How Big? How High? What Shape?

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.

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.

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.

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.

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.