region of cancelled radiation. Although the loss may not be very large, it is definite, as the progressively lower gains of the models demonstrates.

To overcome this modeling problem and permit the exercise to continue, I have adopted a convention for further models of planes. To the base of the upper 33.35' main element, I have added a single wire 1' long. The plane radials join at the base of this section. The feedpoint is a split feed at the junction of the in-line wires. The procedure does not end the slight movement of the electrical center of the antenna toward the radials, but it effectively limits the movement to within the 1' wire. The sum of currents on the radials never exceeds the current on the added wire.

In addition, the revised model reflects at least one of the more common construction practices on the lower HF bands. Many builders join their radials in a single "wad" that rises out of the ground to meet a slightly elevated upper main element. Whatever the practice, a table of models built along the revised pattern yields the following data.

Antenna        Radial length       Gain           Feedpoint Z
               (feet)              (dBi)          (R +/- jX ohms)
Free space     35.6                1.38           22.88 - 0.18
2 wl up                            3.88/6 deg     22.91 - 0.22

Free space     34.5                1.34           23.03 - 0.06
2 wl up                            3.85/6 deg     23.06 - 0.02

Free space     32.5                1.38           22.81 + 0.06
2 wl up                            3.88/6 deg     22.82 + 0.13

Free space     30.0                1.45           22.39 - 0.37
2 wl up                            3.94/6 deg     22.42 - 0.31

The gain of the models has largely stabilized, as has the feedpoint impedance. Radial lengths decrease as the number of radials increases. Although the models do not precisely locate the electrical centers of each antenna, they are perhaps accurate enough for us to bring the vertical antenna with a plane down to earth. Two wavelengths is a long way, and we shall want to pay attention to our landing patterns.

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