Our last episode dealt with basic and advanced monoband NVIS antennas. Although we found a number of differences among the antennas, most of them showed reasonably circular azimuth patterns as determined by the ratio of the broadside to endwise half-power beamwidth. Virtually all of the antennas achieved their maximum upward gain at heights between 0.175 wavelength and 0.2 wavelength. We also saw clearly the relationship between gain and beamwidth, especially when we compared antennas like the dipole, the inverted-V, and the 1-wavelength loop with more complex arrays based on the lazy-H configuration.

In this follow-up set of notes, we shall look at two special needs within the overall NVIS scene: a desire for directional NVIS communications and the requirement--largely a function of newer ALE potentials--for very wide-band communications. To simplify our discussions, we shall place all antennas over bare average ground (conductivity = 0.005 S/m, relative permittivity = 13).

**Directional NVIS Communications**

Curiously, a few years back, I received within a fairly short time period two notes via e-mail. One correspondent wished to know if there might be an effective NVIS antenna for his coastal location, since he wished to direct as much as possible of his signal inland. The second note, a few weeks later, asked is there might be an antenna for his coastal location that would allow NVIS communications out to sea with enough front-to-back ratio to quiet signals from land-based stations in the other direction. Not only do both inquiries have an affirmative response, they both might use the same antenna.

**Figure 1** shows two candidates composed of
AWG #12 copper wire and set at 45' about 0.175 wavelength) for 3.9-MHz
operation. The upper left sketch shows a conventional 2-element
driver-reflector Yagi. The element spacing provides a feedpoint
impedance close to 50 Ohms. As we lower the height of a directional
antenna, the main forward lobe angles ever more upward. The Yagi shown
has a TO angle of about 49°, with an elevation beamwidth that extends
to nearly overhead. The maximum gain approaches 8.2 dBi at the TO
angle, with a 7.5-dB front-to-back ratio. The radiation directly upward
from the Yagi is only down about 3.5 dB or so from the maximum gain, so
NIVS communications at the shortest ranges will be similar in strength
to using a dipole or inverted-V. However, receiving sensitivity to the
rear of the array will be well down from maximum gain. The result is
directive NVIS operation, whether out to sea or inland from the sea.

The way to improve the NVIS directional pattern is not with more antenna gain, but with less. The more compact Moxon rectangle--consisting of AWG #12 copper wire--has a lower maximum gain value: about 7.9 dBi. However, the TO angle is about 55°, with a smoother pattern curve from front-to-rear. Hence, the zenith angle falls within the elevation pattern's beamwidth. As well, the rectangle's configuration provides an additional 2-dB of front-to-back ratio, resulting in further quieting in the unwanted direction. We might obtain similar results from the Yagi by lowering its height somewhat.

Because both antennas are horizontal directional beams, even at low heights, we have a limited horizontal beamwidth. NEC-4 reports a value of 94° for the Yagi and 120° for the Moxon rectangle. These reports derive from the azimuth patterns that we took using the TO angle as the pattern elevation angle. Since both TO angles are quite high, we must use caution in accepting the reported values.

Every azimuth pattern over ground
specifies an elevation angle for the pattern. Only if the elevation
angle is 0° (illicit in NEC-2) will the pattern itself be circular.
Azimuth-equivalent patterns in free-space may use 0° elevation and also
yield a far-field tracing that is flat and circular. Every non-zero
elevation angle entry in fact produces a pattern based on a conical
surface, as suggested by the radically high elevation angle in **Figure 2**.
Let's assume that the figure has sliced the cone from tip to base and
therefore shows only the main forward lobe and not the rearward lobes.
The actual half-power beamwidth on the surface of the cone is the
angular distance between the points on the lobe that are 3 dB down from
the peak gain value.

Unfortunately, limitations of software force us
to project the pattern onto a flat circular plotting form. World maps
suffer a similar problem when we project the features of a globe onto a
flat page. The problem is distortion. With azimuth patterns, we do not
notice the problem with antennas that we use for long-distance
communication, because we normally us fairly low elevation angles.
Hence, the cone and the plotting form are very similar. However, for
NVIS operations, we are interested in high to very high angles, that
is, elevation angles from 45° to 90°. At these angles, the distortion
can be high, and it increases as we increase the elevation angle. The
right side of **Figure 2** may seem to create only mild distortion,
but the sketches show a 2:1 ratio between the angles on a flat surface
and on the conical surface at the left.

We may quickly calculate an approximate corrected horizontal beamwidth value using a simple equation:

BWa = BWr * cos(elevation angle) or BWa = BWr * sin(theta angle)

BWa is the actual horizontal beamwidth, BWr is the NEC report of the beamwidth, and the indicated angles are the elevation or theta angles at which we take the phi/azimuth pattern. The use of an elevation angle or a theta angle will depend on the operative convention of your antenna modeling software. NEC operates using theta angles counting from the zenith downward. We convert theta angles to elevation angle by subtracting from 90°. The equation is only a handy approximation because it does not account for the fact that the pattern has side-to-side curvature on the surface of the cone, but it provides results that are as close as we need for virtually all applications.

One reason that we do not question beamwidth reports for lower angle azimuth patterns relative to the values that occur in free-space patterns is that the cosine of the elevation angle is 0.9 or higher for all such angles that are 25.8° or lower. However, the cosine of the elevation angle decreases ever more rapidly toward zero as we raise the elevation angle. The Yagi reported a beamwidth of 94° at a TO angle of 49°. The cosine of 49° is 0.646 and so the adjusted beamwidth is about 62°. The Moxon reported a beamwidth of 120° at an elevation angle of 55°. The corrected value is about 69°. Although the initial reports seemed to give the Moxon a large horizontal beamwidth advantage over the Yagi, the corrected values tell us that there is not much difference. Since wire NVIS directional antennas require aiming, correcting the high-angle azimuth beamwidth reports is essential if we are to know what coverage we can expect from it. Of course, coverage does not suddenly end beyond the beamwidth limit, but it may weaken rapidly.

**Wide-Band Terminated NVIS-ALE Antennas**

Automatic Link Establishment (ALE) equipment has become almost standard in military circles. By very rapid scanning and synchronization of codes and return codes, the central station can select the most promising frequency for successful communications. Other governmental agencies have seen a potential for adapting this system to emergency communications. Since the scanning central transceiver does its work so rapidly, it does not have time for the delays associated with changing matching networks to effect a match between the equipment and the antenna. As a result, antennas that exhibit a constant impedance over a very wide frequency range have once more become very popular government acquisition items.

Unfortunately, radio amateurs have
also become enamored with these antennas. One of the most common
misconceptions associated with these antennas is that they perform in
all respects as smoothly across the frequency spectrum as the very low
SWR value suggests. In general, we can rarely obtain such smooth
performance over a 2:1 frequency range using an inverted-V
configuration. Let's perform a small experiment. We can use the 3
antennas shown in **Figure 3** as samples. Each antenna is 42.5'
high at the center and 2.5' above average ground at the ends. The
distance between the center pole and the wire end is 50'. Each leg is
therefore 64' long, for a total AWG #12 wire length of 128'. These
dimensions apply to all three variations on the inverted-V
installations. The operating range is 3.75 MHz to 7.5 MHz. Each antenna
is initially a bit shorter than ½ wavelength electrically so that we
may obtain adequate NVIS patterns throughout the passband.

The single-wire unterminated V forms a performance baseline for our comparisons. At the antenna feedpoint, we shall expect (and ignore in this context) a wide set of excursions for the resistive and reactive components. The resistance will begin quite low and reach a very high value at or near the upper frequency limit. The reactance begins as a moderate capacitive value and climbs to a very high inductive value. These progressions are normal for an antenna that begins at just under ½ wavelength and reaches about 1 wavelength at the upper frequency limit.

More significant for the present context are the data in **Figure 4**,
which graphs the maximum gain and the broadside and endwise beamwidth
values. The gain declines at the lower end of the spectrum as the
antenna reaches ½ wavelength and then becomes even shorter. Otherwise,
the gain level is relatively smooth and consistent with values that we
saw for the inverted-V in the last episode. The broadside beamwidth
shows a continuous climb with increasing frequency. In contrast, the
endwise beamwidth remains relatively constant until we near the upper
end of the passband.

The middle sketch in **Figure 3**
shows perhaps the most popular terminated wide-band antenna used by
amateurs: the terminated folded dipole. There are many versions and a
number of myths surrounding the antenna. The spacing between the AWG
#12 conductors can vary from an inch to a foot or two with no modelable
difference in the basic performance. Far more critical to any
application is the length. An ideal terminated wide-band folded dipole
antenna will be at least ½ wavelength long at the lowest operating
frequency to remain above the performance "knee." The knee represents
an electrical length below which performance falls off precipitously as
the antenna feedpoint resistance without the termination would decrease
from about 70 Ohms toward zero. The series termination would provide a
stable feedpoint impedance, but also dissipate more and more of the
energy. In the inverted-V configuration, the baseline non-terminated
impedance would be closer to 50 Ohms. Above the knee region, the
impedances undulate around the value of the terminating resistor. A
resistor in the vicinity of 800 to 900 Ohms tends to yield the
smoothest SWR curve. Of course, the antenna must include an effective
method of converting the high terminal impedance down to a conventional
coaxial-cable value.

Like the single wire unterminated inverted-V, the
terminated folded version is slightly short relative to the knee in
order to produce acceptable patterns for NVIS operation within the
3.75- to 7.5-MHz passband. Because the amount of shortening below ½
wavelength is small, we should see only the start of the gain decline
below about 4.5 MHz. The graph in Figure 5 confirms this suspicion.
Below about 4.5 MHz, the curve takes a sharper downward direction than
the corresponding gain curve for the unterminated inverted-V. Equally
significant in **Figure 5** are the beamwidth curves for broadside
and endwise directions from the wire antenna. Compare these curves to
the corresponding set in **Figure 4**. The fundamental similarity is inescapable.

An alternative method of developing a wide-band terminated antenna is to place the terminating resistors at the wire ends. These resistors require a ground-return line to provide them with a low impedance common point. The model for this basic configuration uses a wire that is 0.001 wavelength above ground so that the model will run on both NEC-2 and NEC-4.1 Commercial versions of the antenna show variations on the basic theme. Some use fans of different-length elements joined at the terminated ends. Others bring the common line back up to the feedpoint. Most of the variations tend to yield somewhat smoother SWR curves. The modeled basic version uses a 500-Ohm resistor at each end of the wire, with a 1000-Ohm reference impedance. As with the folded dipole type of terminated antenna, the system needs an effective impedance transformation device to allow a coaxial feedline. One difference between the end-terminated system and the folded-dipole type occurs with the SWR performance below the knee region. Whereas the folded version shows a smoother SWR curve, the end-terminated version tends to show a rise in SWR. Hence, the SWR provides a warning apart from gain performance to tell the user when the antenna is too short.

**Figure 6** graphs the maximum gain and the
beamwidth values for the end-terminated antenna in its simplest form.
The gain curve roughly parallels the folded-dipole curve, but with a
slightly lower knee-frequency region--closer to 4 MHz than to 4.5 MHz.
More interesting are the beamwidth curves. The broadside beamwidth is
very close to what we found for the unterminated and the folded-dipole
antenna types. However, the endwise beamwidth shows a greater variation
across the passband than we found with the other two antennas. As well,
the average endwise beamwidth is perhaps 25° greater and exceeds the
broadside beamwidth throughout the passband. One consequence of this
behavior difference is that commercial versions of the antenna tend to
favor flatter installations than the 38° slope of the wires in these
test models. The more level the wire, the lower the endwise beamwidth
of the end-terminated wire, with a resulting equalization of beamwidths
for NVIS operation.

We cannot escape an ultimate comparison of the gain curves for the 3 sample antennas. See **Figure 7**.
The gain differential between the two terminated antennas is
inconsequential compared to the deficit relative to the unterminated
wire. The gain difference runs from a minimum of 5+ dB up to over 6.5
dB across the 2:1 frequency span. Since NVIS operations often call for
working at the margins of acceptable transmitted and received signals,
a central station using a terminated antenna loses ¾ of its transmitted
power and over an S-unit of received signal strength compared to a
simple unterminated wire. While terminated antennas might be used at
field installations to simplify operation, they do not appear to offer
the amateur operator any significant benefits for a durable
installation.

The reason for limiting the 3 antennas to a 2:1
frequency span results from the fact that terminating a given length
antenna does not change the far-field pattern shape. To illustrate this
basic fact, **Figure 8** presents some samples of overlaid endwise
elevation patterns. Only the terminated folded-dipole antenna appears
as the lower-gain entry for comparison with the unterminated antenna.
Adding the end-terminated antenna would only create murky pattern
outlines for the inner or weaker patterns. The essential feature of
these patterns is the strict congruence between the stronger and the
weaker patterns across the passband. Termination affects the radiated
energy of an antenna, but not its patterns. I have included a pattern
for 10 MHz to establish the reason for limiting the antenna passband.
However smooth the SWR curve may be for a given terminated design, the
bell-shaped pattern at 10 MHz indicates an endwise beamwidth that is
usually too narrow for most NVIS operations.

**The Search for a Wide-Band Unterminated NVIS Antenna**

ALE has added a fresh incentive to find a NVIS antenna that provides full unterminated wire antenna gain but with an exceptionally wide operating bandwidth. A more ideal antenna would exhibit relatively uniform gain directly upward with equal beamwidth values, that is, with a virtually circular azimuth pattern at any elevation angle. The half-power beamwidth values should fall within a range from 70° to perhaps 110° to assure adequate energy and receiving sensitivity at about a 45°-elevation range to allow intermediate as well as short-range communications by this mode. The search for such an antenna has taken two basic directions--one relatively futile, the other more promising.

Both directions share a common feature: the use of frequency-independent design techniques. The most obvious technique is to apply LPDA design equations to a dipole array that points straight upward (or downward). In general, an LPDA design with linear elements fails to achieve the desired results due to a conflict between LPDA design criteria and the height range within which NVIS antennas perform best. For any number of elements covering any frequency range, the best height falls within the 0.125-wavelength and the 0.225-wavelength range. To obtain the best LPDA performance in terms of gain and feedpoint impedance we must increase the value of one of the calculation constants (sigma) to a value higher than we find in most horizontally oriented arrays. For the 2.5-11-MHz range (a 4.4:1 frequency span), the result would be an exceptionally tall array. As well, the gain would yield beamwidths well below the desired 70° minimum value.

If we shorten the array by reducing the value of sigma and reduce the number of elements, then LPDA performance over wide frequency range tends to collapse. Numerous anomalous frequencies will appear. At these frequencies, the pattern will show multiple lobes in unwanted directions and the main lobe will not be upward. As well, the impedance curve tends to vary widely. In general, the wider the frequency span for an LPDA, closer that the design constants of tau and sigma must come to the highest permissible values. As a result, if we try to place each element at a height that favors NVIS operation, we end up with an array that fails completely in its mission.

An alternative array that also uses
basic LPDA principles in an expanded format has become popular among
some commercial antenna makers for the corporate and government market:
the log-spiral doublet array. **Figure 9** shows the general outline for one such design. The spiral uses a factor of a^{theta}
to define the rate of radius increase with each wire segment. The
design shown uses a pair of 4-turn spirals 180° apart to end up with
the full structure.

Log-spiral antennas have their greatest use in
the UHF region where the design can attend to the element diameter (or
strip width on a substrate). A wire version in the HF range that uses a
single wire diameter will thus be less ideal and subject to numerous
finicky requirements. Most commercial designs to not use an inner
limiting radius for the spiral. As well most use a conical or modified
conical shape (with 4 or 6 sides). Some offerings use outer-end
resistive terminations, although this practice seems to defeat the
point of using such a complex structure, namely, to achieve full wire
gain over a wide frequency span. Hence, the state of the art relative
to log-spiral NVIS potentials remains uncertain. Nevertheless, **Table 1**
shows the modeled performance of the flat log-spiral design and thus
suggests what may be possible some time in the future. Note that at
only 2 frequencies does the beamwidth drop to less than 70° in one of
the sampled planes. Patterns do not go completely askew until we pass
10.5 MHz. The sample array used here requires a 50-meter diameter just
to contain the wire, with additional space needed for supports.

**Conclusion**

We began by identifying two special needs sometimes associated with NVIS operation. Obtaining a directional NVIS array proved to be the simpler project, since any number of relatively low-gain horizontal arrays might meet the operational criteria for an installation. Very-wide band NVIS operation across a large frequency spread presented the more difficult challenge. If we require relatively slow frequency changes, then we can easily press an inverted-V into service over a 2:1 frequency range for acceptable NVIS patterns. However, the higher rates of ALE frequency change require an antenna that requires no alteration of the impedance matching network in the course of operation. Some typical wide-band terminated antenna types can meet the need, with 2 restrictions. First, for many antennas that we might set up as inverted-Vs or as linear doublets, the operative frequency range for acceptable NVIS patterns remains about 2:1. Second, termination yields considerable loss of gain. Achieving a wide-band unterminated antenna design capable of covering 2.5 to 10 MHz with roughly similar gain levels and acceptable NVIS patterns without a need to switch networks remains a future goal for amateurs and an expensive project for commercial and government installations.

*This item first appeared in *QEX*,
May/Jun, 2007, pp. 50-55. Reproduced with permission. Copyright ARRL
(2007), all rights reserved. This material originally appeared in
*QEX: Forum for Communications Experimenters* (www.arrl.org/qex).*