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+  <meta name="keywords" content="Bobtail Curtain, HF Multi Band, SCV">
+  <title>The 40-Meter Bobtail Curtain as An All-Band Wire Antenna</title>
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+<body>
+  <center>
+    <h1><img src="../images/wirecad.gif" align="left" width="125" height="62" border="2" vspace="5" hspace="10"> The 40-Meter Bobtail Curtain as An All-Band Wire Antenna <img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>Sture Lof, SM5DXV, described to me an interesting adaptation of the 40-meter Bobtail Curtain to all-band use. The use was interesting enough to pass along as a possibility for those who use a wire on all bands.</p>
+  <p>Sture did not provide dimensions, so I went back to the <a href="scv0.html">SCV series</a> at this site and developed an optimized 40-meter (7.15 MHz) antenna. This frequency is at the high end of the European band, but in the middle of the U.S. Band. Actually, dimensions are not that critical, although the rough proportions will tend to provide the maximum gain on 40. As well, I selected the height for the same goal.</p>
+  <center>
+    <img src="bc40ab-1.gif" width="502" height="390" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> provides the dimensions for the antenna, along with the three feeding options for 40 meters, for bands below 40, and for bands above 40. The technique that Sture passed along was to construct the center wire from parallel transmission line. By judiciously connecting the bottom end of the center vertical line, we can achieve an all-band antenna.</p>
+  <p>The dimensions are quite reasonable and only a little longer than an 80-meter dipole. The total length is 149' (74.5' each side of the center vertical), with vertical legs that are 33.5' long. With the top wire at 44' above average ground, the vertical tips are 10.5' above ground, a safe height to prevent accidental contact with these high voltage points on the antenna. However, for convenient feeding, we bring the center wire close to the ground. Therefore, some form of "fencing" to prevent contact is a wise precaution.</p>
+  <h4>The Bobtail on 40 Meters</h4>On 40 meters, the Bobtail curtain operates in its design mode--as three 1/4 wavelength verticals spaced about 1/2 wavelength apart. Instead of using individual feedlines properly phased, we use a top wire that provides the correct phasing. Because the currents on the top horizontal wire are equal and of opposite phase at any distance from the center wire, the horizontal radiation is largely self-canceling. The result is a vertically polarized broadside pattern.
+  <center>
+    <img src="bc40ab-2.gif" width="476" height="309" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The current magnitude distribution, shown if <b>Fig. 2</b>, shows that the peak current on the verticals is at the top of the element, a desirable location for a low angle signal. As well, the maximum current on the center wire is twice the value of the maximum value on the end verticals. Of special note is the current distribution on the center wire. With the wire extended down nearly to ground level, where we locate a matching tank circuit, we need have no concern about the center wire's extra length. The current distribution shows the minimum at the same height as the tips of the end verticals.</p>
+  <p>The most common way to feed a Bobtail is still the use of a matching tank circuit that resembles the left option in <b>Fig. 1</b>. The parallel tank circuit would be similar in appearance and component values to an old fashioned plate circuit for a tube amplifier. The coaxial feedline can either tap the low end of the coil, a few turns above ground--and a good RF ground is essential--or one may use a small link coil over the low end of the tank coil. The parallel transmission line forming the center vertical is shorted and connected either to the top of the coil or to a tap near the upper end of the coil--whichever provides the best match. If the system is near resonance, then the reactance will be high. With the extended center vertical, the resistive component is likely to be much lower. Hence, initial set-up will likely involve a good bit of juggling of the two taps and the setting of the variable capacitor. But once set, the match should cover at least half of 40 meters with a 2:1 SWR on the main feeder line. Be certain to weather-proof the assembly when you finalize the settings.</p>
+  <center>
+    <img src="bc40ab-3.gif" width="400" height="225" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The Bobtail should provide about 5.1-5.2 dBi gain at an elevation angle of maximum radiation (Take-Off or TO angle) of 19 degrees. <b>Fig. 3</b> provides a view of both the elevation and the azimuth patterns of the antenna. In this azimuth pattern, and in all others to follow, the horizontal wires of the antenna stretch from left to right across the graphic. Why many operators prefer a Bobtail to a dipole with the same top height appears in <b>Fig. 4</b>.</p>
+  <center>
+    <img src="bc40ab-4.gif" width="376" height="230" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The elevation patterns are for a 40-meter dipole and the Bobtail, both with a height of 44'. This height is a bit above the average U.S. casual wire height (about 30'-35'), but the dipole pattern is still filled with very high angle radiation. Its maximum gain--6 dBi--occurs at about 44 degrees elevation. The slightly lesser gain of the Bobtail, however, occurs in just those regions favoring DX skip. In addition, the Bobtail has very little high angle sensitivity, and a large amount of QRN and other interfering signals are relatively high-angle incoming energy. For many, the Bobtail is a nearly ideal wire DX antenna, especially considering that it is cheap, low enough for easy maintenance, and durable. Although we need a good RF ground for the base of our matching tank circuit, we do not need a radial system for the antenna on 40 meters. Indeed, you can think of the end verticals as composed of two L-shaped dipoles, while the center vertical is a Tee.</p>
+  <p>If you do not quite have the 150' length needed for the idealized Bobtail, you can make it as short as about 125' by lengthening the verticals to about 38'. The best top height for the shortened Bobtail is about 50' above ground, which places the end vertical tips 12' above the soil. Once again, we can bring the center vertical all the way to the ground without disturbing the pattern. At most, this shortened (lengthwise) version loses only about 0.1 dB of gain or so.</p>
+  <p>However you build your Bobtail for 40, you will discover that setting the matching circuit benefits from a friend with a VHF/UHF transceiver and a field strength meter at least 10 wavelengths distance and broadside to the antenna. Tune for a combination of a good main feedline match and maximum signal strength. It is possible to obtain a good match with most of the energy circulating in the tank and not as much in the antenna.</p>
+  <h4>Converting the Bobtail to 80 and 160 Meters</h4>On 80 and 160 meters, we connect the feedline ends together, but set aside the matching tank circuit. We feed the combined lines against a ground radial system to form a shortened top-loaded vertical. We should use very low loss line to the ATU. It may even be possible to use an automatic ATU at the feedpoint.
+  <p>The top loading consists of a modified Tee. The horizontal wires and the end verticals form the top hat for the vertical antenna. Radiation tends to be at a fairly high angle, and so the antenna is good mostly for local or regional contacts. Because the end wires interact with the central vertical, the pattern will change as we move across 80 and 75 meters.</p>
+  <center>
+    <img src="bc40ab-5.gif" width="600" height="230" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 5</b> shows typical patterns for the ideally shaped Bobtail. As we move upward on the band, the spacing between verticals changes, and so does the overall current distribution. So the pattern can range from a figure 8, with most radiation in line with the antenna, to a clover leaf. The exact dimensions we use for the Bobtail will have a bearing on the exact patterns we achieve. Likewise, the impedance can range from 100 to 1500 Ohms resistively and -1500 to +5000 Ohms reactively. So the matching situation calls for the widest range tuner you can find or make.</p>
+  <center>
+    <img src="bc40ab-6.gif" width="376" height="196" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 6</b> shows the general circular pattern that we achieve on 160 meters, where the current on the outer verticals is low and distorts the pattern very little from normal. Of course, the antenna is short, but the Tee hat is just about long enough to bring the antenna close to resonance. Close does not mean a very low reactance, but a manageable one. However, the resistive component will be low--about 10 Ohms before we add in loss factors resulting from the ground quality and the size of our radial system. Hence, a couple of hundred Ohms of reactance yields a very high SWR to match.</p>
+  <center>
+    <img src="bc40ab-7.gif" width="476" height="306" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 7</b> shows the current distribution along the wires of our top-loaded short vertical at 1.85 MHz. At a height of less than 0.1 wavelength, the antenna cannot be expected to be a stellar performer. If you need DX performance on 160 meters, you will require a quite different design.</p>
+  <p>While certainly less than optimal for 80 and 160 meters, the adapted Bobtail still permits communications on these bands. Of course, one can build a Bobtail for 80 meters (about 296' long at 3.6 MHz) and shift these patterns downward by one band.</p>
+  <h4>The Bobtail Adapted for Use on Bands Above 40 Meters</h4>For all bands above 40 meters, the Bobtail opens up the double center vertical to use the transmission line as what it is: transmission line. so the antenna is no longer a Bobtail curtain. Instead, it becomes a center-fed doublet at 44', with drooping end sections. On some bands, the current in the vertical end sections is insignificant relative to pattern formation. On other bands, it will play a significant role.
+  <p>The following table lists the modeled results for the new doublet. The maximum gain is the gain of the strongest lobe in the pattern. All of the patterns (except 30 meters) have multiple lobes, since the doublet is 216' long from tip to tip. The Hor. Angle indicates the angle between the plane of the wire and the strongest first lobe in the horizontal plane. The TO Angle is the elevation angle of maximum radiation. The feedpoint impedance (Feed Z) shows values taken at the junction of the wire and the transmission line that formerly was our center vertical.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Performance of the Modified Bobtail on the Upper HF Bands
+
+Freq.      Max. Gain  Hor. Angle       TO Angle        Feed Z
+MHz        dBi        degrees          degrees         R +/- jX Ohms
+10.125     5.5        90               31               440 - j 1200
+14.1       7.9        57               21              1800 - j 1500
+18.118     8.2        43               17              2500 + j  200
+21.1       8.5        28               15               300 + j  310
+24.94      6.8        21               14               270 - j  125
+28.1       8.5        39               11              1000 - j  800
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Not listed in the table is 80 meters. The user can operate the antenna as a low doublet with drooping ends on 80 meters. 44' is low and yields high angle radiation, but the pattern will be an oval that is nearly circular. So it may complement the use of the antenna in the hatted-vertical mode described above.</p>
+  <p>In the chart, bands with the lower gain values tend to have the most activity by the vertical ends sections of the doublet. We can check out 30 meters as an example.</p>
+  <center>
+    <img src="bc40ab-8.gif" width="376" height="345" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows the azimuth pattern at the TO angle for 10.125 MHz. The total pattern is composed of vertically and horizontally polarized components. If you examine just the horizontal component, you will find a slightly distorted figure 8. However, the vertical end wires are active enough to produce radiation off the ends of the doublet. Hence, the total pattern is bi-directional with significant side lobes less than 10 dB below the strength of the two main lobes.</p>
+  <center>
+    <img src="bc40ab-9.gif" width="600" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 9</b> gives us just the total patterns for the remainder of the upper HF bands from 20 through 10 meters. Each pattern uses the TO angle. 20, 17, and 10 meters show the least activity in the vertical end wires. Hence, their patterns have the fewest lobes--commensurate with the length of the antenna in wavelengths--and the deepest nulls in the direction of the plane of the antenna. In all cases, the antenna runs horizontally across the pattern.</p>
+  <p>15 and 12 meters show higher levels of activity in the vertical wires. The chief indicator is the ragged pattern outline, indicating many individual lobes, some created by the length of the horizontal wire, others created by the phase relationship between the two active end vertical wires. As well, the null that we would expect off the ends of the doublet is very shallow.</p>
+  <center>
+    <img src="bc40ab-10.gif" width="376" height="345" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Let's open up the 12-meter pattern and take another look at how the lobes form. See <b>Fig. 10</b>. The vertically polarized component of the field obviously is at work in making the end null shallow. As we gradually move toward a position broadside to the wire, we can see that some lobes in the total field result from horizontal component lobes, others result from vertical component lobes, and still others are combinations of the two. The complexities of a pattern like this suggest some points to remember.</p>
+  <p>First, for wires with even modest geometric complexity, a random guess at the lobe structure based on what a linear doublet might produce is likely not to give too much guidance as to the pattern shape. If you model your antenna, be as precise as possible with every twist and turn to arrive at the most usable result.</p>
+  <p>Second, if you ask someone else about your pattern shapes, do not expect precision in the answer that you get. You will receive--in a best-case scenario--only as much precision as you put into the question.</p>
+  <p>However, once we reach the bottom line, we get the following result: if we can effect a match with the orders of impedance indicated in the chart, we have a doublet that will be as effective as most other single- wire doublets. For the ham with room for only one wire antenna, then, the Bobtail is not a bad choice.</p>
+  <p>However, let's remember that the antenna here emerged from a desire for an effective DX antenna on 40 meters. The other bands were bonuses. Indeed, if one also has a beam for upper HF DX work, then the ability to tune the Bobtail as a doublet on the upper bands gives one a good back-up antenna for when the rotator freezes or when an element breaks, or (more benignly) for a second receiver checking for openings on other bands.</p>
+  <p>One caution: only consider the bobtail curtain in any form if you have the room to keep the elements in a straight line and apart from each other as the dimensions suggest. Do not try to bend the bobtail. Even a shallow Vee shape with a 150-degree included angle (where straight is 180 degrees) will reduce gain by a full dB on the primary band. A 120-degree included angle will reduce performance to a nearly circular pattern with a gain level not much different from a single monopole.</p>
+  <p>So the all-band Bobtail is not for everyone. But it may serve well for some.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 05-27-2003, 02-04-2005. &COPY; 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.</i></p>
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+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#bobtail-curtain'>Bobtail Curtain</a>, <a href='../topics.html#hf-multi-band'>HF Multi Band</a>, <a href='../topics.html#scv'>SCV</a></p><br>
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content/scv/bct.html

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+<!DOCTYPE html>
+<html lang="en">
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+  <meta charset="UTF-8">
+  <meta name="keywords" content="Bobtail Curtain, HF Lower, SCV">
+  <title>Triangulating Bobtail Curtains</title>
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+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">Triangulating Bobtail Curtains<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>The bobtail curtain is a vertically polarized array used by many operators on the lowest amateur bands. Essentially a wire antenna, the array requires only 1/4 wavelength for the vertical portion of its elements plus safety clearance from the ground. Hence, it is shorter than most vertical antennas, but provides a very good bi-directional pattern at low elevation angles. This collection of notes has featured the bobtail curtain in several places. In the basic SCV series, see "<a href="scv5.html">Part 5: Shorties, Double-Wides, and Twins</a>." As well, see <a href="scvhv.html">"Voltage Feeding SCV Loop"</a>. You may also wish to explore <a href="bc40ab.html">"The 40-Meter Bobtail Curtain as An All-Band Wire Antenna."</a>.</p>
+  <p>Recently, Ed Boutwell, W4ZSB, tried a promising arrangement on 20 meters: a triangle of bobtails. I translated the idea to 40 meters, where bobtails are more common and explored its properties in some details. These notes provide the results of that expedition into geometry. However, to provide enough background for those notes in this location, let's begin by reviewing some basic bobtail properties.</p>
+  <p><b>The Single Bobtail Curtain</b></p>
+  <p>The bobtail curtain is actually a set of 3 1/4 wavelength vertical elements that we top-feed in phase. Although developed earlier, the bobtail is an electrical outgrowth of the smaller half-square, a set of 2 vertical 1/4 wavelength elements that we also top-feed and phase-feed. Ideally, a half-square works best when the tops of each element have the same current magnitude and phase angle. A 1/2 wavelength horizontal wire between the two verticals provides the necessary phasing while the radiation from that connecting wire largely cancels itself, leaving only a bi-directional (mostly) vertically polarized radiation pattern broadside to the plane of the wires.</p>
+  <p>The bobtail curtain extends the half-square by adding a further half wavelength horizontal wire and a third vertical 1/4 wavelength wire. However, that change produces some interesting changes in the antenna's operation. <b>Fig. 1</b> shows the outline of a bobtail curtain and indicates one of the major changes.</p>
+  <center>
+    <img src="bct-1.gif" width="600" height="250" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The total horizontal length of a bobtail is about 1 wavelength. We can call the antenna an SCV (self-contained vertical array) because its entire structure is above ground and it requires no ground-plane radial system to complete the antenna. As the diagram indicates, we feed the center vertical, and the horizontal phasing wires supply energy to the outer verticals. (The green dots in the diagram simply indicate the segmentation used for this particular model of a bobtail.) As a consequence of the feedpoint, the center vertical requires twice the current of each outer vertical. The relative current magnitude curves show the difference in current between the center and outer vertical in the binomial current distribution.</p>
+  <p>The diagram shows the feedpoint at the top of the center vertical. Actually, we may feed the element anywhere along its length. The top-most point may show an impedance that is under 50 Ohms, so we may wish to bring the feedpoint lower to match common coaxial cables. Alternatively, we may feed the vertical at its end using standard voltage-feeding techniques. We may even extend the center element to near ground level (but leave the outer verticals alone) to place the usual high-Z tank tuner more conveniently. In all cases, the current will be highest at the top of the center vertical element.</p>
+  <p>The current distribution curves also show the relative phase angle of the currents. The horizontal wires show the reversal of current phase that largely, but not completely, cancels the horizontal radiation component from the antenna. The curves on the end vs. center elements sometimes trouble viewers, who think that the elements may therefore be out of phase. However, the diagram does not show the voltage magnitude and phase along the wires. The simplest way to demonstrate that the bobtail elements are in phase with each other with respect to radiation is to compare what happens when we purposely reverse the phase of the outer verticals with respect to the center vertical.</p>
+  <center>
+    <img src="bct-2.gif" width="500" height="225" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The left side of <b>Fig. 2</b> shows a typical bobtail patterns. It is the same pattern that we get when feeding 3 1/4 wavelength verticals in phase, with the center vertical fed twice the current of each outer vertical. If we phase the outer elements 180 degrees relative to the center vertical, then we obtain the pattern on the right, and the elements become an end-fire array. This is not the pattern that we derive from the bobtail with its single feedpoint.</p>
+  <p>I noted that the bobtail curtain horizontal wires largely but incompletely cancel the horizontal radiation component from the array. An array of 3 1/4 wavelength vertical would shows almost no horizontal radiation component--just enough to indicate the effects of the radiation being composed of both direct and ground-reflected components. If the bobtail could cancel all of the horizontal radiation, it would produce a similar set of components to its total field. However, see <b>Fig. 3</b>, which shows the components of the bobtail.</p>
+  <center>
+    <img src="bct-3.gif" width="447" height="336" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The brown vertical-component lines show a beamwidth that is somewhat narrower than the total field beamwidth. The difference emerges from the remnant horizontal component, shown in blue. The peak strength of the horizontal component is about 10 dB below the maximum gain level. Because the horizontal lobes are not broadside to the plane of the wires, they do not affect the maximum signal strength--only the beamwidth. In the broadside direction relative to the wire plane, the signal is virtually only vertically polarized.</p>
+  <p>One of the reasons why low-band operators favor the bobtail is its radiation pattern. The elevation pattern is the key. Let's place a dipole at 50' above ground for 40 meters. Let's also build a bobtail with the same top height. <b>Fig. 4</b> overlays the elevation patterns of the two antennas in the specified places.</p>
+  <center>
+    <img src="bct-4.gif" width="447" height="180" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Admittedly, the dipole shows the higher maximum gain level. Indeed, a full wavelength wire (the same horizontal length as the bobtail) would show about 1.5-dB higher gain yet. However, note the elevation angle at which the dipole and its longer kin achieve maximum gain: well above 30 degrees. In contrast, the bobtail obtains maximum gain at considerable lower angles, usually below 20 degrees elevation. Since most long-distance ionospherically refracted signals are at angles below 20 degrees, the bobtail has an advantage. In addition, much (but not all) of the atmospheric noise comes from closer sources arriving at higher elevation angles. The dipole is far more sensitive to higher-angle radiation than the bobtail. As a consequence, bobtail users who have properly aimed their antennas to broadside target regions usually report better DX communications, not only with stronger signals, but as well with a better signal-to-noise ratio, especially on the lower HF bands.</p>
+  <p><b>Fig. 1</b> indicated a set of dimensions applicable to the bobtail. The dimensions include an overall horizontal (h) value, with half of h devoted to each side of the center vertical. The diagram also indicates a vertical dimension (v) for the length of the main radiators. Finally, the dimensions include a base height of the vertical bottoms above the terrain (ht). Let's see how these dimensions play out using the universal AWG #12 copper wire at the center of 40 meters (7.15 MHz).</p>
+  <p>In fact, there are two rough forms of the bobtail, one based on conventional general ideas and one based on optimizing the array for maximum gain. <b>Table 1</b> provides the dimensions and the modeled performance of the bobtails over average ground (conductivity 0.005 S/m, permittivity 13).</p>
+  <pre>
+Table 1. Bobtail array dimensions and modeled performance
+Version        h feet   v feet   ht feet   h wl     v wl     Gain dBi   TO angle    Beamwidth   Impedance
+Conventional   124.8    38.0     12.0      0.907    0.276     4.90      18 deg      54 deg      42.8 + j3.4 Ohms
+Maximum Gain   149.0    33.5     12.5      1.083    0.244     5.05      19 deg      50 deg      29.1 + j0.0 Ohms
+</pre>
+  <p>The conventional version rests on using 1 wavelength as the measure of the total length and of each side of the array (center-vertical + horizontal-wire + end-vertical). Of course, the total length of each section rests in part on bringing the verticals to resonance. Hence, the length of each section is 1.006 wavelengths. Since each design has its own optimum height above ground, the conventional design shown has a top height of 50'. Actually, the base height is not too sensitive and +/- a foot or so will not affect performance. However, the feedpoint resistance does go down as the antenna height decreases. For the top-fed version shown, the impedance is adequate for a direct connection to common coaxial cables.</p>
+  <p>The maximum-gain versions rests on the empirical work of SM4CAN, which models have confirmed. We can slightly increase the bobtail maximum gain value by extending the value of h and shortening the values of v. The total section length does not significantly increase (1.030 wavelengths). However, for maximum gain, the base height goes down slightly and the shorter vertical sections leave the array top height at 46'. Due to the slight reduction in base height, the improved gain costs us about 1 degree in the elevation angle of maximum radiation. In most circumstances, the ordinary operator might not notice either change.</p>
+  <p>The maximum-gain design imposes one noticeable penalty: a significant reduction in the feedpoint resistance when using a top-feed method. In fact, most users of the SM4CAN-type bobtail use a high-voltage feed system, with the tank circuit close to ground. Since differences of impedance become a simple process of selecting the correct tapping points on the parallel tank circuit, the actual impedance at the junction of the center vertical with the horizontal wires becomes a matter of no concern.</p>
+  <p>There are slight differences in the patterns produced by the two bobtail versions, although once more, they are not likely to be significant in normal operation. <b>Fig. 5</b> shows the differences.</p>
+  <center>
+    <img src="bct-5.gif" width="400" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The conventional design elevation pattern shows very slightly less sensitivity to very high-angle signals than does the maximum-gain version. As well, the conventional version shows a very deep null in line with the wires. In contrast, the longer maximum-gain design shows the beginnings of side lobes. These lobes are 25 dB below the level of the main lobes, and they are consistent with what happens when we set up independent in-phase-fed verticals. Perfect 1/2 wavelength spacing produces the cleanest pattern. However, we can squeeze a bit more gain from the set by widening the spacing slightly. The cost is the emergence of those same sidelobes. Eventually, as we further increase the spacing, the sidelobes grow to levels at which they steal significant energy from the main lobes, which become weaker. However, for small increases in length beyond exact 1/2 wavelength spacing, the lobes can emerge only at the expense of the beamwidth of the main lobes. Note that the beamwidth of the conventional design is almost 5 degrees wider than for the maximum-gain design.</p>
+  <p>It is now time to look at the idea of triangulating bobtail curtains. I would have had to provide most of the graphics and tabular information to use for comparison with the triangles. So the review of basic bobtail properties has seemed like a productive way to frame the data.</p>
+  <p><b>Bobtail Triangles</b></p>
+  <p>A bobtail feeds the center vertical, allowing the horizontal wire to act as a phase lines relative to the outer verticals. Suppose one wished to work in several directions and not just the pair created by a single bobtail curtain. The most compact installation might be a triangle in which the corner verticals performance multiple duties, depending on which of 3 center verticals would be active at any given moment.</p>
+  <p>In principle, by mental visualization only, the verticals at the center of the other two sides and the vertial at the far end across from the actively fed vertical would receive low current levels. As well, they are farther way from the fed vertical and at angles outside the plane formed by the basic bobtail. Would their presence be fatal to the scheme? Or would they somehow enhance the broadside patterns?</p>
+  <p>We can easily model the concept of a triangle of bobtails, using the same materials (AWG #12 copper wire) and frequency (7.15 MHz) that we used for the single bobtails. However, we have multiple possibilities that form a small matrix. In one direction, we have two slightly different bobtail designs. We should see if that difference is significant or not when we triangulate the system. In the other direction, we have two ways to handle the unused feedpoints. One way is to leave them open, and the other is to place a short across the unused feedpoint gaps. We obtain a shorted unused feedpoint in a model simply by removing the source from that wire. To create a genuine open circuit at the unused feedpoint, we need to add a very high resistance load. A resistance of 1e10 Ohms is satisfactory to achieve this goal.</p>
+  <p>Let's begin with the conventional bobtail design that uses the shorter horizontal lines and longer verticals. <b>Table 2</b> shows the data for the system with the unused feedpoints both shorted and open. Note that the table gives two gain values, one for the direction toward the triangle apex ("apex") and one toward the flat side ("side") of the triangle. The difference of these values creates a small front-to-back ratio that is also listed in the table. In addition to the two value sets, I have included the data for a single bobtail of the same design dimensions.</p>
+  <pre>
+Table 2. Bobtail triangle modeled performance: convention design
+Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
+Single              4.90 dBi    4.90 dBi    18 deg     0.0 dB              54 deg      42.8 + j3.4 Ohms
+Shorted Feedpoints  5.08        3.81        18         1.27                59          43.1 + j12.6
+Open Feedpoints     5.19        4.52        17         0.67                58          46.5 + j1.0
+</pre>
+  <p>The data show only slight variations between the properties of a single bobtail and the triangle. In both cases, the gain of the two lobes of the single bobtail falls about midway between the gain values for the triangles in each direction. The remaining differences show up better in the radiation patterns that appear in <b>Fig. 6</b>.</p>
+  <center>
+    <img src="bct-6.gif" width="650" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Both elevation patterns (representing shorted and open unused feedpoints) show a significant increase of the higher-angle sensitivity in the direction from the feedpoint to the opposite apex of the triangle. Compare these patterns to the elevation pattern in <b>Fig. 5</b>, which shows plots both bobtail designs. For the triangle, the azimuth patterns show greater balance between the two broadside lobes when the unused feedpoints are open relative to when they are closed. Regardless of how we handle the unused feedpoints, the triangular array shows increased radiation off the ends, compared to the deep side nulls of the conventional design azimuth pattern in <b>Fig. 5</b>.</p>
+  <p>Before we reach any conclusions about the performance of the bobtail in a triangle, let's perform the same set of modeling tests on the maximum-gain design. <b>Table 3</b> provides the data.</p>
+  <pre>
+Table 3. Bobtail triangle modeled performance: maximum-gain design
+Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
+Single              5.05 dBi    5.05 dBi    19 deg     0.0 dB              50 deg      29.2 + j0.0 Ohms
+Shorted Feedpoints  4.41        5.19        20         0.78                49          29.1 - j3.0
+Open Feedpoints     4.59        5.39        19         0.80                48          28.5 - j0.7
+</pre>
+  <p>As shown in the patterns in <b>Fig. 7</b>, the higher gain occurs away from the apex and toward the fed side of the triangle. Relative to the conventional design, the maximum-gain version shows less performance difference relative to the handling of the unused feedpoints. However, the azimuth patterns shows some differences that the simple numbers cannot reveal. With the feedpoints shorted, the maximum-gain design shows a much higher level of radiation in the plane of the active bobtail than with open unused feedpoints. In both cases, the small sidelobes that we saw in <b>Fig. 5</b> for this type of bobtail curtain are clearly evident and not as insigificant.</p>
+  <center>
+    <img src="bct-7.gif" width="650" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The sensitivity to higher angle radiation occurs in the direction of the triangle apex. However, since this direction in the maximum-gain design is slightly weaker, the increase is less pronounced than in the conventional design.</p>
+  <p>We may account for many of the differences in performance among the various antennas by looking at the relative current magnitude distribution for each of the triangles. <b>Fig. 8</b> provides some simple representations.</p>
+  <center>
+    <img src="bct-8.gif" width="400" height="280" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although matters of scale do not permit magnifying the current along the horizontal wires, we can see indications of it on the wires beyond the active bobtail. This current level decreases with distance from the plane of the active bobtail, but is still sufficient to produce higher-angle radiation toward the apex of all of the models.</p>
+  <p>For each design type, the two current charts clearly show the difference between shorting and opening the unused feedpoints. With open feedpoints, the side center verticals are relatively inert. Hence, with open unused feedpoints, only the apex vertical contributes to the overall pattern formation. The exact magnitude and phase angle of the current on that vertical element is enough to tilt the pattern in one or the other direction. Remember that the apex vertical is closer to the active bobtail in the conventional design than it is in the maximum gain design. When the mid-side verticals are active, that is, when we short the unused feedpoints, we obtain somewhat different results in the two designs. In the conventional design, the active mid-side verticals contribute to a wide beamwidth in the apex direction, relative to the lobe in the opposite direction. In the maximum-gain design, the active mid-side verticals increase the radiation off the ends of the active bobtail plane.</p>
+  <p><b>Conclusion</b></p>
+  <p>If we wish to operate in many directions with a bobtail curtain, setting up a triangle is one way to proceed. We save the construction of 3 verticals relative to having 3 independent bobtails. As well, the performance differences relative to independent bobtails are functionally rather small and may well be acceptable. In fact, unless we had unlimited space, it is dubious whether we could avoid interaction among the elements of independent bobtails oriented in different directions.</p>
+  <p>Perhaps the key limitation of the bobtail curtain triangle is that we cannot cover the entire horizon. The beamwidth is simply too narrow (50-55 degrees) for 3 bi-directional arrays to achieve this goal. However, we may come close enough to satisfy our needs--at least until we need only a few more countries, all of which fall in the crevices between adjacent azimuth patterns.</p>
+  <p>My own interest in the array is neither to recommend nor to discommend its use. Rather, the interesting activity for me is to have seen what happens when we triangulate bobtail curtains.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 03-24-2006. &COPY; 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.</i></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#bobtail-curtain'>Bobtail Curtain</a>, <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#scv'>SCV</a></p><br>
+</body>
+</html>

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="SCV">
+  <title>SCVs Index: A Family Album</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">SCVs Index: A Family Album<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <p>A class of antennas is noted for its ability to provide low-angle, vertically polarized radiation without need for a ground plane. These antennas, whose basic form requires 1 wavelength of wire, are both common and remarkable--a combination that instantly calls for further study. The following series of notes, based on computer modeling studies, attempts to clarify some of the basic properties, potentials, and limitations of these self-contained, vertically polarized wire antennas--or <b>SCV</b>s for short.</p>
+  <ul>
+    <li><b><a href="scv1.html">Part I: The Group Picture</a></b></li>
+    <li><b><a href="scv2.html">Part II: The Delta Branch</a></b></li>
+    <li><b><a href="scv3.html">Part III: The Rectangular Division</a></b></li>
+    <li><b><a href="scv4.html">Part IV: The Open-Ended Cousins</a></b></li>
+    <li><b><a href="scv5.html">Part V: Shorties, Double-Wides, and Twins</a></b></li>
+    <li><b><a href="scv6.html">Part VI: The Bruce Array: An Update</a></b></li>
+  </ul>
+  <p>For a VHF application, see also <a href="../vhf/hs.html"><b>The Half-Square on 2 Meters</b>: Parts 1-3</a></p>
+  <p>The series is also available as a book in PDF format with accompanying models on the <a href="../bookant.html">Books Page</a>.</p><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <p><i>Updated 05-15-1999, 01-14-2003.</i></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index Page</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#scv'>SCV</a></p><br>
+</body>
+</html>

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="SCV, Bobtail Curtain, Half Square, Quad Loop, Delta Loop, Rectangle, HF Lower, Voltage Feeding">
+  <title>SCVs Part 1: The Group Picture</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">SCVs Part 1: The Group Picture<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  In ON4UN's remarkable book on <i>Low Band DXing</i>, there are a number of scattered antenna designs worth noting.<sup>1</sup> All involve about 1 wavelength of wire, with some 2 wavelength variations on the basic antennas. They share a common feature (besides the relatively low cost of wire) for DXers and world-wide contesters using 160, 80, and 40 meters especially. When properly constructed and fed, they exhibit only low angle, mostly vertically polarized radiation. Figure 1 provides a generalized elevation pattern for a typical SCV.
+  <center>
+    <img src="scv1-1.gif" width="624" height="273" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 1. A typical SCV elevation plot. Gain will vary with the type of SCV used.
+  </center>
+  <p>Moreover, these antennas do not need ground planes.</p>
+  <h3>The Family Portrait</h3>I have elsewhere dubbed these antennas as "self-contained, vertically polarized wire antennas." For short, we can call them all SCVs. Here is a list of some of the things these antennas have in common.
+  <p>1. All use about 1 wavelength of wire (except for the doubled versions). As with all 1 wavelength antenna systems, the radiation properties can be altered by changing the feedpoint of the system. A 1 wavelength system is not an SCV unless the feedpoint is selected to maximize vertically polarized radiation.</p>
+  <p>2. SCVs are "closed" systems. A better term might be that they are "complete" systems. They do not require a ground return or ground plane to complete the antenna. Like all vertically polarized antennas near ground relative to the frequency of operation, they do depend to some extent upon the local ground quality for their radiation efficiency. However, they do not depend upon local ground quality for basic operation. Unlike the vertical monopole without its ground plane, the SCVs all model very nicely in free space.</p>
+  <p>3. SCVs come in several varieties, all of which are related. The two most recognizable shapes are the triangle and the rectangle. Triangles (or "deltas") tend to vary from equilateral to right angle. Rectangles can be anything from squares (quad loops) to long flat rectangles, sometimes dubbed "magnetic slot" antennas.<sup>2</sup> Quad loops can be either set up as squares or as diamonds.</p>
+  <center>
+    <img src="scv1-2.gif" width="602" height="449" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 2. Basic types of common 1 wavelength SCVs. For triangles and open- ended antenna types, the horizontal wire may be low or high. The most usual arrangements are shown.
+  </center>
+  <p>As shown in Figure 2, there is a kissing cousin to these closed loops called the "half square."<sup>3</sup> You can in fact trace the evolution from the closed loops to the half square in NEC models. Begin with a triangle fed for maximum vertical radiation. Open the top apex, a voltage maximum, by a very small amount (but not so close at the tips that the program interprets the wires as connected). The properties do not change. The properties evolve as the base wire is extended to a full half wavelength and the open wires are moved to a position at right angles to the base wire.</p>
+  <p>3. For vertically polarized operation, all SCVs need to be fed 1/4 wavelength from a high-voltage maximum, in other words, at a current maximum. For the deltas, this position is 1/4 wavelength from the apex. For rectangles, the proper position is mid-side. This position becomes the side peak for the diamond configuration. In free space models of all these configurations, it makes no difference whether the voltage maximum is up or down, since there is no up or down to free space except in conventionalized graphic plots. However, the apex position may make a considerable difference in performance over real ground, while at the same time creating a challenge for antenna support. The advantage of placing the feedpoint as high as possible may conflict with available physical supports for the wire.</p>
+  <p>4. The horizontal member that each of these antennas share in common functions largely (but not exclusively) as a 1/2 wavelength phasing line. The high voltage maximum in the center of this line effects a phase reversal for currents, so that they are equal in magnitude but opposite in polarity on either side of the maximum. Hence, the resultant radiation cancels to a high but incomplete degree. The feed point and another point opposite it in the structure are current maxima which are approaching 1/2 wavelength separation and which are phased for additive radiation broadside to the wire assembly. Figure 3 illustrates these features with a half square, whose properties are almost ideal.</p>
+  <center>
+    <img src="scv1-3.gif" width="638" height="391" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 3. Current magnitude and phase on a half square antenna. For each type shown in Figure 2, the 1/2 wavelength phasing line extends from the feedpoint to a similar point on the opposite side of the antenna.
+  </center>
+  <p>Nonetheless, the resultant radiation pattern is a combination of vertically and horizontally polarized radiation, as illustrated in Figure 4, a typical azimuth pattern for an SCV. This pattern illustrates the degree to which horizontally polarized radiation--either from the "phasing" line or from angled portions of the vertical wires--fails to be cancelled. Although the vertically polarized radiation provides for the antenna's maximum gain, the horizontally polarized radiation increases the beamwidth of this bi-directional array.</p>
+  <center>
+    <img src="scv1-4.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 4. Vertically polarized, horizontally polarized, and total field radiation for a half square. Patterns of the other SCVs are similar.
+  </center>
+  <p>For those who like terminological mysteries, the rectangles are symmetrical with respect to top and bottom horizontal wires. Which we should call the phase line and which we should call part of the vertical members of the array is a debate best left to medieval scholastics. In effect, both upper and lower horizontal members perform both functions.</p>
+  <p>5. All of the SCVs can be arrayed in pairs (or triplets) aligned broadside for either phased or parasitical operation. Therefore, it is possible to create beam arrays, and with some stubs and relays, make the beams switchable in direction. SCVs follow the common parasitical arrangements that require reflectors to be larger than driven elements, which are in turn larger than directors.</p>
+  <p>For additional bi-directional gain, SCVs can be placed side-by-side with a common feedpoint. The near-1/2 wavelength spacing of vertical members with the requisite phase reversals along the line(s) yields additive radiation broadside to the array. Hence, there have been open double rectangles, open double deltas, and the bobtail curtain.<sup>4</sup> Figure 5 illustrates the shapes of these antennas, along with one other: the double magnetic slot--or double side-fed rectangle. This antenna provides feedpoint impedance transformation from a normally very low value to one more favored by hams.</p>
+  <center>
+    <img src="scv1-5.gif" width="638" height="410" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 5. Several types of 2 wavelength "double" SCVs.
+  </center>
+  <h3>Brief Profiles of the Family Members</h3>To become better acquainted with the basic properties of the different versions of the SVC, let's examine some free space models of some of the family members. Table 1 provides some basic construction data on various SCVs, all cut from #12 wire for 7.15 MHz in our initial comparison. Table 1 also provides the approximate free space maximum gain broadside to the antenna. Also listed is the free-space feedpoint impedance.
+  <pre>             Basic Properties and Free-Space Performance of Common SCVs
+
+Antenna Name          Abbreviation 7.15 MHz Dimensions       Free Space      Feedpoint
+                                      (in feet)              Gain (dBi)   Impedance(Ohms)
+
+Equilateral Delta         EQD    48.8'/side, base down, apex up   2.9       120
+
+Right-Angle Delta         RAD    60.8' base, 43' sides, base down 3.3        51
+                                      apex up
+
+Double Right-Angle Delta  DBD    121.6' base, 43' sides (twice),  5.1        35 (note 1)
+                                      base down, apex up
+
+Square Quad Loop          QSQ    36.3'/side                       3.2       130
+
+Diamond Quad Loop         QDI    36.3'/side                       3.1       130
+
+Rectangle (Magnetic Slot) REC    56' horizontal, 12.8' vertical   4.4        15
+
+Double Magnetic Slot      DMS    56' horizontal, 13.0' vertical,  4.7        80 (note 1)
+                                      3' separation
+
+Open Double Magnetic Slot ODS    110.8' horizontal, 11.1' vertical; 5.7    30 (note 1, 2)
+                                    fed on end wire (center-wire
+                                    feed possible)
+
+Half Square               HS     62.4' horizontal, 39' vertical    4.6       65
+
+Bobtail Curtain           BC     125' horizontal, 38' vertical;    6.3     40 (note 1, 3)
+                                    fed on center wire
+
+Note 1:  A 2 wavelength system; unmarked antennas are 1 wavelength arrays.
+
+Note 2:  Impedance value for end-wire feed.  Antenna impedance with center-wire feed
+is about 9 Ohms.
+
+Note 3:  For center-wire feed of the bobtail, impedance is about 40 Ohms at the
+junction with the horizontal wire, about 55 Ohms at 60% up the vertical, and
+about 70 Ohms at the middle of the vertical.
+
+Table 1.  Basic properties and free-space performance of common SCVs.</pre>
+  <p>It is clear that the deltas and the squares are very comparable performers, although the right-angle delta (RAD) carries a feedpoint impedance compatible with coaxial cable feedlines. Interestingly, we find also that the rectangle (REC) provides superior gain to the square (QSQ) or diamond (QDI), despite its flattened appearance. However, remember that the sides of the rectangle, where the high current maxima lie, are more nearly 1/2 wavelength apart, providing for better radiation addition. The feedpoint impedance of the single rectangle is, unfortunately, lower than most hams wish to handle. Of the 1 wavelength SCVs, the half square (HS) is the best performer with respect to gain, since its vertical members are a full half wavelength apart, and the feedpoint impedance is coax- compatible.</p>
+  <p>Within Table 1, I have added 2 wavelength wire arrays, namely, the double right-angle delta (DBD), the double magnetic slot (DMS), the open double slot (ODS), and the bobtail curtain (BC). Unlike the side-by-side 2 wavelength models, the DMS winds the loops in parallel, with a mobius crossing at the end away from the feedpoint. Not only does the wire doubling in the double magnetic slot increase the feedpoint impedance, but as well, it adds something to the gain. The spacing between the wires is not critical; the model uses a 3' spacing. The open double slot adds more gain with a moderately usable feedpoint impedance (but only if fed on an end wire, since the impedance of the antenna is about 9 Ohms if fed on the center wire).</p>
+  <p>The final gain winner in the group is the bobtail curtain (BC). Fed about midway up the center vertical toward the horizontal wire, the impedance is about 70 Ohms, while at the junction with the horizontal wire, the impedance is closer to 40 Ohms. With patience, a builder can find an exact 50-ohm point between the two. Of course, the free ends of the half- square and the bobtail curtain lend themselves to voltage feed via a simple tapped high-Q parallel tuned circuit, as shown in Figure 6.</p>
+  <center>
+    <img src="scv1-6.gif" width="379" height="319" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 6. Typical network for matching low-impedance transmission lines to high impedance feed points on an open-ended SCV (half square or bobtail curtain).
+  </center>
+  <h3>With Feet on the Ground</h3>Although Table 1 suggests the relative differences in performance among the types of SCVs, it does not tell the entire story. To get some sense of real-world performance from these antennas, I set up a little exercise. Since the number of different installations is nearly endless, I established some rules for a hypothetical ham installation. In general, I set 50' as the maximum height of installation for a 40-meter SCV, with a desired minimum height of 20' up. However, this set of restrictions would have eliminated most of the antennas. So for the half square and bobtail. I lowered minimum height to 10' for the free ends. I followed general conventions of placing the horizontal wires of the triangles in the lower position, while the half square and bobtail horizontal wires were high.
+  <pre>                Performance of Common 7.15 MHz SCVs Over Average Ground
+
+Antenna    Height Range  Gain in dBi  Front-to-Side  Take-Off Angle  Feedpoint Impedance
+            (in feet)                  Ratio (dB)      (degrees)          (Ohms)
+
+EQD        20 - 62.3      1.5           - 3             18           135 (Note 2)
+
+RAD        19.6 - 50      1.9           - 5             20            60
+
+DBD        19.6 - 50      3.7           -12             20            40
+
+QSQ        20 - 56.3      1.6           - 4             18           145
+
+QDI        20 - 71.4      1.5           - 4             16           135 (Note 2)
+
+REC        37.2 - 50      3.0           -12             17            15
+
+DMS        37.0 - 50      3.3           -12             17            80
+
+ODS        38.9 - 50      4.5           -25             16            30
+
+HS         11.0 - 50      3.4           -15             18            65
+
+BC         12.0 - 50      5.0           -28             18            40 (junction-fed)
+                                                                 56 (60% up center wire)
+                                                                    70 (mid-center wire)
+
+Note 1:  All antenna #12 copper wire over average earth (conductivity
+ = 0.005 S/m; dielectric constant = 13).
+
+Note 2:  This antenna is not physically apt under the terms of the exercise.
+
+
+Table 2.  Performance of common 7.15 MHz SCVs over average ground.</pre>
+  <p>Table 2 sets out the results in terms of gain, front-to-side ratio, take-off angle, and feedpoint impedance. Technically, the diamond and square quads must be eliminated for violating the upper height limit, along with the equilateral delta. Their numbers are included for reference. The deltas can be operated with their horizontal wires high, for some improvement in performance. Operating the half-square and the bobtail with their horizontal wires low is possible, but at the cost of performance.</p>
+  <p>The table also provides front-to-side gain ratio numbers that give an indication of the degree of bi-directionalness of the arrays. The higher gain arrays have higher front-to-side ratios and "peanut" patterns, while the lower gain models tend to have more oval patterns.</p>
+  <p>In the immediate family of 1 wavelength SCVs, the rectangle and the half square provide the greatest gain. However, the single rectangle has a very low feedpoint impedance, and the double magnetic slot is recommended in its place. The open double slot almost matches the bobtail, and its smaller vertical-plane footprint allows greater height and a lower take-off angle.</p>
+  <p>However, none of the SCVs permit unlimited heights without losing much if not all of the low angle radiation advantage. As you elevate any of the SCVs, a second lobe appears at a high angle. Eventually, at a height specific to each antenna type, the higher angle secondary lobe becomes the primary lobe.</p>
+  <center>
+    <img src="scv1-7.gif" width="637" height="271" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 7. Elevation patterns for a right-angle delta antenna at three different heights.
+  </center>
+  <p>Figure 7 shows the elevation patterns for a 40-meter right angle delta at three heights: with the base at 20, 40, and 60 feet up. Figure 8 shows the same set of elevation patterns for a half square where the lowest heights of the free ends are 11, 31, and 51 feet. The lobe development is virtually indistinguishable between these two antennas (or between any other two of the SCVs).</p>
+  <center>
+    <img src="scv1-8.gif" width="637" height="268" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 8. Elevation patterns for a half square antenna at three different heights.
+  </center>
+  <p>The entire purpose in using an SCV is to accept the lower gain of the SCV in exchange for the ability of the antenna's vertically polarized pattern to attenuate signals from high elevation angles. The high angle radiation is generally thought to contain most of the non-DX QRM and also the land-mass QRN that makes hearing low-band DX so difficult. The SCVs form a natural filter. Since modern receivers have gain to spare on the low bands, relative to the basic noise level, the lower gain of the SCV is no disadvantage for reception. The low angle of radiation can also be effective when transmitting.</p>
+  <center>
+    <img src="scv1-9.gif" width="640" height="282" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 9. Elevation patterns for a dipole and a half square antenna, both with maximum heights of 50 feet.
+  </center>
+  <p>However, if we elevate an SCV too high, it loses its filtering ability without gaining anything significant in low angle radiation. In fact, for raw gain, a simple dipole at the hypothetical exercise height of 50' would do about. Compare the dipole and half square elevation patterns in Figure 9. Note that the half square very low angle radiation exceeds that of the dipole at the same elevation angles, despite the fact that the dipole has an overall gain advantage. One might almost suggest separate antennas for transmitting (the dipole) and receiving (the SCV)--or at least an A-B switch.</p>
+  <h3>What's Left to Tell?</h3>This family portrait has aimed to set up the SCV family tree. However, it leaves many questions unanswered. Here are a few of them.
+  <p>1. Although we might simply presume that we can scale the 40-meter results to the other low bands, do the antennas actually perform the same way for each band?</p>
+  <p>2. The rectangle is a crushed square, and the right angle delta is a crushed equilateral triangle. What are the limits of crushing these geometric shapes before performance deteriorates.?</p>
+  <p>3. All of the models in this preliminary family reunion have been over uniform average ground (conductivity = 0.005 S/m; dielectric constant = 13). How do the antennas perform over different types of both local and distant ground for each of the three lowest bands?</p>
+  <p>4. Will any of the changes of soil and shape make any difference in the elevation patterns shapes as they change with antenna height?</p>
+  <p>We shall look at these questions in future episodes. Since I cannot possibly build and test each type of antenna over all the various soils and in all the various shapes possible, we shall do our exploration by modeling in NEC-4, which is reliable for this class of antennas.<sup>5</sup> However, we must note at the outset that antenna modeling provides suggestive results relative to the real world. Because modeling programs presume level ground, they cannot provide detailed information about these antennas on the many sorts of terrain where hams live and use them.</p>
+  <p>At the same time, our project is just the sort of thing at which antenna modeling excels: the accumulation of systematic data over a wide range of questions. Antenna building must be very selective due to the cost and effort involved and because of the great care that must be used to obtain repeatable and accurate results. For its results to be definitive, the range test must go beyond the anecdotal: all variables must be accounted for in detail to ensure that the results can be formulated as generalizations applicable to other situations that are relevantly similar.</p>
+  <p>One advantage of modeling in the present case is that each antenna and installation situation can be directly compared with the others, since most of the intervening variables present in real world antennas are equalized in the model set-up. Hence, modeling is a wholly appropriate vehicle for comparing relevantly similar types of antennas--namely, the SCV family.</p>
+  <p>However, the final choice for an antenna at any site is a mixture of performance potential and physical possibility. If you have only one high support point, then a delta may be necessary, since two-point support antennas are automatically ruled out. If available supports are wide- spread but not exceptionally high, then the rectangles and open-ended arrays jump to the forefront.</p>
+  <p>Nonetheless, even if your choice is forced by features of the antenna site, learning more about SCVs in general cannot be a bad thing. You never know when someone may ask you a question.</p>
+  <h3>Notes</h3>1 John Devoldere, ON4UN, <i>Antennas and Techniques for Low-Band DXing</i>, 2nd Ed. (Newington: ARRL, 1994). See especially Chapter 10, "Large Loop Antennas," for information on rectangular and triangular loops. However, half squares and bobtail curtains are relegated to Chapter 12, "Other Arrays."
+  <p>2 For the "magnetic slot" and "double magnetic slot," see Russell E. Prack, K5RP, "Magnetic Radiators--Low Profile Paired Verticals for HF," <i>The ARRL Antenna Compendium</i>, Vol. 2 (Newington: ARRL, 1989), pp. 39-41.</p>
+  <p>3 The half square antenna actually appeared after its larger sibling, the bobtail curtain. See Ben Vester, K3BC, "The Half Square Antenna," <i>QST</i> (March, 1974), 11-14. Additional notice appeared in <i>Radio Communications</i> for January, 1977 (p. 36). See also Robert Schiers, N0AN, "The Half-Square Antenna," <i>Ham Radio</i> (December, 1981), 48-50. All three of these early sources show the antenna as voltage-fed from one of the free ends.</p>
+  <p>4 For the bobtail curtain, see Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," <i>CQ</i> (March, 1948), 21-23 and 92-95. See also Smith follow-up articles, "The Bobtail Curtain and Inverted Ground Plane," Parts 1 and 2 in <i>Ham Radio</i> (February, 1983), 82-86, and (March, 1983), 28-30. For the open double magnetic slot, see Lew Gordon, K4VX, "The Double Magnetic Slot Antenna for 80 Meters," <i>The ARRL Antenna Compendium</i>, Vol. 4 (Newington: ARRL, 1995), pp. 18-21.</p>
+  <p>5 NEC-4 is a proprietary code of the Lawrence Livermore National Laboratory, University of California, from whom a user-license must be obtained. Commercial implementations include the following:</p>
+  <p>a. EZNEC Pro: Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007; e- mail: [email protected].</p>
+  <p>b. GNEC: Nittany Scientific, 1733 West 12600 South, Suite 420, Riverton, UT 84065; [email protected].</p>
+  <p>Because the horizontal baseline of many of these antennas is lower than 0.2 wavelengths, MININEC models of them are less likely to be reliable than NEC-2 or NEC-4 models.</p>
+  <p>Also see the <a href="../model/nec.html">Antenna Modeling Programs</a> page.</p>
+  <br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 4-29-98. &COPY; L. B. Cebik, W4RNL. A print version of this note appears in</i> The National Contest Journal <i>September 1998. 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.</i><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="scv2.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40">Go to Part 2</a>
+  <p><a href="scv0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to SCV Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#bobtail-curtain'>Bobtail Curtain</a>, <a href='../topics.html#delta-loop'>Delta Loop</a>, <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#half-square'>Half Square</a>, <a href='../topics.html#quad-loop'>Quad Loop</a>, <a href='../topics.html#rectangle'>Rectangle</a>, <a href='../topics.html#scv'>SCV</a>, <a href='../topics.html#voltage-feeding'>Voltage Feeding</a></p><br>
+</body>
+</html>

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+  <meta charset="UTF-8">
+  <meta name="keywords" content="SCV, Delta Loop, HF Lower">
+  <title>SCVs Part 2: The Delta Branch</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">SCVs Part 2: The Delta Branch<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  In casting about for a reasonable way to organize the material in this series of self-contained vertically polarized wire antennas (SCVs), it finally struck me that the antenna types themselves formed the core of family divisions. Although there are fascinating parallels among the 3 main family branches: the deltas, the rectangles, and the open-ended types, practical considerations often dictate which type of antenna one will install. Deltas go where there is only a single support up high. Rectangles take the least space, considering both height and length, and therefore might be favored most on 160 meters. Half-squares are the tallest and widest and thus favor 40 meters.
+  <p>So I decided to treat each branch of the family separately and simply call attention to similarities to their cousins where apt. Today, the deltas get their due. We shall restrict our attention to apex-up configurations, since that is the most common form. Raising the baseline to the top, with the apex down, increases gain a bit over ground. However, with the requirement for a span up high, other members of the SCV family may be better candidates.</p>
+  <p>As a reminder from the first episode, the chief purpose in using an SCV is to acquire a low angle of maximum radiation with little or no response to high-angle radiation from which emerges most of the QRM and QRN that otherwise covers up weak DX signals. Most SCV antennas have significantly less maximum gain than a dipole, but they outdo the dipole at low radiation angles unless the dipole is at least 1/2 wavelength high. For any given path angle, the required height for the dipole to equal the SCV varies with the inherent gain of the SCV in question. Deltas encompass the lower gain members of the SCV family.<sup>1</sup></p>
+  <center>
+    <img src="scv2-1.gif" width="419" height="491" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 1. The two common forms of the delta: the equilateral and the right-angle.
+  </center>
+  <p>Deltas have two common forms, as sketched in Figure 1: the equilateral and the right-angle versions. It was long ago discovered that the right angle delta has slightly more gain than the equilateral delta (3.3 dBi vs. 2.9 dBi in free space on 40 meters). Moreover, when each is fed 1/4 wavelength down from the apex, the equilateral delta has a feedpoint impedance close to 115 Ohms, while the right-angle delta impedance is close to 50 Ohms, for a direct coax feed system. Note that the equilateral delta requires a feedpoint about 25% up one of the legs to place it 1/4 wavelength down from the apex. For the same 1/4 wavelength spacing from the apex, the right-angle delta feedpoint is about 12% up one of the legs.</p>
+  <p>However, it is not clear that the right-angle delta is the ultimate in gain for the apex-up triangular system. As one drops the height of the triangle and spreads the baseline to compensate in order to maintain resonance, the gain of the triangle increases from the equilateral mode to the right-angle mode. In fact, free space models suggest that a good bit more shortening and spreading is possible before one passes the point of maximum free space gain (which holds up in practice over ground). Figure 2 shows the progression. At a certain dimension, the increase in gain created by bringing the feedpoint and the point opposite to it on the other sloping side closer to 1/2 wavelength apart begins to be off set by reduced vertically polarized radiation do to the radically increasing slope of the upper wires.</p>
+  <center>
+    <img src="scv2-2.gif" width="631" height="330" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 2. The progression in shape of the delta toward maximum gain and beyond.
+  </center>
+  <p>Interestingly, the ratio of baseline length to height from the baseline to the apex for maximum gain is frequency dependent. If we let R be the ratio of baseline length to height and F be the frequency in MHz, then</p>
+  <center>
+    <img src="scv2e1.gif" width="192" height="60" border="2" vspace="5" hspace="9">
+  </center>
+  <p>This near-equation was derived using #12 AWG copper wire antennas and holds good throughout the HF range. It shows some significant drift as one approaches 2 meters, where the #12 wire diameter becomes a more significant portion of a wavelength.</p>
+  <p>For 40 meters the correct ratio of length to height is about 2.9:1, while at 80 meters the ratio is about 2.6:1. (The right-angle delta, of course, has a ratio of 2:1, while the equilateral triangle has a ratio of about 1.15:1. The loss relative to maximum gain is only a few tenths of a dB.) As the length-height ratio increases, the feedpoint impedance decreases. On 80, resonance yields a resistance of 27 Ohms, while the more radically sloped maximum gain delta for 40 has a feedpoint impedance of about 22 Ohms. In exchange for that decrease in feedpoint impedance, the maximum possible gain for the delta increases, about 3.26 dBi for 80 and 3.43 dBi for 40.</p>
+  <p>The actual shapes of the deltas we build are largely a function of space available. High towers or trees and narrow yards tend to get equilateral (or nearly so) triangles, while lower supports and bigger yards get right-angle (or nearly so) models. But all of these antennas work over ground of varying quality. Because there are some interesting behavioral differences, let's look separately at the two most common types of deltas.</p>
+  <h3>The Equilateral Delta</h3>Because equilateral deltas for 80 and for 40 (the bands for which they are most commonly apt) are different percentages off from maximum gain configuration, we should not expect them to behave in an exactly scaled manner. The feedpoint impedances for the two bands are almost identical when scaled for both antenna size and height above ground. However, in some instances, the gain and elevation angle of maximum radiation will shows significant differences.
+  <p>I modeled in NEC-4 a series of 80-meter (3.6 MHz) equilateral deltas with the baseline elevated in 10-foot increments from 10 feet through 70 feet.<sup>2</sup> Since the model was 96' wide and 83' high, as shown in Figure 3, the maximum height of 153' seemed a reasonable limit for the exercise. Over most soils types, that is already too high for maximum SCV performance.</p>
+  <center>
+    <img src="scv2-3.gif" width="495" height="477" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 3. Dimensions of the modeled equilateral deltas for 80 and 40 meters.
+  </center>
+  <p>Table 1 summarizes the results of the exercise for very poor, poor, average, and very good soil as commonly defined in terms of conductivity and dielectric constant:</p>
+  <pre>Soil Type             Conductivity (S/m)             Dielectric Constant
+Very poor soil           0.001                             5
+Poor soil                0.002                            13
+Average soil             0.005                            13
+Very good soil           0.0303                           20</pre>
+  <p>These initial tests presumed a common soil type for many wavelengths in every direction from the antenna, and as always in modeling, level, uncluttered ground.</p>
+  <pre>  3.6 MHz Equilateral Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor        10             -0.66             25                   186 + j21
+(C=0.001,        20             -0.25             23                   156 - j 7
+  DC=5)          30              0.05             22                   137 - j15
+                 40              0.29             20                   125 - j15
+                 50              0.50             19                   117 - j13
+                 60              0.69             19                   113 - j 9
+                 70              0.86             18                   111 - j 5
+
+Poor             10              0.78             23                   190 + j36
+(C=0.002,        20              1.08             21                   162 - j 0
+  DC=13)         30              1.27             20                   143 - j12
+                 40              1.40             19                   130 - j16
+                 50              1.48             17                   121 - j15
+                 60              1.51*            16                   114 - j11
+                 70              1.49             15                   111 - j 7
+
+Average          10              1.28             22                   196 + j41
+(C=0.005,        20              1.48             20                   167 + j 1
+  DC=13)         30              1.58             18                   147 - j13
+                 40              1.62*            17                   132 - j18
+                 50              1.59             16                   122 - j17
+                 60              1.50             15                   114 - j13
+                 70              1.34             14                   110 - j 8
+
+Very Good        10              3.61             16                   196 + j54
+(C=0.0303,       20              3.85             14                   172 + j 8
+  DC=20)         30              4.04             14                   153 - j10
+                 40              4.20             13                   137 - j17
+                 50              4.29             12                   125 - j18
+                 60              4.32*            12                   116 - j15
+                 70              4.24             11                   111 - j11
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of equilateral delta = 96' baseline length, 83' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 1.  3.6 MHz equilateral delta:  properties over various soils at various heights.</pre>
+  <p>For each type of soil, the antenna height that yields maximum gain is flagged--and that height differs for each type of soil. Over very poor soil, maximum gain is not achieved within the table limits, while for poor soil, the maximum gain baseline height is 60 feet. For good soil, that height drops to 40 feet, while over very good soil it increases once more to 60 feet. Hence, if your soil differs from average, then generalizations based on average soil can be misleading.</p>
+  <p>The elevation angle of maximum radiation (or take-off angle) behaves more as one might expect. For any given antenna base height, the take-off angle decrease directly with the improving quality of soil. In contrast, the feedpoint impedances for the antenna show only a trace of change with changes in soil type. Even at the lowest heights, where ground effects are the largest, the spectrum of soil types yields only a 10-Ohm change (about 5%) in the resistive component of the feedpoint impedance.</p>
+  <p>The 40-meter equilateral delta was 48.5' wide by 42' high, as shown in Figure 3. I ran it at 5-foot intervals from a baseline of 5' up to a baseline of 50' at a frequency of 7.15 MHz. Table 2 shows the results. (If you wish to compare the two tables, double the height of the 40-meter entry to find the roughly corresponding 80-meter entry.) Once more, over very poor soil, a maximum gain height is not achieved. However, the maximum gain height is 35-40' for poor soil, 25-30' for average soil, and 25' for very good soil. This continuous downward trend is distinguished from the odder trend in the 80-meter antenna.</p>
+  <pre>   7.15 MHz Equilateral Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor         5             -0.08             26                   177 + j26
+(C=0.001,        10              0.41             24                   151 + j 1
+  DC=5)          15              0.78             23                   135 - j 7
+                 20              1.09             21                   125 - j 7
+                 25              1.36             20                   118 - j 5
+                 30              1.60             20                   114 - j 2
+                 35              1.80             19                   112 + j 1
+                 40              1.97             18                   112 + j 4
+                 45              2.12             18                   112 + j 7
+                 50              2.26             17                   114 + j 8
+
+Poor              5              1.06             24                   186 + j40
+(C=0.002,        10              1.41             22                   160 + j 6
+  DC=13)         15              1.66             21                   142 - j 6
+                 20              1.85             19                   130 - j 9
+                 25              1.99             18                   121 - j 8
+                 30              2.08             17                   115 - j 5
+                 35              2.13*            16                   112 - j 1
+                 40              2.13*            15                   111 + j 2
+                 45              2.11             15                   111 + j 6
+                 50              2.07             14                   112 + j 8
+
+Average           5              0.96             23                   192 + j42
+(C=0.005,        10              1.24             21                   164 + j 5
+  DC=13)         15              1.41             20                   144 - j 8
+                 20              1.52             18                   131 - j11
+                 25              1.58*            17                   121 - j10
+                 30              1.58*            16                   115 - j 6
+                 35              1.53             15                   111 - j 2
+                 40              1.44             14                   110 + j 2
+                 45              1.33             14                   110 + j 6
+                 50              1.21             14                   112 + j 9
+
+Very Good         5              2.84             18                   198 + j55
+(C=0.0303,       10              3.06             17                   171 + j11
+  DC=20)         15              3.21             16                   152 - j 6
+                 20              3.31             15                   136 - j12
+                 25              3.35*            14                   124 - j12
+                 30              3.31             13                   116 - j 9
+                 35              3.17             12                   111 - j 5
+                 40              2.94             11                   109 + j 0
+                 45              2.63             11                   108 + j15
+                 50              2.27             10                   101 + j 8
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of equilateral delta = 48.5' baseline length, 42' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 2.  7.15 MHz equilateral delta:  properties over various soils at various heights.</pre>
+  <p>At most baseline heights, the 40-meter equilateral delta gain over average soil does not come up to its gain over poor soil. However, the TO angles for each soil level show the normal progression lower as the soil quality improves for any given height of the baseline. Moreover, the feedpoint impedances also show their normal progression for any given height from one soil type to the next better. In short, using average soil as a sample of the 40-meter equilateral delta modeled performance sells the antenna somewhat short.</p>
+  <center>
+    <img src="scv2-4.gif" width="638" height="280" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 4. Typical elevation patterns for the equilateral delta below, at, and above the baseline height for maximum gain.
+  </center>
+  <p>Although it is not possible to create a single generalization governing elevation pattern shape for every soil type, some general expectations are possible. As illustrated in Figure 4, elevation patterns at baseline heights well below the height of maximum gain tend to be bulbous, with a higher angle of maximum radiation. Elevation patterns at the height of maximum gain tend to show the first signs of a secondary high angle lobe. At heights where the gain declines significantly from its maximum value, the secondary lobe is considerable. At such heights, the advantage of the antenna is lost: rejection of high-angle QRM and QRN diminishes to make the antenna's low gain a distinct disadvantage. In general, for each soil type or its closest approximation, it may be best to hold the baseline height of the antenna at or slightly below the level for maximum gain.</p>
+  <h3>The Right-Angle Delta</h3>Because right-angle deltas are closer in shape to the ratio of length to height necessary for maximum gain from the shape, they display higher gain at any given baseline height than the corresponding equilateral delta. The dimensions for the 80-meter right-angle delta are shown in Figure 5. The baseline is 120' long, with a 60' height.
+  <center>
+    <img src="scv2-5.gif" width="550" height="435" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 5. Dimensions of the modeled right-angle deltas for 80 and 40 meters.
+  </center>
+  <p>Because the right-angle delta is shorter than the equilateral delta, the 80-meter antenna was modeled at baseline heights of 10 through 90 feet without exceeding the maximum apex height of roughly 150 feet. Table 3 shows the results for our four defined soil types. Immediately apparent is the higher gain at lower heights and the higher maximum gain obtainable at each height.</p>
+  <pre>   3.6 MHz Right-Angle Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor        10             -0.45             28                    94 + j28
+(C=0.001,        20              0.07             26                    76 + j 6
+  DC=5)          30              0.38             24                    66 - j 2
+                 40              0.61             22                    59 - j 4
+                 50              0.81             21                    54 - j 3
+                 60              0.99             20                    51 - j 2
+                 70              1.15             19                    49 - j 0
+                 80              1.29             18                    49 + j 1
+                 90              1.42             18                    49 + j 3
+
+Poor             10              1.05             25                    95 + j38
+(C=0.002,        20              1.46             23                    79 + j10
+  DC=13)         30              1.68             21                    68 + j 1
+                 40              1.83             20                    61 - j 3
+                 50              1.92             19                    56 - j 4
+                 60              1.95             17                    42 - j 3
+                 70              1.97*            16                    50 - j 1
+                 80              1.92             15                    49 + j 0
+                 90              1.85             15                    48 + j 2
+
+Average          10              1.63             24                    97 + j42
+(C=0.005,        20              1.94             22                    81 + j12
+  DC=13)         30              2.08             20                    71 + j 1
+                 40              2.14             18                    63 - j 4
+                 50              2.15*            17                    57 - j 5
+                 60              2.09             16                    53 - j 4
+                 70              1.96             15                    50 - j 2
+                 80              1.77             14                    48 - j 0
+                 90              1.53             13                    47 + j 1
+
+Very Good        10              3.92             18                    94 + j48
+(C=0.0303,       20              4.21             17                    82 + j17
+  DC=20)         30              4.41             15                    73 + j 3
+                 40              4.58             14                    65 - j 3
+                 50              4.72             13                    59 - j 5
+                 60              4.80*            13                    54 - j 5
+                 70              4.80*            12                    50 - j 3
+                 80              4.69             11                    48 - j 1
+                 90              4.48             10                    47 + j 1
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of right-angle delta = 120' baseline length, 60' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 3.  3.6 MHz right-angle delta:  properties over various soils at various heights.</pre>
+  <p>Also apparent is the fact that the height of maximum gain parallels roughly the pattern shown for the 80-meter equilateral delta. The height of maximum gain over average soil is less than that for either poor or for very good soil. Nonetheless, the progressions of feedpoint impedances and take-off angles are normal.</p>
+  <p>One of the chief selling points for the right-angle delta is that the feedpoint impedance is generally compatible with coaxial cable feed systems. Because the models used are based on a free space model, the model is not a good approximation of coaxial cable under a baseline height of about 40 feet.</p>
+  <p>The 40-meter right-angle delta charts are based on a free space resonant model with a 60.8' baseline and a 30.4' height. The model was run at 5-foot intervals up to a baseline height of 50 feet, which is well beyond the point at which high angle lobes begin to dominate the elevation pattern. Once more, as shown in Table 4, the gain over average soil is anomalously low relative to the gain over poor and over very good soil. However, take-off angles and impedance progressions are regular as the soil type improves. In addition, elevation patterns follow the same general order as for the equilateral delta. The recommended height to maximize available gain but avoid significant high angle lobes is at or just below the height of maximum gain for the relevant soil type.</p>
+  <pre>    7.15 MHz Right-Angle Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor         5             -0.11             28                    88 + j30
+(C=0.001,        10              0.46             26                    73 + j 9
+  DC=5)          15              0.86             24                    63 + j 2
+                 20              1.19             23                    57 + j 0
+                 25              1.47             22                    53 + j 0
+                 30              1.72             20                    51 + j 2
+                 35              1.94             19                    49 + j 3
+                 40              2.14             19                    48 + j 5
+                 45              2.30             18                    48 + j 6
+                 50              2.45             17                    49 + j 7
+
+Poor              5              1.18             26                    92 + j40
+(C=0.002,        10              1.64             24                    77 + j13
+  DC=13)         15              1.92             22                    67 + j 4
+                 20              2.14             21                    60 + j 0
+                 25              2.29             19                    55 - j 0
+                 30              2.41             18                    52 + j 0
+                 35              2.48             17                    50 + j 2
+                 40              2.51*            16                    48 + j 3
+                 45              2.50             15                    48 + j 5
+                 50              2.46             15                    48 + j 4
+
+Average           5              1.17             25                    95 + j42
+(C=0.005,        10              1.57             23                    79 + j13
+  DC=13)         15              1.77             21                    68 + j 3
+                 20              1.90             20                    61 - j 1
+                 25              1.97             18                    56 - j 1
+                 30              2.00*            17                    52 - j 0
+                 35              1.97             16                    49 + j 1
+                 40              1.90             15                    48 + j 3
+                 45              1.79             14                    47 + j 5
+                 50              1.66             14                    48 + j 7
+
+Very Good         5              3.19             20                    96 + j49
+(C=0.0303,       10              3.49             19                    82 + j17
+  DC=20)         15              3.66             17                    72 + j 5
+                 20              3.79             16                    64 - j 0
+                 25              3.87             15                    58 - j 2
+                 30              3.88*            14                    53 - j 2
+                 35              3.81             13                    50 - j 0
+                 40              3.65             12                    48 + j 2
+                 45              3.39             11                    47 + j 4
+                 50              3.06             11                    47 + j 6
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of right-angle delta = 60.8' baseline length, 30.4' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 4.  7.15 MHz right-angle delta:  properties over various soils at various heights.</pre>
+  <p>Like the 80-meter right angle delta, the 40-meter right-angle delta approaches coaxial cable compatibility fairly rapidly as the baseline height increases. In fact, a height of about 15' is all that is needed for a direct coax feed system, although a balun choke is likely wise, given the placement of the feedpoint for maximum vertically polarized radiation.</p>
+  <center>
+    <img src="scv2-6.gif" width="639" height="512" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 6. Feedpoint resistance and reactance of the modeled 80-meter right-angle delta across the band.
+  </center>
+  <p>Figure 6 shows the free space impedance sweep of the 80-meter right angle delta across the band. Figure 7 shows the equivalent sweep for 40 meters. In both cases, read the value of resistive component from the left Y-axis and the value of the reactance from the right Y-axis.</p>
+  <center>
+    <img src="scv2-7.gif" width="630" height="514" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 7. Feedpoint resistance and reactance of the modeled 40-meter right-angle delta across the band.
+  </center>
+  <p>On 80 meters, the resistive component varies a total of about 26 Ohms, well within the range of coax matching. On the narrower 40-meter band, the change is only about 5.6 Ohms. The right-angle delta is indeed a stable antenna relative to its feedpoint resistance.</p>
+  <p>On both bands, the reactance varies much more widely across the band: 126 Ohms on 40 meters and over 475 Ohms on 80 meters. However, in both cases, the reactance changes linearly with frequency. By making the antenna inductively reactive at the lowest frequency of operation, it may be feasible to insert a remotely operated variable capacitor to compensate for the inductive reactance, leaving a net feedpoint impedance that is both resistive and within the range of direct coaxial cable feed.</p>
+  <p>On 80 meters, even a very good capacitor may only permit operation across most, but not all of the band. On 40 meters, most of the band may be covered within a 2:1 SWR limit without any matching components at all. In some cases, built-in antenna tuning units within some transceivers may suffice for any compensation needed, since coax line losses are quite small on the lower bands. However, for equipment sensitive to even fairly low SWR levels, such as numerous linear amplifiers, an external matching system is advisable.</p>
+  <h3>Improving the Local Soil</h3>
+  <p>A question bound to arise in the minds of some builders whose soil is poor or worse is whether performance improvements can be had by improving soil conditions in the local area of the antenna.<sup>3</sup> The answer lies in how much soil the antenna builder controls and how high the antenna is.</p>
+  <p>Soil improvement can consist of a radial system, but it should not be confused with a tuned radial system as might be needed with a monopole connected to it. Soil improvement might also be accomplished by a wire grid or other less exact mesh of wires designed to improve soil quality over a region within which the antenna is generally centered.</p>
+  <p>To see what modeling might suggest about the matter, I took equilateral and right-angle deltas for 80 meters and placed them over very poor soil. Then, I created a radial zone of very good soil centered beneath the antenna. For the first step I used a zone 0.25 wavelength in radius and hence extending just beyond the antenna limits. The second step was a zone with a radius of 0.5 wavelength, followed by succeeding 0.5 wavelength increases in the radius until no further improvement was recorded. Test models were placed with their baselines at 20, 40, and 60 feet.</p>
+  <p>The results of the investigation appear in Table 5 for the equilateral delta and in Table 6 for the right-angle delta. Several interesting features emerge from a comparison of the two tables. First, a short zone of improvement can actually reduce antenna performance from its desired gain vs. take-off angle goals. The effect occurs over a larger improvement zone as the antenna height increases.</p>
+  <pre>         3.6 MHz Equilateral Delta:  Soil Improvement Performance Changes
+
+In the sample tables below, the antenna is presumed to be over very poor soil (C=0.001;
+DC=5) for an indefinite distance in every direction.  Soil improvement in the
+immediate vicinity of the antenna is achieved at the designated radius to the
+level of very good soil (C=0.0303; DC=20).
+
+Very Good Soil               Gain in dBi             Take-Off Angle
+Radius in feet                                        in degrees
+
+Baseline = 20'
+  0                                -0.25                23
+ 68 (.25 wl)                       -0.06                31
+136 (.50 wl)                        2.32                25
+272 (1.0 wl)                        3.68                19
+408 (1.5 wl)                        3.85*               16
+544 (2.0 wl)                        3.85                16
+680 (2.5 wl)                        3.85                16
+
+Baseline = 40'
+  0                                 0.29                20
+ 68 (.25 wl)                       -0.10                21
+136 (.50 wl)                        0.96                27
+272 (1.0 wl)                        3.31                20
+408 (1.5 wl)                        4.09                16
+544 (2.0 wl)                        4.20*               13
+680 (2.5 wl)                        4.20                13
+
+Baseline = 60'
+  0                                 0.69                19
+ 68 (.25 wl)                        0.55                19
+136 (.50 wl)                        0.55                19
+272 (1.0 wl)                        2.16                20
+408 (1.5 wl)                        3.57                16
+544 (2.0 wl)                        4.14                14
+680 (2.5 wl)                        4.32*               12
+
+Note 1.  *=maximum gain at the baseline height equal that of the antenna over
+continuous very good soil.
+
+
+Table 5.  3.6 MHz equilateral delta:  soil improvement performance changes.
+
+            3.6 MHz Right-Angle Delta:  Soil Improvement Performance Changes
+
+In the sample tables below, the antenna is presumed to be over very poor soil
+(C=0.001; DC=5) for an indefinite distance in every direction.  Soil
+improvement in the immediate vicinity of the antenna is achieved at the
+designated radius to the level of very good soil (C=0.0303; DC=20).
+
+Very Good Soil                   Gain in dBi       Take-Off Angle
+Radius in feet                                      in degrees
+
+Baseline = 20'
+  0                                 0.07                26
+ 68 (.25 wl)                        1.11                38
+136 (.50 wl)                        3.53                25
+272 (1.0 wl)                        4.21*               17
+408 (1.5 wl)                        4.21                17
+544 (2.0 wl)                        4.21                17
+680 (2.5 wl)                        4.21                17
+
+Baseline = 40'
+  0                                 0.61                22
+ 68 (.25 wl)                        0.15                22
+136 (.50 wl)                        2.29                28
+272 (1.0 wl)                        4.30                19
+408 (1.5 wl)                        4.58*               14
+544 (2.0 wl)                        4.58                14
+680 (2.5 wl)                        4.58                14
+
+Baseline = 60'
+  0                                 0.99                20
+ 68 (.25 wl)                        0.74                20
+136 (.50 wl)                        0.74                20
+272 (1.0 wl)                        3.52                20
+408 (1.5 wl)                        4.58                16
+544 (2.0 wl)                        4.80*               13
+680 (2.5 wl)                        4.80                13
+
+Note 1.  *=maximum gain at the baseline height equal that of the antenna
+over continuous very good soil.
+
+
+Table 6.  3.6 MHz right-angle delta:  soil improvement performance changes.</pre>
+  <p>Second, the range required for the achievement of maximum gain (equivalent to that of a continuous zone of very good soil) is shorter for the right-angle delta than for the equilateral delta. Since only 0.5 wavelength intervals were checked, the table does not give the precise point where maximum gain over very good soil was attained. However, the half wavelength difference appears consistently at all three antenna baseline heights. At least in part, the differential occurs because of the height of the high current feedpoint of the antennas. The right-angle delta feedpoint is about 7' or so above the baseline, while the equilateral delta feedpoint is about 20' above the antenna baseline. These differences are consistent with the differentials with height changes in the size of the soil improvement zone to achieve maximum gain.</p>
+  <center>
+    <img src="scv2-8.gif" width="639" height="282" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 8. Elevation patterns of identical equilateral delta over a. continuous very good soil and b. an improved very good soil area with very poor soil beyond.
+  </center>
+  <p>Third, the maximum achievable gain is that which occurs if the soil were very good continuously from the antenna to the far end of the Fresnel zone. However, this does not mean a full equivalency of performance. Figure 8 shows elevation patterns for two deltas of identical design at identical heights above ground. One is modeled over continuous very good soil, while the other is modeled over an improved (very good) soil zone to 2.5 wavelengths, with very poor soil beyond. Although the upper portion of the two patterns is identical, the area below the angle of maximum radiation is deficient for the soil improvement case. The missing radiation is unfortunately the lowest angle radiation so desired by most SCV users.</p>
+  <center>
+    <img src="scv2-9.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 9. Typical equilateral and right-angle delta azimuth patterns at the elevation angle of maximum radiation.
+  </center>
+  <p>The SCV Azimuth pattern, as we noted last time, is a broad oval, as representatively shown in Figure 9. The right-angle delta, besides showing a marginal gain benefit, also shows a slight increase over the equilateral model in side rejection. However, both patterns should be interpreted as broad ovals with side performance down only 4 to 5 dB below the main lobes. Beyond the SCV Deltas</p>
+  <p>The are many variations of the delta which we shall not cover. Most variations alter the feedpoint, using either the lower corner or the center of the baseline. These designs gradually lose the dominance of vertically polarized radiation as the feedpoint moves away from 1/4 wavelength down from the apex of the triangle. The resultant total pattern increases in gain, but as well in higher angle radiation. However, the delta in these configurations tends to perform better as an all-band antenna fed by parallel transmission line to an antenna tuner. In addition, the antenna is somewhat simplified mechanically.</p>
+  <p>Since our concern is with SVCs, we shall bypass these variations and turn next time to another family member rightfully called an SCV.</p>
+  <h3>Notes</h3>1 These notes should be read as only a slight addition to the excellent material in John Devoldere, ON4UN, <i>Antennas and Techniques for Low-Band DXing</i>, 2nd Ed. (Newington: ARRL, 1994), especially Chapter 10, "Large Loop Antennas," pp. 10-5 to 10-10. Everyone interested in contesting or DXing on 160-40 meters should have a copy of this remarkable book on the shelf.
+  <p>2 All modeling in this particular exercise was done in EZNEC Pro, NEC-4 version, available from W7EL. The ground system used throughout is the Sommerfeld-Norton.</p>
+  <p>3 See also <i>Low-Band DXing</i>, pp. 9-8 to 9-9 and 9-30 to 9-31. Unlike Devoldere, I prefer to call the phenomenon at hand "soil improvement" rather than establishing a radial system. It is not at all clear that lacing the underground area beneath a delta or other SCV with copper wire achieves something close to perfect ground. Hence, I have used more conservative soil improvement figures associated with very good ground (C=0.0303; DC=20).<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <p><i>Updated 5-19-98. &COPY; L. B. Cebik, W4RNL. A print version of this note appears in</i> The National Contest Journal<i>. 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.</i><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="scv3.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40">Go to Part 3</a>
+  <p><a href="scv0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to SCV Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#delta-loop'>Delta Loop</a>, <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#scv'>SCV</a></p><br>
+</body>
+</html>

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+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="SCV, Quad Loop, Rectangle, HF Lower">
+  <title>SCVs Part 3: The Rectangular Division</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">SCVs Part 3: The Rectangular Division<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  So far, we have looked at the delta loop SCVs. To review, the SCV antennas are the class of self-contained, vertically polarized, 1 wavelength wire antennas and include deltas, quad loops, and open-ended arrays such as the half-square and bobtail curtain. Basic designs require about 1 wavelength of wire, but doubled versions also work very well. These antennas only become SCVs when their feedpoints are located so as to maximize vertically polarized radiation and minimize horizontally polarized radiation. Under those conditions, they have less raw gain than when fed for horizontally polarized radiation, but they exhibit very low angle bi-directional patterns broadside to the array with very little response to high-angle radiation. Hence, they are favored by many DXers who will trade gain for a better signal-to-noise ratio for distant signals. Moreover, they require no ground plane.
+  <p>For 160 meters, where everything is big, the SCV with the smallest vertical and horizontal dimensions is the side-fed rectangle. Squares are much taller with less gain, while half squares are also taller with only a small margin of extra gain over the rectangle. Deltas are also taller, and longer corner-to-corner than the rectangle. Hence, for most installations requiring an SCV, the rectangle should be the antenna of choice.</p>
+  <center>
+    <img src="scv3-1.gif" width="494" height="440" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 1. The basis of the rectangular SCV in the quad square loop.
+  </center>
+  <p>The side-fed rectangle was popularized in recent times by K5RP, who called it a magnetic slot in his Antenna Compendium, Vol. 2 article.<sup>1</sup> One may get a grip on the side-fed rectangle more easily by deriving it from the side-fed square (or quad) loop. See Figure 1. When used for horizontally polarized radiation, the bottom fed loop has been long known to lower its feedpoint impedance and increase its gain if elongated vertically. K6STI reported some time back in QST on using the loop in this configuration to achieve a 50-Ohm impedance.<sup>2</sup> Also, this configuration is the basis for the Hentenna, an elongated loop with good gain and an impedance matching system.</p>
+  <p>In free space, there is no up or down. Therefore, laying the square loop on its "side" gives us the same antenna with the field at 90 degrees to the bottom-fed version. Likewise, tilting the elongated loop over on its side produces the magnetic slot or single rectangle. When placed over the earth rather than in free space, the antenna produces mostly vertically polarized radiation. Like its brother, the square loop, it needs no ground plane.</p>
+  <p>Maximum free space gain from the rectangle occurs when the long unfed sides are about 3 times longer than the short fed side and the loop is brought to resonance. This shows clearly in Figure 2, which tracks free space models (using #12 copper wire). This 3:1 figure is normally not very critical, as the gradual slope of the curve demonstrates. The resonant feedpoint resistance for the 206' long by 68' high version is just above 30 ohms, which is a bit low until we introduce proximity to the earth into the picture.</p>
+  <center>
+    <img src="scv3-2.gif" width="635" height="516" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 2. Shape vs. gain in the 160-meter rectangular loop.
+  </center>
+  <p>In fact, the ratio of long side to fed-side of the rectangle for maximum free space gain is frequency dependent. Based on free space models of rectangles resonated at frequencies from 1.8 to 146 MHz, the ratio (R) of the long side to the short side for maximum gain (where F is the frequency in MHz) is as follows:</p>
+  <center>
+    <img src="scv3e1.gif" width="210" height="51" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Like the counterpart relationship between the baseline length and the height of deltas, this approximation holds fairly well into the 2-meter region, at which the #12 wire basis for the models becomes an appreciable part of a wavelength.<sup>3</sup> However, the curve approaching maximum gain is shallow, and little is lost from being slightly off the ideal mark.</p>
+  <p>Although the ratio of long-to-short side increases for maximum gain in an elongated loop with increases in frequency, the feedpoint impedance follows normal rules: the more extreme the elongation, the lower the feedpoint impedance at resonance for the resulting loop. At 2 meters, where the ratio approaches 6:1, the feedpoint impedance is in the vicinity of 7 Ohms.</p>
+  <h3>The Single Rectangle</h3>
+  <center>
+    <img src="scv3-3.gif" width="476" height="450" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 3. Dimensions of the rectangular loops used in this study.
+  </center>
+  <p>Figure 3 sets the dimensions used in this study for the single rectangle. (We shall look at the K5RP double rectangle a bit farther on.) I shall leave it to builder ingenuity as to how one might hang up this antenna. But before we string a long length of wire, we should ask how high to string it.</p>
+  <center>
+    <img src="scv3-4.gif" width="636" height="520" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 4. Gain and take-off angle for rectangles at various heights.
+  </center>
+  <p>Figure 4 provides modeling data on the single rectangle for bottom wire heights ranging from 20' to 140' up. The antenna top wire will be 68' higher. The left axis records gain over average soil for the various heights. Note that as the bottom wire reaches the 90-100' mark, the gain levels off and then decreases with further increases in antenna height. The second curve referenced to the right axis records the continuous decrease in the elevation angle of maximum radiation, which runs from 23 degrees for the lowest height surveyed to 14 degrees for the highest.</p>
+  <center>
+    <img src="scv3-5.gif" width="639" height="284" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 5. Three elevation patterns of the rectangle at various heights.
+  </center>
+  <p>On the very dubious assumption that we have some choice in how high to place the rectangle, we can also use elevation patterns of the antenna as a guide. Figure 5 provides three patterns with the bottom wire at 20' up, 100' up, and 140' up. The decrease in gain with the 140' pattern is already evident, along with the reason for that decrease. Above the height for maximum gain, a secondary lobe begins to appear at a very high angle. With sufficient elevation (above 1/2 wavelength or so), the secondary lobe becomes dominant and the overall low angle gain of the antenna begins to decrease dramatically. However, I doubt anyone will ever test this modeling result by placing the bottom wire of the rectangle above 270' up.</p>
+  <center>
+    <img src="scv3-6.gif" width="637" height="517" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 6. 160-meter rectangle feedpoint resistance and reactance.
+  </center>
+  <p>We can see the span of expected feedpoint impedances in Figure 6. At 140' up, the feedpoint impedance approaches that of free space models. The resistive component increases in a regular curve as the antenna is lowered to more usable heights, in accord with reductions in gain as the antenna passes the 90' level on its way down. Also notable as an earth-effect is the increase in inductive reactance with lower heights, a fact suggesting that builders of rectangles at low heights might wish to shrink them to bring them to resonance. (However, before adjusting the antenna size, see the notes on matching below.) Notice that the feedpoint resistance of the antenna at its target frequency (here, 1.85 MHz) is well within the range of direct coaxial cable feed.</p>
+  <center>
+    <img src="scv3-7.gif" width="643" height="520" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 7. Rectangle resistance and reactance across the 160-meter band.
+  </center>
+  <p>As one might expect, the SWR bandwidth of this antenna, like most 160- meter antennas, is fairly narrow. More important is the information in Figure 7, a track of the resistance and reactance across the band for the antenna when the lower wire is at 20' up. Similar data accrue for higher antenna elevations, but with a shift in the resistance curve according to height.</p>
+  <p>The range of resistance is rather narrow--under 12 ohms across the band, as read from the left axis. Moreover, the reactance (as read from the right axis) changes in a very linear fashion. It would be simple enough to enlarge the antenna until it displays inductive reactance across the band. A remotely tuned series capacitor might then compensate for the reactance, leaving a resistive impedance suitable for coaxial cable.</p>
+  <pre>160-Meter Single Rectangle Gain and Feedpoint Impedance Over Various Soils
+
+Antenna Height Gain in dBi         Take-Off Angle Feedpoint Impedance
+  (in feet)                           (degrees)          (R +/- jX Ohms)
+
+   20-88'
+Very Poor Soil    0.34             27             65.1 + 30.0
+Poor Soil         1.86             25             62.4 + 34.1
+Average           3.09             22             60.6 + 36.8
+Very Good         5.24             16             55.7 + 37.4
+
+   60-128'
+Very Poor Soil    1.09             23             42.5 -  1.7
+Poor Soil         2.55             21             43.1 +  0.2
+Average           3.63             19             44.0 +  1.3
+Very Good         5.78             14             44.2 +  3.1
+
+  100-168'
+Very Poor Soil    1.24             20             33.3 -  5.1
+Poor Soil         2.67             18             34.3 -  4.8
+Average           3.71             16             35.2 -  4.9
+Very Good         6.16             13             36.1 -  4.4
+
+
+Soil types          Conductivity (S/m)       Dielectric Constant
+
+Very Poor Soil      0.001                     5
+Poor Soil           0.002                    13
+Average             0.005                    13
+Very Good           0.0303                   20
+
+Table 1.  160-meter single rectangle gain, TO angle, and feedpoint
+impedance over various soils, with different antenna heights above ground.</pre>
+  <p>The data developed so far has been over average earth, as it is called. Unfortunately, many of use live over earth significantly poorer than average, while a few lucky souls live on very good earth. Table 1 provides some guidance as to expectations for various types of soil ranging from very poor (conductivity (C) = 0.001 S/m; dielectric constant (DC) = 5) to very good earth (C = 0.0303; DC = 20). The figures reflect single side- fed rectangles at base heights of 20, 60 and 100 feet. Similar tables might be drawn up for any vertically polarized antenna and show similar differences from one soil type to the next. However, unlike the delta loops, which showed some aberrant progressions with changes in soil conditions, the course of values shows relative smooth curves from one soil type to the next for rectangles.</p>
+  <p>The tables are based on uniform soil in every direction from the antenna for distance great enough to fully affect the far field. Of great interest is the lack of significant change in the antenna feedpoint impedance with changes in soil type. It is dubious whether one can effect significant performance improvements in this or any other SCV by doctoring the soil in the immediate vicinity of the antenna. On the other hand, the soil at a distance of 2 wavelengths and more form the antenna is usually beyond control.</p>
+  <center>
+    <img src="scv3-8.gif" width="637" height="279" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 8. Elevation patterns over very poor and very good soil.
+  </center>
+  <p>The better the distant soil, the better the low angle radiation from the antenna. Figure 8 shows the contrast between very poor and very good soil. Equally important with the gain improvement is the lowered angle of maximum radiation. Were the curves graphically equalized, the higher-angle response would be very little different. However, the low-angle response from the antenna over very good soil is very much enhanced. Intermediate soil types provide intermediate curve shapes.</p>
+  <h3>The Double Rectangle</h3>For various reasons, some antenna builders prefer to feed their antennas with parallel transmission line and use an ATU to effect a match. One effective way to do this is to use the antenna as an impedance transformer by doubling it and making a mobius-strip crossing at the end opposite the feedpoint. This is the double rectangle shown in Figure 3, and developed by K5RP.
+  <p>The sketch shows two significant features. First, the loop must be slightly fatter vertically for maximum gain relative to the single loop. Second, the spacing between the loops has very little effect on antenna gain. In fact, models of the double loop with a space that ranges from 1' up to 12' showed only a 0.01 dB difference in gain.</p>
+  <p>What did change with changes in spacing was the required total loop size for resonance. The closer the wires, the larger the loop size. Part of this size increase stems from the fact that the crossing wires are longer for wider spacing, thus occasioning smaller outside dimensions. However, the other part is a function of minor interactions between the loops. With a constant length of 206' for the double rectangle array, the loop height was 70' with a 12' spacing and 71' for a 2' spacing.</p>
+  <p>The remainder of the data was generated on the basis of a 2' space between the wires, simply because that is most likely a more convenient construction distance. Spacers can be almost anything that insulates and is light weight. It is essential that the crossing wires at the far end of the array be well insulated from each other, although spacing appears not to be critical.</p>
+  <center>
+    <img src="scv3-9.gif" width="638" height="517" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 9. Gain and take-off angle of the double rectangle at various heights.
+  </center>
+  <p>The double rectangle exhibits almost a half dB of additional gain beyond that of the single rectangle. Figure 9 shows the gain and take-off angle for lower-wire heights from 20' to 140' up, which permits direct comparison with the corresponding chart for the single rectangle. The curves are highly congruent, with peak gain at about 100' up (with the top wire at 171' up). Since the resolution of take-off angles is one degree, the "stair-step" form of that curve should be no surprise, and 1-degree differences between the graphs for the single and double rectangles are meaningless.</p>
+  <center>
+    <img src="scv3-10.gif" width="640" height="522" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 10. Feedpoint resistance and reactance of the double rectangle.
+  </center>
+  <p>The "transformer" action of the double rectangle configuration appears clearly in Figure 10. The forms of both the resistance and the reactance curves are almost identical to those of the single rectangle, but the double rectangle values are almost exactly 4 times those for the single rectangle. Both resistance and reactance are multiplied.</p>
+  <p>The curve suggests that almost any parallel feedline might be used to feed the double rectangle. A link-coupled tuner should be able to handle the range of resistance and reactance across 160-meters. In fact, the more typical network tuner with its 4:1 output balun should not be heavily challenged by the impedances presented by the double rectangle.</p>
+  <pre>160-Meter Double Rectangle Gain and Feedpoint Impedance Over Various Soils
+
+Antenna Height Gain in dBi         Take-Off Angle Feedpoint Impedance
+  (in feet)                           (degrees)          (R +/- jX Ohms)
+
+  20-91
+Very Poor Soil    0.54             27             274 + 120
+Poor Soil         2.07             24             264 + 139
+Average           3.30             22             258 + 151
+Very Good         5.46             16             237 + 156
+
+  60-131
+Very Poor Soil    1.38             23             171 -   6
+Poor Soil         2.83             21             174 +   2
+Average           3.90             19             178 +   7
+Very Good         6.06             14             179 +  14
+
+ 100-171'
+Very Poor Soil    1.60             20             131 -  18
+Poor Soil         3.01             18             136 -  17
+Average           4.05             16             139 -  17
+Very Good         6.50             12             143 -  15
+
+
+Soil types          Conductivity (S/m)       Dielectric Constant
+
+Very Poor Soil      0.001                     5
+Poor Soil           0.002                    13
+Average             0.005                    13
+Very Good           0.0303                   20
+
+Table 2.  160-meter double rectangle gain, TO angle, and feedpoint
+impedance over various soils, with different antenna heights above ground.</pre>
+  <p>Like the single rectangle, soil quality affects the far field pattern fairly strongly without affecting the feedpoint impedance very much. Table 2 presents data for the double rectangle at the same baseline heights as for the single rectangle in Table 1. The increase in gain for the double rectangle is everywhere apparent in the table. However, the chief effect of the table is likely to be to make many folks wish they lived surrounded by very good earth. I did not have the heart to present the salt-water data.</p>
+  <h3>The Result</h3>Unlike the patterns for vertical monopoles and dipoles, the SCV family of antennas display a highly bi-directional pattern. Figure 11 presents the azimuth pattern for a double rectangle over average soil with a baseline height of 100' up and a take-off angle of 16 degrees. The single rectangle presents a similar pattern. Note the cloverleaf in the center of the pattern: it represent remnant horizontally polarized radiation which is not eliminable from any of the SCV configurations.
+  <center>
+    <img src="scv3-11.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 11. Azimuth pattern for a double rectangle showing both vertical and horizontal components.
+  </center>
+  <p>In general, deltas and square loops have more broadly oval patterns with less front-to-side rejection than the rectangle. The half-square pattern is similar to that of the rectangle with a slightly greater front- to-side ratio.</p>
+  <p>To increase gain further--and in the process double the front-to-side ratio--requires no more altitude, but double the linear space for the antenna. K4VX's open double rectangle with a common center wire or the familiar bobtail curtain provide about 1.5 dB added gain and over 20 dB front-to-side ratio, with comparable take-off angles to the single and double rectangles shown here.<sup>4</sup> They are certainly antennas worth investigation if one has a linear space well over 400' long.</p>
+  <p>These notes are based on computer models of the rectangle, which itself has already been proven in the field. Where computer modeling is at its best is in developing systematic guidance data, and that has been the aim of these notes. Computer models assume level terrain, but the individual contemplating an antenna such as these might well use terrain analysis software by N6BV or K6STI to adjust expectations for the particular antenna site and its environs. The more data we gather in advance, the more realistic will be our expectations for any antenna we might think about building. The 160-meter rectangle makes a good case-in- point.</p>
+  <h3>But What About 80 Meters?</h3>In our haste to review the rectangle at 160 meters, we have bypassed data for 80 meters, where the antenna is certainly a candidate for SCV use. The ideal ratio of length to fed-side for a 3.6 MHz rectangle is about 3.6:1. #12 AWG copper wire models in free space yielded maximum gain with dimensions of about 110' long by 31' high, at a figure about 0.25 dB higher than the 160-meter model. However, the feedpoint impedance was about 8 Ohm lower. These latter two properties result from the narrower shape of the 80-meter rectangle.
+  <pre>3.6 MHz Single Rectangle:  Properties Over Average Soil at Various Heights
+
+Soil Type Baseline  Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+
+Average    10        2.21            25            50 + 38
+(C=0.005,  20        2.76            23            40 + 15
+  DC=13)   30        2.98            21            34 +  7
+           40        3.08            20            30 +  3
+           50        3.11*           18            27 +  2
+           60        3.08            17            25 +  2
+           70        3.01            16            23 +  2
+           80        2.88            15            22 +  3
+           90        2.69            14            21 +  4
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of single rectangle = 110' baseline length, 31' height.
+          Construction:  #12 AWG copper wire.
+
+Table 3.  3.6 MHz single rectangle:  properties over average soil at
+various heights.</pre>
+  <p>With these variations in mind, you can anticipate the values for the 80-meter rectangle that appear in Table 3. Only the values for average soil are shown, since the values for other soils are proportional, using the 160-meter charts as a guide. The height of maximum gain is just about half that for 160 meters. However, over ground, the gain is not as high as the corresponding 160-meter rectangle at twice the height.</p>
+  <p>Only at low heights is it advisable to feed the 80-meter single rectangle directly with coax. Indeed, the single rectangle above 160 meters is probably a worse choice than its companion double rectangle. Like the 160-meter version of the double rectangle, the 80-meter antenna displays a slight gain over a single rectangle with relative insensitivity to the spacing of the two wires. The sample model placed the wires 1' apart, with the cross-over wires spaced about 0.5' apart. Also like the 160-meter version, the model maintained the same length, but increased the height over the single rectangle by a small amount, ending up with a total height of 32.3' for resonance in free space.</p>
+  <pre>3.6 MHz Double Rectangle:  Properties Over Average Soil at Various Heights
+
+Soil Type Baseline  Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+
+Average    10        2.40            25           212 + 132
+(C=0.005,  20        2.98            23           164 +  39
+  DC=13)   30        3.23            21           138 +   6
+           40        3.36            19           120 -   8
+           50        3.42            18           107 -  14
+           60        3.43*           17            97 -  15
+           70        3.37            15            90 -  13
+           80        3.26            15            85 -   9
+           90        3.08            14            82 -   5
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of double rectangle = 110' baseline length, 32.3'
+height.
+          Construction:  #12 AWG copper wire.
+
+Table 4.  3.6 MHz double rectangle:  properties over average soil at
+various heights.</pre>
+  <p>Table 4 shows the modeled values over average soil at heights ranging from 10 to 90' (with resultant top-wire heights ranging from 42.3' to 122.3'). The added gain over the single rectangle is evident, as is the reduced gain relative to corresponding 160-meter double rectangles. Like the 160-meter models, the height of maximum gain for the double rectangle is slightly and perhaps insignificantly higher than for the single rectangle.</p>
+  <p>The feedpoint impedance at low heights is likely to benefit from the use of parallel feeders and an antenna tuner. At higher levels, a quarter- wavelength matching section of 75-Ohm cable will provide a 50-Ohm coax match over a small portion of the band. However, the large scale changes in reactance suggest that parallel feeders and a tuner may be best for operation over the entire band.</p>
+  <p>This basic data, when combined with sensible adjustments to the 160- meter data, should provide reasonable guidance for our expectations should we decide to build one of these antennas. Before we make such a decision, we shall want to compare these data with those in the last episode on deltas. But let's not be too hasty. Final decisions should await a fuller story on the open-ended cousin to these two loops: the half-square.</p>
+  <h3>Notes</h3>1. For the "magnetic slot" and "double magnetic slot," see Russell E. Prack, K5RP, "Magnetic Radiators--Low Profile Paired Verticals for HF," <i>The ARRL Antenna Compendium</i>, Vol. 2 (Newington: ARRL, 1989), pp. 39-41. However, the elongated loop or "oblong" and its relationship to the square quad has been well-known for a long time. See, for example, the reference to this subject in Karl Rothammel, Y21BK, <i>Antennenbuch</i> (Berlin: Militarverlag der DDM, 1984), pp. 230, where a ratio of about 2.4:1 is recommended for the vertically polarized version. Reference is made therein to work by G6LX.
+  <p>2. Brian Beezley, K6STI, "A Gain Antenna for 28 MHz," <i>QST</i> (July, 1994), 70.</p>
+  <p>3. In the HF region, we can use a simpler approximation: (2.8 + 1.4 log F), where F = the frequency in MHz for #12 copper wire. When expressed in terms of natural logarithms, R approaches the Fibonacci constant times ln (100 F).</p>
+  <p>4. For the open double magnetic slot, see Lew Gordon, K4VX, "The Double Magnetic Slot Antenna for 80 Meters," <i>The ARRL Antenna Compendium</i>, Vol. 4 (Newington: ARRL, 1995), pp. 18-21.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 5-19-98. &COPY; L. B. Cebik, W4RNL. A print version of this note appears in</i> The National Contest Journal<i>. 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.</i><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="scv4.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40">Go to Part 4</a>
+  <p><a href="scv0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to SCV Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#quad-loop'>Quad Loop</a>, <a href='../topics.html#rectangle'>Rectangle</a>, <a href='../topics.html#scv'>SCV</a></p><br>
+</body>
+</html>

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="SCV, Half Square, HF Lower">
+  <title>SCVs Part 4: The Open-Ended Cousins</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/scvbut.gif" align="left" width="125" height="65" border="2" vspace="5" hspace="9">SCVs Part 4: The Open-Ended Cousins<img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  Having examined the low-band properties of the delta and rectangular loop, we next turn to the open-ended cousin of these SCVs: the half square. Although developed after its double-wide brother, the bobtail curtain, the half square is the more fundamental antenna.<sup>1</sup> As shown if Figure 1, it consists of two (roughly) 1/4 wavelength vertical legs connected by a (roughly) 1/2 wavelength horizontal wire. The horizontal wire functions as a phasing line between the verticals, although its radiation is imperfectly cancelled.
+  <center>
+    <img src="scv4-1.gif" width="514" height="301" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 1. Basic outline of the half square antenna.
+  </center>
+  <p>The first question often asked about the half square is whether it really belongs to the SCV family. Like the loops, the half square may operate without a ground plane--in fact, a small ground plane may reduce its gain and other desirable properties. Moreover, one may model the antenna in free space and make versions pointing either up or down for any frequency. For low band use, the down-pointing half square is favored because it places the high-current points at the corners at maximum achievable height.<sup>2</sup></p>
+  <center>
+    <img src="scv4-2.gif" width="599" height="404" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 2. Evolution of the half square from the delta.
+  </center>
+  <p>One can establish the SCV credentials of the half square by a simple free space modeling project. Begin with a right-angle delta, as shown in Figure 2. Separate the wires at the high-impedance apex point by a little. Then widen the separation, adjusting the model to maintain something close to resonance. Table 1 shows the first steps of this progression. In effect, nothing happens when the wires at the apex do not touch. By gradually, straightening the sloping delta wires toward the vertical and by lengthening the baseline until the feedpoint is in a corner, once evolves the half square. Finally, for low-band use, flip the antenna over so that the open ends point down. Of course, in free space, from which the figures in the table emerge, the flip is gratuitous, since there is no up or down.</p>
+  <pre>         Partial Evolution of a Right-Angle Delta to a Half Square
+
+Antenna Description           Gain dBi       Feedpoint Impedance
+                                          (R +/- jX Ohms)
+
+Right-angle delta:
+60.8' base; 30.4' height       3.31               51 + j 6
+
+Right-angle delta: apex
+wires separated 0.2'           3.31               51 + j 6
+
+Height increase to 30.41';
+apex spread 0.4'               3.32               51 + j 7
+
+Height increase to 30.7';
+apex spread 2.0'               3.36               51 - j 1
+
+Height increase to 31.1';
+apex spread 4.0'               3.41               53 + j 5
+
+Note:  Frequency:  7.15 MHz; Wire: #12 AWG copper; model in free space.
+
+Table 1.  Partial evolution of a right-angle delta to a half square.</pre>
+  <p>The more ideal separation between the vertical elements of the half square produces a sharper bi-directional pattern than the SCV loops develop. The side rejection will vary from 10 to well over 15 dB, for a familiar peanut-shaped pattern. An example appears in Figure 3. Whether the this pattern is an advantage or a disadvantage depends upon the oeprator's needs.</p>
+  <center>
+    <img src="scv4-3.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 3. Basic azimuth pattern of the half square at the elevation angle of maximum radiation when the antenna is at the height of maximum gain.
+  </center>
+  <p>Like the other SCVs, the half square has a ratio of horizontal to vertical lengths that yields maximum gain in free space (and over ground). However, that ratio appears to be independent of frequency, except for some residual effect of wire size. The ratio of horizontal length to vertical height for maximum gain is about 1.6:1.<sup>3</sup></p>
+  <p>For most antennas, there is sufficient band-to-band variation that giving formulas for cutting wires can be more misleading than helpful. However, the relatively invariant relationship between the horizontal and vertical dimensions of the half square for a maximum-gain configuration tends to assure a good utility for such formulas here. Where H is the horizontal length in feet, V is the vertical height in feet, and f is the frequency in MHz,</p>
+  <center>
+    <img src="scv4e1.gif" width="396" height="85" border="2" vspace="5" hspace="9">
+  </center>
+  <h3>80-Meter and 40-Meter Maximum Gain Half Squares</h3>An 80-meter half square designed for maximum gain at 3.6 MHz requires a horizontal wire about 124.5' long and two vertical end wires, each 77' long, when all wires are #12 AWG copper. The maximum free space gain of this antenna is about 4.6 dBi. When the antenna is placed over ground at some achievable height, the free space gain cannot be realized until the soil is very much better than average.
+  <pre>        80-Meter Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        1.74            23            80 + j13
+(C=0.001,  10        1.92            22            74 + j 5
+  DC=5)    15        2.05            22            70 + j 1
+           20        2.14            21            67 - j 3
+           25        2.21            20            65 - j 1
+           30        2.27            20            63 - j 1
+
+Poor        5        3.24            21            80 + j17
+(C=0.002,  10        3.34            20            75 + j 7
+  DC=13)   15        3.40            20            71 + j 2
+           20        3.42*           19            68 - j 0
+           25        3.42*           18            66 - j 1
+           30        3.41            18            64 - j 2
+
+Average     5        3.75            20            81 + j19
+(C=0.005,  10        3.79*           19            75 + j 8
+  DC=13)   15        3.79*           18            71 + j 2
+           20        3.76            18            68 - j 0
+           25        3.71            17            66 - j 1
+           30        3.63            16            64 - j 2
+
+Very Good   5        6.30            15            80 + j20
+(C=0.0303, 10        6.36            15            75 + j 9
+  DC=20)   15        6.40            14            72 + j 3
+           20        6.42*           14            69 - j 0
+           25        6.42*           13            66 - j 2
+           30        6.40            13            64 - j 3
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 124.5' horizontal length,
+77' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 2.  80-meter half square over various soils at various heights.</pre>
+  <p>Table 2 shows the results of modeling the 80-meter half square over various soils. The listings can be quite short, since--for all but very poor soil--the half square reaches maximum gain when the vertical ends are quite close to the ground. Indeed, the most desirable height from the point of view of gain is lower for average soil than it is for either poor or very good soil. However, like the other SCVs, the half square shows a consistent pattern of feedpoint impedances for corner-fed models regardless of the soil type immediately beneath the antenna. The antenna is close to resonant in the vicinity of 70 Ohms, although very close proximity to the ground raises that number by as much as 10 Ohms.</p>
+  <p>A corresponding maximum gain half square for 7.15 MHz would be 62.45' horizontally and 39' vertically, using #12 AWG copper wire. Because the #12 wire is a larger fraction of a wavelength in diameter, the antenna's free space maximum gain is nearly 4.7 dBi. However, like the 80-meter model, the 40-meter half square does not achieve this gain over ground unless the soil is far better than average.</p>
+  <pre>        40-Meter Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        2.41            23            73 + j 4
+(C=0.001,  10        2.72            22            67 - j 1
+  DC=5)    15        2.94            21            64 - j 2
+           20        3.13            20            62 - j 2
+           25        3.29            19            61 - j 1
+
+Poor        5        3.57            21            75 + j 6
+(C=0.002,  10        3.72            20            68 - j 1
+  DC=13)   15        3.78            18            64 - j 3
+           20        3.80*           17            62 - j 2
+           25        3.78            16            61 - j 1
+
+Average     5        3.40            20            76 + j 6
+(C=0.005,  10        3.46*           19            68 - j 1
+  DC=13)   15        3.42            17            64 - j 3
+           20        3.33            16            62 - j 3
+           25        3.20            15            61 - j 1
+
+Very Good   5        5.50            17            76 + j 7
+(C=0.0303, 10        5.51*           15            69 - j 2
+  DC=20)   15        5.44            14            65 - j 4
+           20        5.26            13            62 - j 4
+           25        5.05            12            60 - j 2
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 62.45' horizontal length,
+39' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 3.  40-meter half square over various soils at various heights.</pre>
+  <p>Table 3 shows the figures for 40-meter half square performance over various types of soil. Once more, the antenna shows maximum gain when the ends are fairly close to the ground, although that height varies with soil type. Unlike the 80-meter antenna, modeling suggests that the half square for 40 performs slightly better over poor soil than over average soil, although the difference is marginal, since the progression of take-off angles, or elevation angles of maximum radiation, is normal and decreases regularly with improvements in soil type. The progressions of feedpoint impedances is also quite normal to our expectations. Again, because the #12 wire is "fatter" on 40 than on 80, the resonant feedpoint impedance is a few Ohms under that of the corresponding 80-meter half square.</p>
+  <p>Although the tables flag a height (or two) as reflecting maximum gain heights for soils that are poor or better, the entries for very poor soil show no flags. The reason for the absence of a flag is that over very poor soil, half squares for 80 and 40 continue to show increases of gain with increases of height. Table 4 extends the 40-meter "very poor soil" set of values up to a height of 60' for the lowest point of the antenna. The continued increase in gain and lowering of the take-off angle are clearly apparent.</p>
+  <pre>        40-Meter Half Square Over Very Poor Soil at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        2.41            23            73 + j 4
+(C=0.001,  10        2.72            22            67 - j 1
+  DC=5)    15        2.94            21            64 - j 2
+           20        3.13            20            62 - j 2
+           25        3.29            19            61 - j 1
+           30        3.45            18            61 + j 0
+           35        3.60            18            62 + j 1
+           40        3.76            18            62 + j 1
+           45        3.92            17            63 + j 1
+           50        4.10            16            64 + j 1
+           55        4.29            16            64 + j 1
+           60        4.48            15            64 + j 0
+
+Table 4.  An extension of the 40-meter half square over very
+poor soil at various heights.</pre>
+  <p>However, an illusion accompanies this progression, as shown in Figure 4. The elevation patterns in the figure are for antenna base heights of 10, 25, and 40 feet, respectively. As one raises the antenna, gain increases, but so too does a secondary high-angle lobe. In the process of acquiring more gain, the half square users also acquires high-angle radiation in the receive mode, thus decreasing the QRM and QRN filtering benefits of the half square. Whether there is a cut-off point to the height of the antenna over very poor soil--and where that point might be-- is a decision only the antenna builder can decide.</p>
+  <center>
+    <img src="scv4-4.gif" width="637" height="282" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 4. Elevation patterns of a half square over very poor soil for three heights. Note the increasing gain, but as well, the increasing high-angle secondary lobe.
+  </center>
+  <p>In general, the half square over almost any soil type provides maximum gain at heights closer to the ground than is true of the other SCVs. Like its relatives, the half square elevation pattern begins to produce secondary high angle lobes as soon as it passes the height of maximum gain. Exceeding that height by very much may yield stronger reception to closer- in, high-angle signals and partially or wholly defeat the basic purpose in using an SCV in the first place.</p>
+  <h3>80-Meter and 40-Meter 50-Ohm Resonant Half Squares</h3>From the numbers in Table 3 and Table 4, it is clear that the feedpoint impedance of a maximum gain half square is somewhat distant from 50 Ohms. However, one of the benefits of using a corner feedpoint for the antenna is the ability to feed the antenna with standard 50-Ohm coaxial cable. Therefore, I redesigned the half square models to come somewhat closer to a 50-Ohm feedpoint impedance.
+  <p>The 80-meter (3.6 MHz) model required horizontal stretching to 155' with the verticals shortened to only 60' to arrive at a 50-Ohm antenna in free space. This is a horizontal-to-vertical ratio of about 2.58:1, which is a considerable departure from the maximum gain ratio of 1.6:1. When subjected to the same systematic modeling over various soils as the maximum gain models, Table 5 emerged. All of the gain figures are down significantly from the maximum gain model, with the decreases growing worse as the soil type grows worse. Moreover, the heights for maximum gain also decrease, while the take-off angles increase. Whether these reductions in performance warrant the move to a 50-Ohm model is, once more, a user decision.</p>
+  <pre>80-Meter 50-Ohm Resonant Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5       -0.29            25            66 + j 9
+(C=0.001,  10       -0.12            24            61 - j 1
+  DC=5)    15       -0.02            24            57 - j 7
+           20        0.03            23            54 - j10
+           25        0.06            22            52 - j13
+           30        0.08            21            51 - j15
+
+Poor        5        1.61            23            61 + j16
+(C=0.002,  10        1.66*           22            57 + j 4
+  DC=13)   15        1.66*           22            54 - j 3
+           20        1.61            21            53 - j 7
+           25        1.54            20            51 - j10
+           30        1.46            19            50 - j12
+
+Average     5        2.33*           21            60 + j21
+(C=0.005,  10        2.30            21            56 + j 8
+  DC=13)   15        2.20            20            54 + j 1
+           20        2.08            19            53 - j 4
+           25        1.93            18            52 - j 8
+           30        1.77            18            51 - j11
+
+Very Good   5        5.27*           16            52 + j25
+(C=0.0303, 10        5.17            16            51 + j12
+  DC=20)   15        5.04            16            50 + j 4
+           20        4.89            15            50 - j 1
+           25        4.73            14            50 - j 5
+           30        4.58            14            50 - j 8
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 155' horizontal length,
+60' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 5.  80-meter 50-Ohm resonant half square over various
+soils at various heights.</pre>
+  <p>Figure 5 shows the feedpoint resistance and reactance across the 80- meter band for the 3.6 MHz model. Across the band, the change in the resistive component is about 77 Ohms. With some redesign of the antenna, almost all of the band might be fit within a 2:1 SWR curve, assuming that the reactance can be compensated for at the feedpoint. However, the reactance varies by over 500 Ohms, suggesting that additional redesign for a remotely tuned series capacitor might still not yield full band coverage.</p>
+  <center>
+    <img src="scv4-5.gif" width="640" height="519" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 5. Feedpoint resistance and reactance of a 50-Ohm resonant 80-meter half square across the band.
+  </center>
+  <p>40-meters presents fewer problems for a half square designed for 50- Ohm feed. The dimensions of the model used for 7.15 MHz, was 70.5' horizontally and 34.5' vertically (with #12 AWG copper wire). The horizontal-to-vertical ratio is about 2:1, which is much closer to the maximum gain ratio than the 80-meter version achieved. As shown in Table 6, the gain reductions for the 40-meter antenna are less severe than for the 80-meter model, and the heights needed for maximum gain are only slightly lower than those for the maximum gain model for each type of soil. Likewise, increases in the take-off angle are less severe. In general, then, a 40-meter half-square designed for 50-Ohm resonance may be more feasible than an 80-meter version.</p>
+  <pre>40-Meter 50-Ohm Resonant Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        1.85            24            58 + j 4
+(C=0.001,  10        2.15            23            53 - j 3
+  DC=5)    15        2.34            21            50 - j 6
+           20        2.51            20            48 - j 6
+           25        2.68            19            47 - j 7
+
+Poor        5        3.19            22            58 + j 8
+(C=0.002,  10        3.30            20            53 - j 1
+  DC=13)   15        3.31*           19            50 - j 5
+           20        3.28            18            48 - j 6
+           25        3.23            17            48 - j 6
+
+Average     5        3.06*           21            59 + j 9
+(C=0.005,  10        3.06*           19            53 - j 0
+  DC=13)   15        2.97            18            50 - j 4
+           20        2.83            17            49 - j 6
+           25        2.68            16            48 - j 6
+
+Very Good   5        5.34*           17            57 + j12
+(C=0.0303, 10        5.24            16            52 + j 1
+  DC=20)   15        5.06            15            50 - j 3
+           20        4.82            14            49 - j 5
+           25        4.54            13            48 - j 6
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 70.5' horizontal length,
+34.5' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 6.  40-meter 50-Ohm resonant half square over various
+soils at various heights.</pre>
+  <p>The feeding problem is also less severe on 40 meters. The resistive component of the feedpoint impedance, as shown if Figure 6, varies by only 6 Ohms or so, while the reactance varies by a little under 140 Ohms. Therefore, for a corner-fed 40-meter half square, a remotely tuned series variable capacitor becomes a viable option for full band coverage with direct coax feed--assuming the antenna is further optimized to present inductive reactance across the band.</p>
+  <center>
+    <img src="scv4-6.gif" width="629" height="516" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 6. Feedpoint resistance and reactance of a 50-Ohm resonant 40-meter half square across the band.
+  </center>
+  <h3>End-Feeding the Half Square</h3>
+  <p>Corner-feeding the half square eliminates in large measure the need for a more complex matching network when the antenna is used only on the band for which it is designed. Conversely, feeding the antenna in the most traditional manner--at the open end of one of the verticals--requires a parallel tuned circuit resonated on the band of choice. The coil is tapped for coaxial cable feed. An additional tap may be used near the top of the tank circuit to effect the most precise match possible.</p>
+  <center>
+    <img src="scv4-7.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 7. Comparison of azimuth patterns of a corner-fed and an end-fed half square. Except for the feedpoint location, the antennas are identical.
+  </center>
+  <p>At the fundamental frequency for which the half square is cut, the use of end or corner feeding makes little difference to performance. Figure 7 shows the slight difference in pattern. With corner feed, the bi-directional pattern is closely symmetrical, with gain maxima at 90 and 270 degrees in the pattern shown. When end fed, the antenna shows a slight displacement of about 5 degrees in the maximum gain points, tilted away from the feed point. In practical terms, the user would be hard pressed to tell the difference.</p>
+  <p>End feeding is often recommended by those planning to use the antenna on more than one amateur band.<sup>4</sup> If the matching network is remotely tuned, it might be pressed into service as a multi-band tuner. Likewise, there is no rule against feeding the corner with a parallel transmission line and using an antenna tuning unit in the shack for other bands.</p>
+  <pre>Corner-Fed vs. End-Fed 80-Meter Half Squares at Higher Frequencies
+
+Frequency Max. Gain T-O Angle Az. Angle of   Feedpoint Impedance
+ in MHz    in dBi    degrees   Max. Gain       (R +/- jX Ohms)
+
+3.6
+a. Corner 3.79      18        90               71 + j   3
+b. End    3.93      18        85             4100 - j4000
+
+7.15
+a. Corner 5.35      20        55             1400 - j  30
+b. End    5.17      20        53             1900 - j3000
+
+10.1
+a. Corner 6.59      16        41             1000 - j 600
+b. End    6.46      19        40              350 - j2000
+
+14.1
+a. Corner 6.78      33        31              600 - j 200
+b. End    7.29      34        30              800 - j1000
+
+Note 1.  Dimensions of half square = 124.5' horizontal length,
+77' vertical height. Construction:  #12 AWG copper wire.
+Height 15' minimum.
+
+Table 7.  Corner-fed vs. end-fed 80-meter half squares at
+higher frequencies.</pre>
+  <p>Table 7 hints at the anticipated results of using an 80-meter half square on 40, 30, and 20. By comparing corner and end feeding systems for a single model of the half square, we discover that there is no significant difference in the patterns. The slight differences in gain, as well as angles of interest, result from one or the other system yielding larger or smaller "bulges" in the pattern in various directions. The chief differences between the two feed point show up in the anticipated feedpoint impedances.</p>
+  <center>
+    <img src="scv4-8.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 8. End-fed 80-meter half square azimuth pattern on 40 meters. The center-fed pattern is similar.
+  </center>
+  <p>On 40 meters, the pattern is roughly square for both feed systems, as is evident from Figure 8. Maximum gain is toward the corners most distant from the feedpoint. In contrast, an 80-meter dipole would become something close to a full wavelength on 40, producing a strong bi-directional pattern approaching 9 dBi if the antenna is a half wavelength up on 40 meters. The half square substitutes coverage for gain.</p>
+  <center>
+    <img src="scv4-9.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 9. End-fed 80-meter half square azimuth pattern on 30 meters. The center-fed pattern is similar.
+  </center>
+  <p>The patterns for the 80-meter half square on 30 and 20 meters are not too different from each other, as Figure 9 and Figure 10 make evident. The square becomes elongated, with further gain in the most favored directions. 20-meter use shows the disadvantage of a high-angle main lobe, although the lobe is very broad vertically. The feedpoint impedances for both bands require the use of a tuner with a considerable range of adjustment.</p>
+  <center>
+    <img src="scv4-10.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Figure 10. End-fed 80-meter half square azimuth pattern on 20 meters. The center-fed pattern is similar.
+  </center>
+  <p>The patterns are certainly not those favored for DXing. However, they offer the contester and the general operator some advantages in coverage not offered by highly directional (including highly bi-directional) antennas. However, in some applications, the antenna tuner settings will be very sharp and require readjustment with small frequency excursions.</p>
+  <p>Although the half square can be pressed into multiband service, its principle use remains as a vertically polarized low-angle low-gain antenna that offers a fairly high signal-to-noise ratio for DX signals. Of the SCVs surveyed, it shows the strongest preference to be mounted as low as the structure permits for maximum gain over most soil types. However, a maximum gain 80-meter model would top out in the 90 to 100 foot level, while a 40-meter model also designed and installed for maximum gain would need to be 50 to 60 feet high. Except over very poor soil, further increases in height will likely not yield superior performance overall, when we combine considerations of both gain and the elevation angle of maximum radiation.</p>
+  <p>Moreover, unless one needs only a bi-directional pattern, full coverage may require two half squares at right angles to each other. However, with a little remote switching, it is possible to design the right angle array with a common feed vertical and to detune the unused wires. Of course, having the land on which to install such a system is a prior necessity.</p>
+  <p>So far in this series, I have not attempted to compare the various types of SCVs, although I have compared SCVs within each type. Because each type of SCV has its own installation requirements, "better" and "worse" become complex terms that measure not only the performance and feedpoint figures for the antennas, but as well, all of the mechanical properties and their relationship to the prospective user's land. Nevertheless, the prospective SCV user should remember that these antennas as a class are not general purpose antennas. Rather, when installed within the limits suggested for each type within the class, they provide low-gain, low-angle radiation free from higher lobes and thus forming a natural filter against QRM and QRN from closer sources. In some cases, users may want them for receiving purposes only and use a dipole or similar antenna for transmitting (in which application high angle QRM and QRN are not relevant).</p>
+  <p>Installing SCVs too high, especially half squares, can easily defeat the main functional advantage of the antennas. Designing them for 20 meters is a marginal enterprise, and above 20 meters, other antenna types will normally out-perform the SCVs. The SCVs do come into their own again until the VHF region, where they can be mounted many wavelengths above ground and their largely vertical polarization combined with a beamwidth around 60 degrees may be superior in some applications to Yagis turned on their side.</p>
+  <p>Except for these very general comments, I have avoided comparisons with other types of antennas. Although a thorough comparison would be useful, the amount of material there is to present on SCVs and the shortage of space within which to present it suggests that this must be (as they sometimes say in textbooks) "an exercise left to the reader."</p>
+  <p>In fact, there are a number of directly related SCV questions left to look at. Some hams have built shrunken SCVs. Others have built double wides (for example, the double-humped delta, the open double magnetic slot, and the bobtail curtain). Still others have managed some reversible SCV beams. We should take at least a brief look at each of these ideas in one last installment.</p>
+  <h3>Notes</h3>1 The half square antenna actually appeared after its larger sibling, the bobtail curtain. See Ben Vester, K3BC, "The Half Square Antenna," <i>QST</i> (March, 1974), 11-14. Additional notice appeared in Radio Communications for January, 1977 (p. 36). See also Robert Schiers, N0AN, "The Half-Square Antenna," <i>Ham Radio</i> (December, 1981), 48-50. All three of these early sources show the antenna as voltage-fed from one of the free ends. For the bobtail curtain, see Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," <i>CQ</i> (March, 1948), 21-23 and 92-95. See also Smith follow-up articles, "The Bobtail Curtain and Inverted Ground Plane," Parts 1 and 2 in <i>Ham Radio</i> (February, 1983), 82-86, and (March, 1983), 28-30. See also John Devoldere, ON4UN, <i>Antennas and Techniques for Low-Band DXing</i>, 2nd Ed. (Newington: ARRL, 1994), Chapter 12, "Other Arrays."
+  <p>2 VHF half-square designs will appear in a forthcoming issue of <i>Communications Quarterly</i> (See <a href="../vhf/hs.html">The Half-Square on 2 Meters</a> for an earlier version of the article). Unfortunately, some half square users have oversold the antenna, especially for upper HF use. See, for example, Hannes Coetzee, ZS6BZP, "A Visit to the Half Square Antenna," <i>Communications Quarterly</i> (Spring, 1998), 83-90. At normal heights (1/2 wavelength or more), a dipole will usually outperform the half square on the upper HF bands. Its use on the lower bands is, in concert with the other SCVs, to sacrifice gain for a low-angle bi-directional elevation pattern that suppresses high-angle QRM and QRN. Its most apt application is where elevating a horizontal antenna in its entirety above 1/2 wavelength is not feasible.</p>
+  <p>3 If expressed as a ratio of vertical to horizontal dimensions, the ratio is 0.62:1. Allowing for wire thickness effects, this is the Fibonacci constant:</p>
+  <center>
+    <img src="scv4e2.gif" width="136" height="61" border="2" vspace="5" hspace="9">
+  </center>
+  <p>(This equation yields a value of about 0.618034, which also yields an inverse ratio of about 1.618034. The numbers are decimally longer for those addicted to transcendental numbers). The reference to Fibonacci is incidental in this context; the basic ratio for the half square holds up at least throughout the HF region.</p>
+  <p>4 See, for instance, Joe Everhart, N2CX, "End-Fed Half-Wave Antennas," <i>QRPp</i> (Spring, 1998), 11-15.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 5-21-98. &COPY; L. B. Cebik, W4RNL. A print version of this note appears in</i> The National Contest Journal<i>. 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.</i><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="scv5.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40">Go to Part 5</a>
+  <p><a href="scv0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to SCV Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-lower'>HF Lower</a>, <a href='../topics.html#half-square'>Half Square</a>, <a href='../topics.html#scv'>SCV</a></p><br>
+</body>
+</html>