## Getting the Most Out of Antenna Patterns

### L. B. Cebik, W4RNL

Ham journals are filled these days with antenna pattern graphics, like the pair shown in Figure 1.1 The patterns are supposed to be highly informative about antenna performance. Unfortunately, to the new ham, they can be somewhat bewildering. Even the experienced ham may not be getting from them all the information that is compactly presented in the patterns. So let's start from scratch, seeing how these patterns represent antenna data that is useful to us, whether we plan to buy an antenna or build our own.

Figure 1: Free space azimuth (E-plane) and elevation (H-plane) far field patterns for the common dipole.

Although modern antenna modeling software produces data that can yield many different kinds of antenna patterns, the most common ones are called total far field patterns. They combine all calculated radiation from an antenna in every direction and produce a pattern that is related to a constant strength. In Figure 1, we can see that the pattern bulges and indents. Incidentally, the bulges are called lobes and the indentations are called nulls.

Hypothetically, if we stand on a line proportional to the pattern line distance from the center point (where the antenna is located), we shall receive a radiated signal of constant strength, no matter where on the line we stand. Likewise, if someone moves a transmitter along the line, then the antenna we are using will receive a signal of constant strength, no matter where along the line we place the transmitter. In short, antenna patterns reflect both transmission and reception characteristics of the antenna being patterned, where the lobes indicate stronger signals and the nulls indicate weaker ones.

Mastering the art of reading antenna patterns intelligently requires that we learn a number of ideas and conventions. Some relate to antenna theory itself. Some emerge from antenna modeling. Still others come from actually building and testing antennas on carefully constructed ranges. So our short story cannot end here. However, if we learn to sort out the key factors that are relevant to a particular antenna pattern we encounter, we can read them as easily as the words on this page.

### Free Space: A Starting Point for E and H Planes

Let us begin in free space. Unlike the reflective surface of the earth, free space is a region in which there is nothing but the antenna. In fact, the patterns in Figure 1 are free space patterns of a common horizontal resonant half-wavelength dipole fed at the center. Figure 2 shows a complete 3-dimensional view of the antenna pattern. The antenna is grossly exaggerated in size to clarify its position through the center of the pattern. In reality, it would be too small to be seen.

Figure 2: The common dipole (greatly exaggerated in length) with its 3-dimensional far field pattern in free space.

The first thing to notice is that the pattern is symmetrically even all around the wire when viewed from the wire end. That symmetry shows up in Figure 1B. However, the radiation is not so even when viewed as a slice through the pattern in the plane of the wire. That is the view shown in Figure 1A.

The difference between the two patterns reflects a fundamental property of antennas. They emit (and receive) radiation in two planes, conventionally called the E and H planes. The radiation in the E-plane is parallel with the wire. An antenna pattern taken parallel to the wire is also called an E-plane pattern. If we slice the 3-D pattern at any angle, but always barely include the antenna wire's total length, we shall in free space obtain the pattern of Figure 1A. Every plane will show the same indentations in field strength off the ends of the dipole wires.

There is also radiation at right angles to the wire. By convention, if we take a slice, normally through the center of the antenna element, but at right angles to the wire, we have an H-plane pattern. This is the pattern of Figure 1B.

However, the two patterns in the figure are not marked E- and H-plane. Instead, they carry a more conventional designation used these day: azimuth and elevation. We use these terms because most of our actual antennas are place above the earth, and the planet gives us a nearly flat reference plane to give meaning to the ideas of horizontal and vertical, and also to azimuth and elevation.

Figure 3: Free space E-plane and H-plane views of a 3-element Yagi.

When we have more complex antenna arrays, the E-plane and H-plane patterns become even more rigorous. See Figure 3. Here we have a 3-element Yagi. The E-plane not only parallels the length of the main element, but as well passes through the plane formed by the 3 elements. The H-plane is at right angles and is normally centered on the driven element, to which is connected the signal source. The elements of this antenna form a horizontal line across the H-plane.

E-plane and H-plane patterns for antennas are convenient is free space. In a region of space, we do not have any reflecting surfaces, so it does not matter in what orientation we place an antenna. We can always derive E-plane and H-plane patterns. The patterns are significant in just this way: when we place an antenna horizontally relative to the earth, the E-plane pattern will dominate the azimuth pattern we derive. When we place the antenna at right angles to the earth at any height, that is, when we make it vertical, the H-plane pattern will dominate the azimuth pattern we derive.

In Figure 1, I could have set up the antenna vertically instead of horizontally in the software frame of reference. Had I done that, then the same two patterns would have emerged, but in reverse order. The elevation pattern would now correspond to the E-plane and the azimuth pattern would be the H-plane. In free space, that is the only difference of note. However, once we return to earth, the difference in orientation will make a big difference in how the antennas work.

Just to make life a little more complicated, we should note in passing that in NEC, the most used antenna modeling core, the native orientation to antenna positions is not azimuth and elevation. NEC refers to ? (phi) and ? (theta) angles. Phi corresponds to azimuth, referenced to a zero point. However, theta is a "zenith" angle. That is, instead of counting in degrees up from the ground (or whatever is designated as the horizontal plane in free space), it counts down from directly overhead. If you see the "theta" notation, you can obtain the elevation angle just by subtracting the theta angle from 90 degrees.

### Variations on a Theme

Let's dwell a bit on the hypothetical Yagi in Figure 3. For the moment, we shall consider only the free space E-plane pattern, which is the azimuth pattern in most pattern-generating software. One of the key dimensions you must track is the progression of angles around the perimeter of the outer circle. To illustrate this point, consider Figure 4, Figure 5, and Figure 6. All three patterns show the same antenna model with their lengths plotted along one axis (call it the X-axis) and their distance apart plotted along a second axis (call it the Y-axis). The Z-axis would represent height, either measured from the ground or--in free space--measured above and below the plane made by the X and Y axes. We can call this last dimension the Z-axis.

Figure 4: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in AO 6.5.

Figure 5: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in EZNEC 2.

Figure 6: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC-Win Pro.

I plotted these antennas in this way to illustrate that you may see different conventions used by different software in the production of antenna patterns. The Figure 4 pattern orients zero degrees at the top of the graph, with 90 degrees to the right. In Figure 5, zero degrees is to the right, with 90 degrees at the top. Figure 6 places zero degrees at the top with 90 degrees to the left. Yet, they all present the same pattern information.

Pattern-producing software may place varying amounts of supplemental data about the antenna on the pattern graphic. Very often, the pattern-maker has options on whether to include the data in the graphic or separately. Figure 4 present basic pattern-identifying information in the corners. Figure 5 provides an optional chart of data overlaid on an unused portion of the graph. Figure 6 is bare in the presented version, but might have had other information added.

Figure 7: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC4WIN.

Figure 7 represents a pattern of the same antenna with a chart of fairly complete antenna data to the side. Notice that its data, as well as the data in the other graphics, tend to show small variations. Different modeling software--even when using the same calculation core--tends to show operationally insignificant variations in data output. Maximum gain figures that vary under 0.1 dB and front-to-back ratios that vary by under 1 dB are normally insignificant.

### Free Space and Signal Strength

Before we come down to earth, let's consider how we determine how good an antenna may be. There are very many dimensions to this question, but the relevant one here is how we measure the antenna pattern. The patterns we have looked at contain both lobes and nulls, points showing gain maxima and minima. Figure 7 provided a list of all the lobes of the 3-element Yagi, giving their angular direction. Figure 5 gave us information on the main lobe (the strongest) and the side-lobe (or secondary lobe--the second strongest). Conveniently for our exercise, this lobe was directly to the rear of the main lobe.

One of the key figures of antenna merit is gain. We measure the gain of an antenna by looking at the point in the 3-D pattern that shows the highest level of radiation field strength. We compare that with a arbitrary but standard field and register in decibels (dB) how much stronger or weaker the antenna field is.

In free space, the most common standard is the isotropic source, a hypothetical antenna point that radiates equally well in all directions. So the unit of maximum gain for our test antenna is measured in dBi, decibels stronger or weaker than an isotropic source that might be placed in the same position.

There are alternative measures you may encounter. Of these, the most prevalent is dBd, decibels gain relative to a dipole. In free space, the standard hypothetical lossless dipole of immeasurably thin wire has a gain of 2.15 dBi. Hence, the translation from dBi to dBd and back again is simple arithmetic. Consequently, in antenna modeling--from which most antenna patterns emerge--dBi has become the de facto standard.

In range testing antennas, measurement using dBd still have an important place. However, the reference is not to a hypothetical lossless thin wire dipole, but to a dipole that has real dimensions and material losses. Signals transmitted from it or received by it are carefully measured. Then test antennas are likewise measured and compared to the standard dipole. The gain of the test antenna may then be specified in dBd. However, the dipole used as the standard for the test must be completely described, since dipole characteristics can vary slightly according to the material used as well as the antenna height in terms of wavelengths or fractions of a wavelength.

The measurements just noted apply mostly to horizontal antennas. Dipoles are less universally used as standards in the testing of vertical antennas.

With the increasing use of antenna modeling software--especially NEC and MININEC--as vehicles of comparison of antenna designs, dBi is becoming the most common measure of maximum antenna gain in the most favored direction.

### Front-to-. . .: Back? Rear?

As shown in the Yagi patterns, many antennas exhibit unidirectional patterns, that is, patterns with maximum gain in only one direction. Unlike the bidirectional pattern of the common dipole in Figure 1, the Yagi beam (and many other antennas) has a much higher gain in one (forward) direction that in the other (reverse) direction. How much difference there is between the two directions is a measure of how well the antenna may suppress signals from the rear relative to signals from the forward direction.

There are several ways of measuring the difference. Perhaps the most common is the 180-degree front-to-back ratio, sometimes simply called the front-to-back ratio. To obtain this value, we simply subtract the gain to the rear from the gain forward along a straight line running from the point on the pattern of maximum gain through the pattern center where the antenna is and out the rear of the pattern. Using the data presented in Figure 5, if the forward gain is +8.11 dBi and the rear gain is -19.15 dBi, then the front-to-back ratio is 27.26 dB. (In dBd, for our free space model, the forward gain would be 5.96 dBd, while the rear gain would be -21.30 dBd, for a net front-to-back ratio of the same 27.26 dB. Note that the 0.01 difference in the numbers here and those in the figure is a function of rounding in the software; the difference is insignificant.)

However, note the rear portion of the antenna pattern. The 180-degree direction represents a special portion of the pattern where signal rejection is greatest. However, gain to the rear off to the sides of the "dimple" is higher, meaning less rejection of signals. For this reason, alternatives to the 180-degree front-to-back ratio are often used.

One system, sometimes called the averaged front-to-rear ratio, averages the gain for a rear quadrant of the antenna. This figure of merit gives an average front-to-rear ratio that many believe is a better measure of actual antenna performance in signal rejection. A further alternative is the worst-case front-to-rear ratio, which simply compares the forward gain with the highest gain found in the rear quadrants of the antenna.

When interpreting statements about antenna performance, you can examine the antenna pattern and often determine what standard of rear performance is being used, even if an author does not tell you.

### Polar Plots and Linear Graphs

The antenna patterns display so far use the most common format: the polar logarithmic plot. The antenna is at the center of the graph, and far field strengths are plotted in a circle for all relevant directions. In free space, the plots for azimuth and for elevation both encompass 360 degrees. Although the outer circle can be specified at any level, most patterns use the antenna's maximum signal in the favored direction as the graph edge. Inner circles, as shown in Figure 4 through Figure 7, represent lesser signal levels, measured in dB lower than the level of the outer ring.

However, note that the inner circles are not equally spaced, but represent a logarithmic progression. The higher the negative number toward the center, the more compressed the circles become. This most common log plot is often said to show with greatest clarity the high gain features of the pattern.

Figure 8: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a polar plot with linear divisions.

Figure 8 shows a common alternative: the polar linear plot. Here, the circles of decreasing gain are equally spaced, which tends to clarify the details of the low gain portions of the pattern. When looking at an antenna pattern, it is always necessary to note whether a log or linear plot is being used, especially when assessing matters like front-to-back ratio. The rear pattern lobes appear very different in the two figures, even though exactly the same data is being displayed by both.

Figure 9: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a linear graph.

A third way to present antenna pattern data is with a standard linear graph. Figure 9 shows the same antenna plot on a graph where the X-axis is linearly divided into 360 degrees and the Y-axis represents the antenna's gain. When made large enough, linear graphs can show very fine pattern detail. However, they are to this date fairly rare in amateur literature.

So where are we so far? Actually, we have come a fairly good distance. Although we are still in free space, we have distinguished the common antenna pattern azimuth and elevation orientations from E-plane and H-plane representations of the pattern. We have also compared the various gain measures (dBi, dBd), with dBi becoming perhaps the most used measure. We have also seen how to measure front-to-back ratio, with reference to features on the antenna pattern. Then, we looked at three ways to present antenna patterns, with the polar log plot being the most common.

Having looked at all these options, we shall standardize the rest of our work. We shall use azimuth and elevation polar plots with log scaling, and when we refer to front-to-back ratio, we shall employ the 180-degree ratio as our general standard. We select these options not because they are always the best ones, but because they are the ones you will encounter most often in amateur radio antenna literature. Now we can come back to earth.

### Down-to-Earth Reflections

An antenna over real ground changes the way in which we use antenna patterns. Let's consider the elevation pattern first. A typical horizontally oriented Yagi pattern is shown in Figure 10, the same one as used in the free-space patterns of Figures 4-7. Notice that half of the free space pattern is missing, the part that would be below ground if the earth did not reflect antenna signals.

Figure 10: Elevation pattern of a 3-element Yagi 1 wavelength over average ground.

Second, notice that the pattern is elevated. Due to signal reflections, the elevation angle of maximum radiation (also called the Take-Off angle) is not at zero degrees. Since we are dealing with far field patterns instead of ground waves, there is essentially no signal at zero degrees, and antenna modeling patterns will not show line of sight radiation in its far field patterns.

Third, notice that the forward lobe is not a line, but a lobe having a certain vertical thickness. The common way to designate this thickness is by measuring the number of degrees between points where the signal is reduced in strength by 3 dB relative to its maximum strength. This figure is called the vertical beamwidth of the antenna pattern.

For horizontally polarized antennas, such as our Yagi, the pattern of lobes, the take-off angle of the lowest (and usually strongest) lobe, and the vertical beamwidth will vary with the antenna height, as measured in fractions of a wavelength. Suppose we have 2 3-element Yagis, one for 10 meters and one for 20 meters. We place the 20 meter Yagi at a height of 70 feet and the 10 meter Yagi at a height of 35 feet. Since each antenna is at 1 wavelength height, we would expect very similar elevation patterns from them--in fact, just the pattern shown if Figure 10.

We shall take another look at polarization of the antenna in a while, since it make a considerable difference in antenna performance over real ground. But first, let's get acquainted with what happens to the azimuth pattern when we place our Yagi over real ground.

An azimuth pattern at zero degrees elevation--the horizontal plane--will show nothing. In fact, most NEC-based programs will disallow your attempt to take that pattern. Instead, we take azimuth patterns at some higher angle of interest. The question now is what is interesting.

Figure 11: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 14 degrees (elevation angle of maximum radiation).

In the absence of any other considerations, most folks who present azimuth patterns over real ground do so at the take-off angle. Figure 11 is an illustration, using our handy Yagi. The pattern shape is quite similar to the free space azimuth pattern in Figures 4-7. However, there are some important differences.

The free space azimuth pattern was a true horizontal pattern. The pattern over ground is a cone elevated from the horizontal by the specified elevation angle. Since the take-off angle of this antenna is 14 degrees, the azimuth pattern is a cone 14 degrees above the horizon. You can picture this best by drawing a line straight across the elevation pattern at point 14 degrees up from the horizontal on each side of the graph.

The pattern shows a front-to-back line. This ratio is not necessarily the maximum front-to-back ratio for the antenna (although it often is). Rather, it is the front-to-back ratio for the chosen angle (14 degrees). Maximum front-to-back ratio (or front-to-rear) may be at some other angle. To get an idea of where it may be--or whether it might be different enough to be notable--simply look at the elevation pattern in the rearward direction. Or, specify some other elevation angles for the azimuth plot.

Figure 12: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 5 degrees.

Although the take-off angle is a handy reference point in many cases, it may not be the most important one. Antenna builders may be more interested in particular paths to the stations they wish to work. If we work a lot of DX, then lower angles--perhaps in the 5 to 10 degree range--might interest us for some paths. In these cases, the antenna modeler and builder might show a lower angle for his or her chosen azimuth pattern. Figure 12 shows the azimuth pattern for our 1-wavelength high Yagi at a 5 degree elevation angle. Note the reduced gain and slight change of pattern shape. In contrast, near-vertical incidence skip is of interest to a number of amateurs, and very high angle radiation may dictate what azimuth pattern they choose. Hence, it pays always to 1. compare both elevation and azimuth patterns and 2. read any accompanying text to find out why the pattern variables were chosen.

Finally, note that the maximum gain in both our patterns over ground is considerably greater (when taken at the take-off angle) than the same antenna in free space. The signal reflected off the earth is not lost. Rather, it combines with the unreflected signal. At some elevation angles, the two are in phase and add up to a stronger signal--between 5 and 6 dB stronger. At other angles, they are out of phase and cancel, resulting in nulls rather than lobes. In general, for horizontal antennas, the number of lobes counting from the ground up to a point overhead (90 degrees up) is about 1 more than the number of wavelengths in height of the antenna. Remembering this fact will help you both to understand antenna patterns and to anticipate them as you read specifications in the text.

As a rule of thumb, the lobes and nulls above the horizon can be calculated by a simple equation:

where Ae is the angle of the lobe or null, N is the lobe or null number counting from the ground up, and h is the antenna height in wavelengths or a fraction of a wavelength. For lobes, the value of N will be an odd integer (1, 3, 5, 7, etc.), while for nulls, the value of N will be even (0, 2, 4, 6, etc.). Our Yagi at a 1 wavelength height has lobes at about 14 degrees (the main lobe) and at 49 degrees. This calculation is only a rough guide, since the exact structure of the antenna and the terrain may alter the angles by small amounts.

### Does the Good Earth Make a Difference?

Most antenna patterns derived from antenna modeling software presume a flat, uncluttered terrain for the antenna. Because we live in spaces that may be littered with building, objects, and vegetation, and also because our terrain, both near and far, may be anything from flat to mountainous, model patterns only approximate the actual antenna performance we can achieve.

In general, the ground immediately beneath and around an antenna affects antenna efficiency and the feedpoint impedance. The far field pattern is most affected by the quality of earth several wavelengths from the antenna and beyond.

The quality of the ground beneath an antenna can vary from exceptionally poor to salt-water good. Modeling software records the quality of the earth in a composite of two figures: conductivity, which is measured in Siemens per meter, and a dielectric constant, which has no unit of measure. For the most part, the larger either of these figures, the better the quality of ground. The range of possible ground conditions is very wide. Average soil has a conductivity of 0.005 S/m with a dielectric constant of 13. Salt water values are 5.0 S/m and 81. At the other end of the scale, extremely poor soil found in heavy inductrial areas may show values of 0.001 S/m and 3. Antenna handbooks usually have tables and even maps to help to determine the quality of ground in your area.

The effect of terrain upon horizontally polarized antennas, such as our model Yagi, tends to be slight. To see this point in action, look at Table 1, which lists the gain and take-off angles for our model Yagi at various heights above 3 types of ground: "Very Poor" (0.001 S/m; 5), "Average" (0.005 S/m; 13), and "Very Good" (0.0303 S/m; 20). Note that the take-off angles are very stable, while the gain figure increase only a little as the ground quality increases.

```                               Table 1
Gain and Take-Off Angle of a 3-Element Yagi Over Various Soil Conditions

Ground Type
Very Poor      Average        Very Good
(C=0.001/DC=5) (C=0.005/DC=13) (C=0.0303/DC=20)

Antenna Height    Gain (dBi)/    Gain (dBi)/    Gain (dBi)/
(Wavelengths)         TO angle       TO angle       TO angle

0.50 wl             11.7 / 24      12.3 / 25      12.8 / 26

0.75 wl             12.6 / 17      13.1 / 18      13.4 / 18

1.00 wl             13.0 / 13      13.4 / 14      13.7 / 14

1.25 wl             13.2 / 11      13.6 / 11      13.8 / 11

1.50 wl             13.4 /  9      13.7 /  9      13.9 /  9

1.75 wl             13.5 /  8      13.7 /  8      13.9 /  8

2.00 wl             13.6 /  7      13.8 /  7      14.0 /  7

Note:  The model used for these representative values is aluminum and the
check frequency is 14.175.  As always, modeling is done over flat terrain
and does not account for terrain variations.  C is conductivity as measured
in S/m; DC is a dielectric constant and has no units.  TO angle is the
elevation angle of maximum radiation and is in degrees above the horizon.

Table 1:  Representative values for gain and take-off angle of a 3-element
Yagi over various soil conditions.```

We can make the same point by noting that when the E-plane of an antenna is parallel to the earth, the effects of ground quality are relatively small. However, if the E-plane is at right angles to the earth, the situation changes considerably. Of course, this situation corresponds to having a vertical antenna.

Figure 13: Vertical dipole for 40 meters place 10' above ground at the antenna base.

Using the same three soil types, we can take a simple vertical dipole and illustrate the difference. In this case, I modeled a full-length vertical dipole with the bottom 10' off the ground, as shown in Figure 13. The resulting patterns for the three ground qualities can be combined in a single graphic of the multiple polar plots, as shown in Figure 14. Note that the best ground quality produces the lowest take-off angle and the greatest signal strength, while the worst produces a weaker field strength at a higher angle.

Figure 14: Elevation patterns for the 40-meter vertical dipole over three different soil types.

At the same time, notice the absence of strong higher angle lobes in any of the three patterns in Figure 14. You will begin to see why many operators prefer vertical antennas for DX work, especially on the lower HF bands, where getting a horizontal antenna high enough to have a low-angle lobe of maximum radiation is often not feasible.

These sample patterns should do more than acquaint you with the terminology and geometry of antenna patterns. They should be the beginning of the development of your expectations when seeing antenna plots of either horizontal or vertical antennas. Polarization: the Simple and the Complex

Most modeling programs from which antenna patterns emerge can show not only the total far field of the antenna, but as well show both the vertically polarized and horizontally polarized components of that field. Linear antennas, such as the vertical dipole or the Yagi, tend to have negligible radiation cross polarized to the general orientation of the antenna. However, Many antenna types yield both types of radiation.

Figure 15: Azimuth pattern of a half-square antenna at a 16-degree elevation angle over average soil showing the total field and its horizontally and vertically polarized components.

Figure 15 shows the azimuth pattern at 19 degrees elevation of a half square, the general outlines of which have been superimposed on the plot. Although the maximum gain of the antenna's total field is a function of the vertically polarized radiation, the width of the field is considerably enlarged by the presence of horizontally polarized radiation, which shows itself in the cloverleaf pattern.

Figure 16: Elevation patterns of a right-angle delta loop, taken broadside to the loop, for side-feed (for maximum vertically polarized radiation) and for bottom-center-feed.

At HF, polarization becomes skewed in the ionosphere, and we normally think of the total field as making up the effective far field. However, for many types of loop antennas (quads, deltas, rectangles, etc.), where we feed the antenna can make a difference in the ratio of horizontally to vertically polarized radiation, and this, in turn can have an effect on the overall total field of the antenna. Consider Figure 16, which shows elevation patterns of the same delta loop. On the right, it is fed at the center of the horizontal wire, while on the left, it is fed 1/4 wavelength down from the triangle's apex. The patterns are significantly different, to say the least.

Figure 17: Azimuth patterns for a 3-element 2-meter Yagi 30' above average soil for both horizontal and vertical orientations of the beam. The outer ring represents the same field strength in both patterns.

Even where antennas are linear, we should expect pattern differences according to whether they are set up for horizontal or vertical polarization. Consider a small Yagi for 2 meters, elevated about 30' up. Figure 17 shows the azimuth pattern at the take-off angle for the antenna when it is horizontal and when it is vertical. Vertically, it shows less gain and a much wider beam width than when horizontal. If we want to achieve a vertically polarized pattern whose shape resembles that of the horizontal Yagi, we have to turn to a different antenna design. Despite its higher gain, we cannot simple press the horizontal Yagi into service, because in line-of-sight, we shall likely lose more to cross-polarization losses than the extra gain will give us.

### Comparisons, Both Educational and Practical

Now that we know how to read antenna patterns with reasonable accuracy, let's look at some ways in which comparing antenna patterns can assist us in understanding antennas. The following examples are only starters, chosen for their variety. Getting a comprehensive look at antennas is a lifetime's vocation.

1. The Center-Fed Doublet: One of the most common antennas is still one of the most misunderstood. Because the center-fed doublet yields a dipole-like pattern at its lowest frequency of operation, many hams believe that it provides a dipole-like azimuth pattern at all its frequencies of operation. Generating some azimuth patterns can tell us very quickly whether this belief is true or false.

Figure 18: Azimuth patterns for a 135' doublet 50' above average soil when used on 80, 40, 20, and 10 meters. In each case, the doublet is oriented left-to-right in the pattern graphic.

Let's make our doublet 135' long and use it from 80 meters through 10 meters. We shall make it of #14 copper wire and place it at 50' in the air. Ignoring ground clutter and terrain variables, we would get the patterns of Figure 18 on 80, 40, 20, and 10 meters. Notice that the elevation angle of maximum radiation is different for each band. In fact, on 80 meters, because the take-off angle is so high, an arbitrary angle of 45 degrees was selected for the azimuth pattern.

The antenna is 1/2 wavelength long at 80 meters, 1 wavelength long at 40 meters, etc. For your reference file, you can count the number of lobes and relate them to the antenna length in terms of wavelengths. Also note that as the antenna becomes longer relative to the frequency of operation, the direction of the strongest lobes moves from a broadside direction toward the ends of the antenna.

Besides acquainting you with the antenna patterns on various bands, the azimuth patterns are also useful for practical antenna planning. First, decide which bands are your favorites and, as well, which directions from your station are best for making your most desired contacts. If you have a choice of directions in which to string up the doublet, you can to some measure erect the antenna for maximum signal strength on your favorite bands in your most desired directions. The azimuth patterns can be a useful planning tool.

2. Directional Beams and Elevation Patterns: In the maze of antenna materials, we often find it difficult to see how antennas are related. For example, in a number of talks I have given to beginners in ham radio, questions have arisen about how dipoles and various size Yagis may be kin to each other. The questioners are often surprised by how close the relationship is.

Figure 19: Composite elevation patterns for a dipole, a 2-element Yagi, and a 3-element Yagi, each placed 1 wavelength above average soil.

One simple demonstration I have used is to combine the elevation patterns of a dipole, a 2-element Yagi, and a 3-element Yagi, all at the same height. A representative version of this pattern combination appears in Figure 19. I have added labels to the portions of the curves that might get confusing.

From the figure, two significant features appear. First, all three antennas have the same lobes and nulls at almost identical angles. Second, the symmetry of the dipole pattern fore and aft of the vertical center line disappears steadily as the parasitical elements direct the main lobe in one direction. Hence, both kinship and differences appear at once.

Combining curves is something that an antenna modeler can do with ease. The casual reader of amateur magazines may see only individual patterns. However, by examining either the graphic or the text for further information on gain, front-to-back ratio, and other features of the antennas, one can get a pretty good view of two or more antennas in combination. In fact, one can transpose the pattern of one antenna upon the other for greater clarity. However, be sure that the transposed patterns are truly comparable before transposing them.

3. Directional Beams and Azimuth Patterns: There is a myth that pervades amateur radio: for every operating purpose whatsoever, always choose the highest gain, highest front-to-back antenna you can afford. Like all myths, this one has some truth, but not all truth.

To sort out what is true and what is false in the myth, let's combine in one graphic the azimuth patterns for a good 2-element Yagi and a good 3-element Yagi. We shall place both at 1 wavelength in height so that the elevation angles for the patterns will be the same. The result appears in Figure 20.

Figure 20: Composite azimuth patterns at 14 degrees elevation of a 2-element Yagi and a 3-element Yagi, each 1 wavelength above average soil.

Obviously, the 3-element Yagi has superior gain and front-to-back ratio. As such, it may indeed be the better antenna for serious DXing, where we wish to maximize our signal to the distant receiving station and suppress as much as possible all the potential QRM from the sides and rear of our station. However, serious DXing is not the only important type of amateur operating activity.

Many contesters and net operators do not want to suppress completely signals from the sides and rear. They wish to know that someone worth working is present, but not so loud as to interfere with the current station being worked. Hence, they tend to prefer antennas with some front-to-back ratio and some gain, but not the ultimate in each. For their type of operation, the 2-element Yagi may in fact be the preferred antenna.

In this example, I have given a choice of only two antennas. However, the basic principle can be applied to a host of antenna types. A comparison of antenna patterns, when placed against a list of operating goals and the needs one has to achieve those goals, can be a valuable tool in antenna selection.

4. Truth--Pattern Shape and Pattern Detail: The shape of an antenna pattern is not the whole story, and one can easily fall into traps of hasty interpretation. To illustrate the point, let's look at Figure 21 and fall into one kind of trap together.

Figure 21: Azimuth patterns for two 2-element Yagis (A and B) along with a composite pattern graphic of the two (C), with each antenna 1 wavelength above average soil.

Part A of the figure shows the free space azimuth pattern of a 2-element Yagi. The main lobe is, as expected, quite round with a good beam width. The rear quadrant shows a very high 180-degree front-to-back ratio. In most respect, this pattern appears to be superior to the free space pattern shown in Part B, where the 180-degree front-to-back ratio is under 20 dB.

Part C of the figure springs the trap. The patterns in parts A and B are overlaid, demonstrating the far lower gain of the initial pattern. In fact, the gain for A is only 3.8 dBi, while the gain for B is nearly 6.6 dBi. In addition, the 180-degree front-to-back ratio for B is a little under 19 dB and is the worst case of the entire rear quadrant. By contrast, the 29 dB 180-degree front-to-back ratio of A covers only a small part of the rear quadrant and drops to a worst-case value of just over 16 dB.

Without the added data, we might not have realized that the performance of the two antennas was so radically different. Even without the pattern overlay, the data for both the forward and rear quadrants of the antenna pattern make those differences clear. In fact, A is based on a model of a highly loaded and shortened 10 meter beam, while B is based on a model of a full-size 10-meter beam with phasing line connecting the two elements.

When comparing antenna patterns, be certain that you have a complete data set before you start the work of comparison. As we have seen, free space patterns are not directly comparable, even though similar, to patterns over ground. When comparing patterns taken over ground, be certain that the heights are comparable and that the ground types are similar. Wherever antennas are of different types, examine both the azimuth and elevation patterns of each.

These considerations become very important when trying to make purchase decisions among commercial beams. The manufacturers do not present their information with a common format, and therefore, comparisons are very difficult, even where patterns are offered. If a significant number of manufacturers do submit antenna models to ARRL in conjunction with its new advertising policy, then it will be much easier to comparatively examine models of competing antennas. However, even then, we shall have plenty of other evaluative work to do.

Antenna patterns do not tell anything like the whole story with antennas. We have already seen the need to place the performance figures in juxtaposition with our operating goals and needs. In addition, we shall have to factor in such considerations as cost, weight, available space, installation complexity, and maintenance, not to mention the legalities which are becoming an increasing burden to antenna installation.

### In the End, There is No End

We have barely scratched the surface of the things we can learn from antenna patterns, when we learn to read them accurately and carefully. By examining the azimuth and elevation patterns for single antennas, we can gauge their performance in terms of gain, front-to-back specifications, lobes and nulls, beam width, and polarization composition. We can also compare antennas, both within a single type and among types, analyzing high and low angle lobes, lobe direction and shape, and numerous other properties.

In the end, the information you can gain from antenna patterns will help you make intelligent decisions about the best antenna for your station location. When combined with all of the other types of information you can and should gather, the more information you draw from antenna patterns, the more satisfying your ultimate decision is likely to be.

### Notes

1. The antenna patterns used to illustrate the ideas in this article are taken from several commercial implementations of either MININEC or NEC-2, the most frequently used antenna modeling calculation cores. The most familiar implementations of these cores come from the following sources (listed in alphabetical order):

• AO (MININEC) and NEC-Wires (NEC-2): Brian Beezley, K6STI, 3532 Linda Vista, San Marcos, CA 92069; e-mail: k6sti@n2.net. (No longer sold.)
• EZNEC (NEC-2) and ELNEC (MININEC): Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007; e-mail: w7el@teleport.
• NEC-Win (NEC-2): Nittany Scientific, 1700 Airline Highway, Suite 361, Hollister, CA 95023-5621; sale@nittany-scientific.com.
• NEC4WIN95 (MININEC): Madjid Boukri, VE3GMI, Orion Microsystems, 197 Cr. Joncaire, Ile Bizard, Quebec, Canada H9C 2P7; e-mail: mboukri@cam.org.

Nothing in these notes should be interpreted either as an endorsement or as a criticism of any particular software.

In addition to the commercial implementations noted above, there are other antenna modeling software packages available, some based on the most used cores and some based on individual or proprietary cores. Also obtainable are some specialized output packages for specific graphical purposes.

Updated 7-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. An earlier version of this items appeared in CQ (Jan. and Feb, 1999).

Go to Main Index