# Horizontal Wire Loops How Big? How High? What Shape?

### L. B. Cebik, W4RNL

A number of years ago, I provided some extensive notes on horizontally oriented, horizontally polarized wire loop antennas (HOHPLs). See Horizontally Oriented, Horizontally Polarized Large Wire Loop Antennas. I have received enough e-mail as a result of those notes to convince me that perhaps there is such a things as cramming in too much information so that the result is a collection of difficulties in sorting it all out. As well, when I wrote those notes, the most common practice with horizontal loops was using a 1 wavelength circumference at the lowest operating frequency. Since then, I have changed the recommendation that I usually make, depending on the space available to the loop builder.

So let's begin again and work with a different plan. My plan of attack is based on the 3 most asked questions:

• How Big?
• How High?
• What Shape?

Since we shall defer the question of shape until last, we shall need a paradigm model with which to begin. Let's use a nearly perfectly circular loop as our starting point, as outlined in Fig. 1. The loop uses 40 wires to form the circle, so the approximation is quite good. For our first 2 questions, the feedpoint will be on the right, in the +X direction. (We shall alter that for our last question for reasons that will become apparent when we arrive at questions of shape.) Note the orientation of the X, Y, and Z axes in the outline drawing. These axes lines will be important to orienting ourselves to some of the patterns in upcoming figures.

A circular loop as a starting point has some advantages over beginning with other shapes. With both regular and irregular polygons, we tend to find performance differences depending on whether we feed the antenna at a corner or somewhere within a side. Since a circle has no sides (or infinitesimal ones, at best), we can avoid those differences until we reach our last question.

#### How Big?

The question of how big to make a horizontal loop antenna is a function of frequency, specifically, the lowest frequency of intended use. Virtually any size will work to some degree, but some sizes are better than others. Remember that here, we are speaking of relatively large loops, not mini- or micro-loops used as table-top antennas. Since I cannot know the lowest frequency of intended use, let's express dimensions as a function of a wavelength at the lowest operating frequency. Since a horizontal loop is usually used as a multi-band antenna, we shall likely feed it with parallel transmission line and an antenna tuner. Hence, ultra precision of dimension is not necessary (as it might be for an antenna that must have some particular feedpoint impedance). So if I suggest a length, such as 3 wavelengths, for a loop size, anything relatively close to that size will do fine. "Relatively close" means about +/-15% of the suggested size.

The basic dimension of loop size is normally its circumference, that is, the total length of wire making up the loop. Of course, being a loop implies that there is relative parity of cross dimensions, although distended rectangles, rhombics, etc. will work. However, we have to confine our work to what we can handle, so we shall stay with regular polygons throughout these notes.

For our work, if you wish to translate a length in wavelengths into an English measure, you may use a very simple equation: L(feet) = (984 / F(MHz)) * n, where n is the number of wavelengths specified. If you wish to go metric, then use this equation: L(meters) = (300 / F(MHz)) * n. These equations are not precise, but they are within the limits that we need to convert a horizontal loop into a length of wire.

To see how big to make our loop at the lowest operating frequency, let's put the loop into free-space and examine some 3-dimensional radiation patterns. These patterns will tell us something about why I have changed my recommended length for a horizontal loop. The following table provides the key dimensions of the loops whose patterns appear in Fig. 2. The basic loop size is the circumference, but the diameter gives you an idea of the backyard space needed to hold the loop.

```Some Possible Circular Loop Sizes
(All dimensions in Wavelengths)
Circumference     Diameter
0.5 WL            0.159 WL
1.0               0.318
1.5               0.476
2.0               0.636
3.0               0.955
4.0               1.273
```

The 3-D patterns may seem a bit confusing, but let's align ourselves with Fig. 1 and its axes lines. The X-axis and the Y-axis indicate horizontal directions relative to the orientation of the loop, presumed to be horizontal, even if we are working in free space with no real "ups" and "downs." The Z-axis is the vertical direction at right angles to the plane formed by the loop.

Since each 3-D pattern has about the same total volume, relative to the axis lines, we can see a few trends. First, the 1/2 wavelength loop forms an oval with slightly stronger radiation in the X direction than in the Z-direction. The next two loops (1.0 wavelength and 1.5 wavelength) have stronger radiation along the Z-axis than along either the X- or Y-axes. Not until we reach a circumference of 2 wavelengths does radiation strength occur predominantly in the X-Y plane. Another way of expressing this is to say that when a loop reaches a circumference of 2 wavelengths, it radiates more strongly off the loop edge than it does broadside to the loop.

This conclusion tallies well with our practice of using 1 wavelength loops in quad beams that rely on radiation broadside to the plane of the loop. If we want a 2 wavelength loop to radiate more strongly in the broadside direction, we must break the connection across from the feedpoint. However, our job is not to make a quad beam, but to see what a wire horizontal loop can do for our signals. So we may omit any consideration of broken loops.

The longer loops also show stronger radiation in the X-Y plane than in the +/-Z direction. However, their patterns are so convoluted that it is almost impossible to see exactly where the radiation is going. To get a better handhold on the radiation of all of the loop sizes, let's return almost to earth. We shall place each loop 1 wavelength above average soil. (With horizontal antennas, the actual soil quality makes little difference to the signal, so using average soil will not distort the conclusions that we reach.) Fig. 3 presents the modeled elevation and azimuth patterns for the loops sizes surveyed in Fig. 2. Each pattern indicates the strongest lobe, and the small inset of the loop shows how that lobe is oriented relative to the loop's feedpoint.

The primary feature to note is that for loops with a 1.0- or 1.5 wavelength circumference, the upper elevation lobes are stronger that the lower lobe. Given the high elevation angle (about 35 degrees) of the upper lobe, the lower lobe is obviously that one that we rely upon for most communication (NVIS excepted, of course). When we reach a circumference of about 2 wavelengths, the lower lobe begins to dominate once more. Hence, for skip communications, the smallest advisable circumference for a horizontal loop is about 2 wavelengths at the lowest operating frequency. Smaller loops will work, but at reduced signal strengths.

The second notable feature is the fact that horizontal loops above a helf wavelength over ground answer to the standard lobe development angles that apply to virtually all horizontal antennas and arrays. All of the lower lobes, regardless of loop length, have a 14-degree elevation angle. The length of a loop does not change the elevation angle.

For a given power from the transmitter, all of the loops radiate the same power over the hemisphere above ground. Hence, they differ only in the maximum gain created by the formation of lobes and nulls in the pattern (both horizontal and vertical). The following table summarizes the gain of the strongest lower lobe and gives an indication of the impedance at the feedpoint. That impedance may vary considerably with variations in the actual wire length used to make a loop.

```General Performance Values for Circular Loops
Height: 1 wavelength above Average Ground
Elevation Angle: 14 degrees
Circumference     Gain     Impedance
wavelengths       dBi      R+/-jX Ohms
0.5               7.03     >100k - j85k
1.0               6.09     125 - j110
1.5               5.56     9200 + j6500
2.0               7.23     180 - j125
3.0               8.16     215 - j130
4.0               9.26     235 - j135
```

Loops that are integral multiples of 1 wavelength tend to have lower impedances, while those in the n.5 wavelength caregory tend to have very high impedances. Although the gain value for the 1/2 wavelength loop looks quite usable--when compared to the other values--the feedpoint impedance is not especially promising. As well, a 1/2 wavelength loop becomes a 1 wavelength loop on the next band upward in frequency, and we lose a lot of gain in the lower lobe on that band.

You may relate the improving signal strength maximum values that accompany longer loops with the width of the lobes for those larger loops in Fig. 3. Hence, as we make a loop longer, the beamwidth of the individual lobes grows narrower. As we increase the number of lobes, we also increase the number of nulls, where signal strength decreases to a level that may prevent communications.

Finally, for a circular loop (but not necessarily for other shapes), the number of lobes follows a regular pattern. The number of lobes is twice the loop circumference in wavelengths. Hence, a 4 wavelength loop shows 8 distinct lobes. When we disturb the circular shape of the loop, the flat sides that we produce will alter this pattern of lobes and nulls, and we shall sample those alterations before we finish.

To obtain an estimate on how good a loop may be in our own backyard, let's pause to make a comparison. We shall place a 1/2 wavelength dipole at 1 wavelength above average ground. For that antenna, we obtain the following performance report.

```General Performance Values for 1/2-Wavelength Dipole
Height: 1 wavelength above Average Ground
Elevation Angle: 14 degrees
Dipole Length     Gain     Impedance
wavelengths       dBi      R+/-jX Ohms
0.5               7.98     72 + j2
```

Fig. 4 shows the dipole, its 3-D free-space pattern, and its elevation and azimuth patterns at the specified height. The dipole has as many lobes as a 1 wavelength circular loop, but they are stronger at the prime 14-degree elevation angle.

The loop does not catch up to the dipole until we reach a circumference of 2 wavelengths, where we also have the loop's 4 lobes.

#### How High?

Those who do not seem to have much luck with loops--even when at least 2 wavelengths long--very often have neglected the role of height in the performance of any horizontally polarized antenna. Most of these antennas are aimed at improving performance on the lower HF bands. However, the average height (from my e-mail reports) seems to be between 35' and 50' above ground. This height range covers about 0.06 to 0.11 wavelength on 160 and 0.12 to 0.18 wavelength on 80 meters (low end figures).

So far, we have looked at the circular loop when it is 1 wavelength above average ground. We do not know what the patterns might look like at other heights. Therefore, let's take a 2 wavelength circumference loop and place it at a number of different heights, from a high and improbable 2 wavelengths up to a low value of 0.15 wavelength above ground. The shape of the azimuth pattern will not change significantly from the view at 1 wavelength. However, the elevation patterns will change considerably.

For contrast, let's also look at the numbers for a dipole at the same height. As always, we shall list the maximum gain of the strongest lobe or lobes. More important than gain will be the TO angle, that is, the elevation angle of maximum radiation. The following table summarizes the loop and dipole results. Since the data should be applicable to any lowest frequency of use, the heights are functions of a wavelength.

```Comparative Performance of a Circular 2 wavelength Loop and a Dipole at Various Heights
Circular Loop                   Dipole
Height          Max. Gain     TO Angle        Max. Gain     TO Angle
wavelengths     dBi           degrees         dBi           degrees
2.0             7.36           7              8.05           7
1.0             7.27          14              7.98          14
0.75            7.75          19              7.57          19
0.5             7.43          29              7.91          28
0.25            5.94          47              6.33          60
0.15            4.76          52              6.59          90
```

Both types of antenna show the same or nearly the same TO angles down to 1/2 wavelength above ground. As well, they both show the same pattern of maximum gain levels. The slight depression of the maximum gain value that the dipole shows at a height of 0.75 wavelength appears in the loop at a height of 1 wavelength.

However, the loop shows a faster reduction in gain as it gets close to the ground, but it sustains a lower TO angle with height reductions. If you re-examine the patterns in Fig. 4, you can clearly understand why the dipole TO angle climbs rapidly as we reduce the height below 1/2 wavelength. The dipole in free space shows as much radiation vertically as it shows horizontally. Close to ground, the radiation directed upward dominates. At heights from about 0.15 to 0.25 wavelength, the dipole makes a quite good simple NVIS antenna.

In contrast, if you return to Fig. 2, you will see that the 2 wavelength circular loop has stronger radiation off its edges than it has perpendicular to the plane of the loop. As a result, the loop (at a closed circumference of 2 wavelengths) does not make a particularly good NVIS antenna. If you examine Fig. 5, you will see that the loop lacks radiation straight up. Hence, its TO angle is lower than that of the dipole when close to the ground.

The comparison between the dipole and the circular 2 wavelength loop does not mean that the loop is a stellar performer when close to the ground. For general propagation conditions, angles of 47 and 52 degrees are still to high for strong communications. However, if you look also at the half-power angles in the diagrams (the red line on either side of the main-lobe center line), you will see that the lower of these angles does tend to fall within the set of angles that provide relatively reliable communications in the lower HF region. (See a recent edition of The ARRL Antenna Book for further information on typical propagation angles on the various amateur bands.)

So the reputation of the loop for improved communications relative to a dipole at the same height has some truth to it for antenna heights below 1/2 wavelength. However, examine the gain values for these heights and then subtract another 2-3 dB for working near the half-power angles. Raising the antenna higher not only yields a higher maximum gain value, but also places the TO angle nearer to--if not within--the range of angles providing stronger communications.

For any horizontal wire antenna, there is no substitution for height. This rule of thumb applies up to at least 1.25 wavelengths above ground, if not higher. On the lowest amateur bands (160 and 80 meters), there is always room for height improvement before reaching the limits of the rule of thumb. What we lack normally are the means to support the antenna at the most desirable height.

#### What Shape?

We have so far confined our examination of loops to a circular shape--mostly to ensure that all comparative figures are fair. However, few of us have the means to set up a truly circular horizontal loop on the lowest amateur bands. In most cases, we are lucky to approximate a regular polygon. Hence, it is not possible to cover here all of the possible loop shapes that your circumstances might dictate. In fact, we shall confine ourselves to the circle, the triangle, and the square.

There are two reasons for the confinement. First, polygons with limited numbers of sides have two general feedpoint positions. One is at a corner, where the wire changes direction. The other is the midpoint of a side. Of course, we can feed a loop anywhere along a side, but, again, that would give us too many variables to cover. So we shall look at 1 circle, but 2 triangles and 2 squares.

Second, most horizontal loops are intended for multi-band use. So for each option, we need to look at several options. If a 2 wavelength loop is cut for 160 meters, then 80, 40, and 20 meters constitute a progression of frequencies (F) that include 2F, 4F, and 8F. If we cut the original antenna to be 2 wavelengths at 80 meters, then the corresponding harmonically related bands are 40, 20, and 10 meters for the same F, 2F, 4F, and 8F progression. Space does not permit us to include non-harmonically related bands in the progressions.

As we increase the operating frequency, the height of the antenna also changes when related to a wavelength. Hence, if we start 1 wavelength above ground, the upper bands will see the antenna at 2, 4, and 8 wavelengths above ground. The 14-degree TO angle at a 1-wavelenght height becomes progressively 7, 4, and 2 degrees (with the angle confined to integer values).

Under these conditions, the 2 wavelength circular loop shows the azimuth patterns in Fig. 6. I have moved the feedpoint to the "left" on the antenna so that its position corresponds to the feedpoint position of the remain shapes that we shall explore. Although the lobes increase in number as earlier noted, we might think of them as having equal strength. However, the 8F pattern makes clear the fact that the lobes have slight variations in strength despite the fact that all of the models use lossless wire. The interaction among the sections of the circle are sufficient to create the small differences. These differences will not be small with other shapes.

We might be tempted to mentally draw a line connecting the outermost tips of the lobes and think that the antenna has the resulting near circle as its pattern. However, every pair of lobes has an intervening null. The practical effect of having a large number of narrow lobes and nulls tends to be a rapid fluctuation in signal strength, especially on windy days, that can slightly alter the exact orientation of the wire antenna. At lower frequencies, where the lobes are broad, the antenna is nearly immune to this effect.

One popular arrangement for a 2 wavelength loop is a triangle, since that shape needs the fewest support posts or trees. We shall first look at a triangle fed at a corner, specifically, the left-most corner relative to the orientation of the patterns. Of course, we shall retain the 2 wavelength circumference and the 1 wavelength antenna height.

Fig. 7 shows the patterns that result for each frequency when using a corner-fed triangle. The nearly equal strength of the lobes disappears, even at the lowest frequency. The antenna has a slight beaming effect along a line that runs from the feedpoint to the middle of the side opposite the feedpoint. In all cases, the strongest radiation is in the direction of that far side of the triangle. Therefore, if you use an equilateral triangle for a loop, it pays to orient the atenna toward a primary communications target region.

If we feed a triangle in the middle of a side, as shown in Fig. 8, we obtain patterns that in general terms are not very different from the ones for a corner feedpoint. However, note that the patterns for 2F and 4F are strongest across the antenna and away from the feedpoint side, while the patterns for F and 8F are strongest to the side containing the feedpoint.

When we move to square shapes, a side-fed loop looks square, while a corner-fed square looks like a diamond in terms of the orientation to the patterns. We shall look at the side-fed square first. The patterns are in Fig. 9.

The square has a pattern at F that is very similar to the one for the circle. However, from that frequency upward, everything changes. Each pattern has fewer lobes than the corresponding pattern for a triangle. As well, the strongest lobes are not aligned with the feedpoint and the opposite side of the square. Instead, the strongest lobes occur at oblique angles to the square for 2F through 4F. Since that angle changes with the operating frequency, finding a good orientation for all intended frequencies may be difficulty.

When we feed the square at a corner, we once more align the patterns along a line from the feedpoint corner to the opposite corner of the diamond, at least through 4F. Fig. 10 provides the patterns. At 8F, the strongest lobes are at an angle to the array. The following table provides a summary of the modeled maximum gain values. However, above about 2F (a circumference of 4 wavelengths), the lobes become so narrow that a maximum gain value can be quite misleading as a guide to the general communications capabilities of each antenna.

```Maximum Gain Values for Each Antenna at Each Sampled Frequency
All loops are 2 wavelengths at F.
Frequency              F       2F       4F       8F
TO angle (degrees)     14       7        4        2
Antenna
Circle                             7.27     9.22    10.71    11.57
Triangle, corner-fed               8.34     9.95    14.38     8.41
Triangle, Side-fed                 8.34    10.45    13.24     8.94
Square, side-fed                   8.42    11.29    13.59    14.29
Square, corner-fed                 6.95    11.51    14.28    14.92
Reference Dipole/Doublet           7.99     9.66     9.64    11.16
```

The gain data is only useful in comparing the outer rings of each pattern. Note the reduction in gain for the two triangles when operated at 8 times the lowest frequency. I have included the data for a 1/2 wavelength dipole at F to allow comparisons on the various harmonics when using that antenna as a multi-band doublet. The patterns for the doublet appear in Fig. 11. Only up to 2F (or 1 wavelength) does the doublet show its strongest lobes broadside to the wire. Above that frequency, the strongest lobes depart at oblique angles that change with frequency.

These small demonstrations show that a loop's shape can make a great deal of difference to the azimuth patterns of radiation from it. I shall select no version as better than the others, since I cannot know the lay of the land for each installation. However, it does appear that operating a 2 wavelength loop much above twice the design frequency does yield narrow lobes that may or may not be useful to communications. The remaining body of radiation in the pattern is considerably weaker than the main lobes. For patterns associated with other loop shapes, see the article mentioned at the beginning of this one.

#### Conclusions

Based on what we have explored in the realm of wire horizontal loops, we can draw a few conclusions. These recommendations are based on the idea of using the loop for more than one band.

1. How Big? The loop should be at least 2 wavelengths in circumference, regardless of the final shape. For most purposes, the antenna should be considered for use over a 2:1 frequency range, even though it will load on other bands well above the design frequency. The exception to this recommendation is the case in which the antenna is for NVIS use on the lower band and for normal skip communications above that band. In that case, a 1 wavelength loop at the lower frequency will provide the best compromise.

1. How High? Because the antenna is used mostly on the lower HF bands, it is safe to suggest that the antenna should be as high as feasible. A height of 1 wavelength above ground is certainly not too high, although in most circumstances the antenna will be restricted to lower heights. The exception is the case in which the antenna serves for NVIS communications on the lower band. In that case, the 1 wavelength loop should be between 0.15 and 0.25 wavelength above ground for the strongest upward pattern. On the second harmonic, the antenna will be 2 wavelengths long and between 0.3 and 0.5 wavelength above ground for better, if not ideal, longer-range communications.

3. What Shape? Of the sampled shapes, the circular version produces the most even set of lobes on all frequencies. Hence, a polygon that approaches circularity is more likely to have fewer interactions among the sections of the antenna to produce a pattern with only a few spiky lobes. However, even a circular design will produce 4 main lobes when it is 2 wavelengths in circumference.

None of these recommendations is absolute, since the loop will work at many lengths, heights, and shapes. It is not possible to cover all eventualities in a single set of notes or even many sets of notes. Hence, the prospective loop builder should strongly consider obtaining at least a rudimentary antenna modeling softare package to test any possible design. In that way, you can predict more accuractely the performance of a loop designed to fit a given yard.

Updated 10-21-2004. © 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.