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+  <meta name="keywords" content="Quad, VHF / UHF">
+  <title>In Pursuit of Better VHF Quad Beams</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/quad.gif" align="left" width="91" height="91" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">
+    In Pursuit of Better VHF Quad Beams<br>
+    A Work in Progress</h1>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>In both commercial and home-brew circles, quad beams have long vied with Yagis as the means to a high performance antenna array. Indeed, that very competition has very likely robbed the quad of the independent study necessary to establish its properties well-enough to capitalize effectively on them. In contrast, the development of antenna modeling and optimizing software has contributed to whole new generations of Yagis that effectively utilize parasitic relationships to develop both better patterns and wider operating bandwidth in virtually of all of critical categories.</p>
+  <p>With the exception of only a few investigators, such as Bob Haviland, W4MB, Dan Handelsman, N2DT, and David Jefferies, most quad designers have relied upon one of two methods to develop new antennas. The first method is the set of antique equations, long printed in The ARRL Antenna Book. This design method--which pays absolutely no attention to the diameter of the element wires--yields reasonably accurate thin-wire HF quads that are exceptionally narrow-banded. Neither their SWR curves nor their front-to-back curves will hold up to modern standards across even the HF wide ham bands. Yagis have set a standard of less than 2:1 SWR across a band like 20 or 15 meters, with a front-to-back ratio of at least 20 dB across those bands. Equation-designed quads using the old formulas simply cannot yield antennas that meet such performance standards.</p>
+  <p>The second method of development is trial and error, with emphasis upon error. Chief among the errors is the attempt to keep the boom length for any given number of elements as short as possible. If this initial temptation is overcome, there seems reticence to extend the quad boom longer than necessary for a Yagi with the same number of elements. The results have been narrow-banded quad beams, often with performance deficiencies, especially in the front-to-back category.</p>
+  <p>So I think that we must return to the starting line and redevelop our thinking about quads from scratch. In this work-in-progress, I shall take a long look at 2- and 3-element quad beams, with some observations about 4-element beams. Although I have some 5- and 6-element designs in my collection of models, they are not sufficiently well-developed to admit of systematic discussion. Hence, these notes represent the first part of yet-to-be finished business.</p>
+  <p>However, along the way, you will note some recurrent themes that I might as well summarize at the outset.</p>
+  <p>1. Quad antennas, whether single loops or arrays, are narrow-band arrays by nature--contrary to the long standing myth about them. Because quads often offer a very wide SWR curve in some configurations, the entire set of antennas has received the unwarranted categorization as "low-Q" devices. Unfortunately, this has misled many builders into believing that the quad is a non-critical antenna so that careful construction is not really necessary.</p>
+  <p>In effect, compared to properly design Yagis, the quad array with the same number of elements is a narrow-band antenna. Its front-to-back performance falls off more than 2.5 times as fast as the SWR curve deteriorates. Although some users claim they only care about the gain, the design challenge for me is to discover what it takes to obtain superior performance in all major categories across a given band.</p>
+  <p>2. The physical specifications for a quad array are critically dependent upon the diameter of the elements that compose them. I shall show along the way just how much the quad is dependent in raw performance (such as gain) upon element diameter as much as it is dependent upon the loop circumference for each of the elements and upon the element spacing. The element-diameter factor is elusive in trial-and-error design exercises, but can become clear when optimizing basic quad designs becomes a systematic enterprise. In fact, we shall show that monoband 2-, 3-, and 4-element quad design is amenable to computerized calculations requiring only the element diameter and the design frequency as inputs.</p>
+  <p>3. For optimal performance, the parasitic coupling of quad elements requires considerably more spacing than equivalent coupling of linear elements in Yagi design. Indeed, beyond a certain point, the boom length of an optimized quad with reasonably wide-band performance characteristics may be the limiting factor in comparisons with Yagis of similar performance capabilities. At this point, I might estimate the break-even point to be somewhere between 4 and 5 elements. However, this estimate is very tentative, as the work is nowhere near complete.</p>
+  <p>4. The theoretical gain of a quad over a Yagi with a similar number of elements cannot be attained if the quad elements are significantly smaller in diameter than the Yagi elements. HF quads suffer most in the regard, since the #12 to #16 AWG wire we generally use is often less than 0.1 the diameter of typical Yagi elements for the same frequencies. However, VHF quads suffer similarly when they use thin wire, while the Yagis with which they compete employ aluminum rod or tubing. In many cases, the wire quad will lose up to half of the theoretic advantage over a single linear element solely in terms of wire losses. If we wish a quad to achieve its full theoretical potential relative to Yagis, we shall have to use "Yagi-size" elements.</p>
+  <p>The themes I have just enumerated are more fully developed in a series of articles appearing in AntenneX starting in October, 2000. However, we shall see significant confirming evidence as we look at VHF quad design. For the purposes of keeping everything coherent, all of the quads examined here have a design frequency of 146 MHz. In terms of properties, I have set the 2-meter band in the U.S. (144-148 MHz) as the design bandwidth for both the SWR bandwidth curve and the front-to-back bandwidth curve. Front-to-back figures will be given as the 180-degree front-to-back value, although we shall examine the rear quadrant performance in more detail in the text.</p>
+  <h3>2-Element Quad Beam Design</h3>
+  <center>
+    <img src="2mq-1.gif" width="402" height="424" border="2" vspace="5" hspace="9">
+  </center>
+  <p>To fully appreciate a 2-element quad beam, sketched in <b>Fig. 1</b> for reference, it may be useful to make a few comparisons to comparable 2-element Yagi behavior. In a 2-element driver-reflector configuration, a Yagi exhibits maximum front-to-back ratio in the region of about 0.1 to 0.12 wavelengths spacing, with element lengths optimized. The peak front-to-back ratio is low--about 12 dB--and the curve is shallow as we increase the spacing.</p>
+  <p>The behavior of the Yagi represents a limit for parasitic operation of two 1/2 wavelength linear elements. It is possible to derive much higher front-to-back ratios for any pair of such elements by any one of many methods of phase-feeding both center-points. In fact, for any spacing and set of near-1/2 wavelength element lengths, we can find a set of relative current magnitudes and phases for the two elements to achieve at least 50 dB of 180-degree front-to-back ratio. However, parasitically, the mutual coupling between elements is not sufficient to achieve more than the approximate 12 dB figure at the optimal spacing.</p>
+  <p>A quad loop may--for this exercise--be thought of as two dipoles bent so that the ends meet each other. In this configuration, the current distribution along each of the two dipoles is different from that of a linear dipole. The current at the square loop corners--which approximates the distance from the center to the mid-points of a linear element--is about 14% higher with double the phase shift of the current on the corresponding points of a linear element. The net result is a high level of mutual coupling between elements. Since the optimal distance for achieving maximum front-to-back ratio is a function of coupling, we should expect that the element spacing for a quad would have to be greater than for a driver-reflector Yagi. It is: in the neighborhood of 0.17 wavelengths.</p>
+  <p>For both the Yagi and the quad, the exact spacing required for maximum front-to-back ratio is a function of two other variables: the element lengths and the element diameter. As the element diameter increases, the quad loop lengths (for maximum front-to-back ratio combined with driver resonance) increase and the required spacing between elements increases. It is possible to derive a series of antenna models using NEC--which is highly accurate in this kind of exercise--that track the array dimensions for any element diameter ("wire size") from 3.16E-5 up to 1E-2 wavelengths. Subjecting the results to regression analysis results in a series of equations suitable for automated design of a 2-element quad beam having maximum front-to-back ratios of more than 50 dB. Such a program, in GW Basic format for structural transparency, appears in <b>Appendix 1</b> of this study. One need only enter the element diameter and the design frequency to derive 2-element quad dimensions and some basic performance data.</p>
+  <p>At VHF, few will be tempted to build a quad using wire in the 3.16E-5 range--somewhere in the #80 AWG range. However, the program is calibrated for 3 to 300 MHz, and quads in the 1300 kHz range have been developed from the automated process. There are a few cautions to observe. The program lists a design frequency gain that is correct for about 30 MHz. Since skin effect and its resultant losses do not change linearly with the change in element diameter, the actual gain of an array will be higher than predicted for frequencies significantly lower than 30 MHz and be lower than predicted for frequencies higher than the median. As well, changing antenna materials will result in small deviations from the predictions, especially for very thin element quads. The result of these material changes will be minimal with elements larger than 1E-3 wavelengths in diameter.</p>
+  <p><b>Table 1</b> lists the wires sizes that we shall sample in this study, arranged in an overall 8:1 total ratio in 2:1 increments. The smallest size is just barely thinner than #14 AWG (0.0641"). The largest size (0.5") represent a practical limit to modeling accuracy for the exercise, as the diameter approaches 1E-2 wavelengths. The common logs for the wire diameters (in wavelengths) are also listed, since the properties of antennas tend to vary more directly with the common log of wire size than with the size itself.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Table 1:  Wire Sizes Used in This Study
+
+Wire Size in Inches      Wire Size in             Common Log
+                         Wavelengths              of Wire Size
+     0.0625              0.0007731                -3.1118
+     0.125               0.0015462                -2.8107
+     0.25                0.0030925                -2.5097
+     0.5                 0.0061849                -2.2087
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>My concern to develop the automated program for maximum front-to-back 2-element quads stems from the fact that the maximum front-to-back configuration also yields the widest operating bandwidth for this array type, where bandwidth includes both 2:1 SWR and &gt;20 dB front-to-back ratio. <b>Table 2</b> lists the resultant quad designs based on this analysis.
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 2:  Calculated Data for 2-Element Quads Modeled
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.                                 2.
+Wire Diameter:           0.0625"        Wire Diameter:           0.125"
+Reflector Circumference: 88.480"        Reflector Circumference: 89.672"
+Driver Circumference:    82.304"        Driver Circumference:    82.584"
+Refl-Driver Spacing:     13.140"        Refl-Driver Spacing:     13.324"
+Feedpoint Impedance:     141.1 Ohms        Feedpoint Impedance:     142.3 Ohms
+Free-Space Gain:         7.06 dBi       Free-Space Gain:         7.11 dBi
+&lt; 2:1 swr bandwidth:     18.17 mhz      &lt; 2:1 swr bandwidth:     20.78 mhz
+&gt;20 dB F-B Bandwidth:    3.45 MHz       &gt;20 dB F-B Bandwidth:    4.19 MHz
+
+3.                                 4.
+Wire Diameter:           0.25"          Wire Diameter:           0.5"
+Reflector Circumference: 91.304"        Reflector Circumference: 93.608"
+Driver Circumference:    83.064"        Driver Circumference:    83.936"
+Refl-Driver Spacing:     13.493"        Refl-DriverSpacing:      13.718"
+Feedpoint Impedance:     145.0 Ohms        Feedpoint Impedance:     150.4 Ohms
+Free-Space Gain:         7.14 dBi       Free-Space Gain:         7.17 dBi
+&lt; 2:1 swr bandwidth:     24.63 mhz      &lt; 2:1 swr bandwidth:     31.11 mhz
+&gt;20 dB F-B Bandwidth:    5.29 MHz       &gt;20 dB F-B Bandwidth:    6.87 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The dimensional growth of the array with increasing element diameter is clear in the table. The feedpoint impedances are resonant at the design frequency within +/-1 Ohm reactance. We can summarize a number of the other features of the table better in a selection of graphs that capture frequency sweeps of each design across the 2-meter band. For example, <b>Fig. 2</b> records not only the free-space gain of the array at the design frequency at the design frequency, but as well the rate of change of gain across the band. As one might expect, the fatter the element, the lower the rate of gain change, thus ensuring more equal gain at both band edges. While commenting on element diameter, one should not that, contrary to experience with linear elements, closed loops tend to grow larger with increasing diameter elements and to have higher feedpoint impedances.</p>
+  <center>
+    <img src="2mq-2.gif" width="648" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> extracts the 180-degree front-to-back data, which reflect also the &gt; 20 dB bandwidth entry in the <b>Table 2</b>. Note that the front-to-back bandwidth--when held to this standard--does not exceed 4 MHz until the element diameter reaches 0.125", and with a mid-band design frequency, does not exceed 20 dB at the low end of the band until we use a 0.25" diameter element. We shall shortly explore why it is best to design quad arrays for a position about 1/3rd up from the bottom of the desired operating passband.</p>
+  <center>
+    <img src="2mq-3.gif" width="648" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The SWR curves (relative to the resonant impedance of each array) for these 2-element optimized arrays, as shown in <b>Fig. 4</b>, present little concern to the builder. They are the reason so many builders classify the quad as a "low-Q" antenna, although the front-to-back curves--even for these fat-element arrays--show the inaccuracy of that claim.</p>
+  <center>
+    <img src="2mq-4.gif" width="647" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The use of 180-degree front-to-back values was necessary to achieve maximum operating bandwidth for the antenna. However, these values should not be mistaken for the overall performance in the rear quadrants of a 2-element quad. <b>Fig. 5</b> shows free-space azimuth patterns for the low end of the band for the thinnest and thickest elements used in this study. Note that in each case, the worst-case front-to-back ratio just approaches 18 dB--which tends to hold for all models used across the band. What does not appear as rearward gain in one direction tends to show up as gain in another direction within the rear quadrants. Thus, there is an overall limit to rear quadrant performance for any 2-element single-feed quad array.</p>
+  <center>
+    <img src="2mq-5.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <p>While we are comparing the thinnest and thickest elements in our collection of models, let's look more closely at the wider-band performance of the array--especially at the front-to-back ratio and at the SWR curves. <b>Fig. 6</b> presents the data for each parameter from 140 through 175 MHz, with each array having a design frequency of 146 MHz. Note that the front-to-back curves fall off much more rapidly below design frequency than above it, although the two curves parallel each other closely. With respect to SWR, we would correctly anticipate a steeper curve for the thinner element model. However, for both the 0.625" and 0.5" model, the curves are both more shallow above design frequency than below. The lesson of these curves is simple: for a given desired operational passband, design the quad array for a frequency about 1/3rd the way up from the lower end of that passband in order to achieve roughly equal values of SWR and front-to-back ratio at both ends of the passband. The loss of gain from using this procedure will be rather slight.</p>
+  <center>
+    <img src="2mq-6.gif" width="645" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The actual resonant frequency of the driver is, for small changes in loop diameters, relatively independent of changes in front-to-back ratio--which is largely controlled by the spacing and loop diameter of the reflector. Hence, for special purposes, one may place the resonant frequency of the driver almost anywhere within a passband without moving the frequency of maximum front-to-back ratio significantly. In short, the 2-element quad array can be customized within reason to the builder's desires.</p>
+  <p>Although 2-element quads for 2-meters are "small potatoes" by most array standards, it is necessary to understand the properties of these basic arrays in order to better understand the properties of larger quads. Therefore, let's add a director and see what happens.</p>
+  <h3>3-Element Quad Beam Design</h3>The addition of a director to a quad array introduces a plethora of new variables into beam design. Not only must we account for the spacing between individual elements, we must also account for the relative spacing between driver-director and driver-reflector. Consequently, the number of design variables increases exponentially as we add elements to the array. Little wonder that many builders seek out a simple standard by which to build these antennas.
+  <p>In my own efforts to optimize 3-element quad arrays, I selected two criteria initially: gain and operating bandwidth. Initially, I gave precedence to operating bandwidth, using the &gt;20 dB front-to-back standard. Later, I turned to gain as the paramount criterion, with reasonably-wide bandwidth as the secondary standard. The results proved interesting. For the wire sizes we have selected as most relevant to 2-meter arrays, the arrays ranged between 32" and 36" long. This value is nearly 30% longer than most 3-element 2-meter quads, but the results turn out to be very consistent in each category for operating properties. <b>Table 3</b> lists the resultant arrays for both wide-band and for high-gain applications.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 3:  Calculated Data for 3-Element Quads Modeled
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.  Wire Diameter:                           0.0625"
+                              Wide-Band                High-Gain
+Reflector Circumference:      87.088"                  86.736"
+Driver Circumference:         82.320"                  83.040"
+Director Circumference:       75.92"                   79.336"
+Refl-Driver Spacing:          13.155"                  14.244"
+Driver-Dir Spacing:           22.759"                  18.033"
+Total Boom Length:            35.914"                  32.277"
+Feedpoint Impedance:          74.3 Ohms                54.5 Ohms
+Free-Space Gain:              8.87 dBi                 9.36 dBi
+&lt;2:1 swr bandwidth:           5.72 mhz                 3.91 mhz
+&gt;20 dB F-B Bandwidth:         2.77 MHz                 2.41 MHz
+
+2.  Wire Diameter:                           0.125"
+                              Wide-Band                High-Gain
+Reflector Circumference:      88.008"                  87.512"
+Driver Circumference:         82.632"                  83.352"
+Director Circumference:       75.824"                  79.296
+Refl-Driver Spacing:          13.323"                  14.193"
+Driver-Dir Spacing:           22.234"                  18.050"
+Total Boom Length:            35.557"                  32.243"
+Feedpoint Impedance:          72.4 Ohms                52.1 Ohms
+Free-Space Gain:              8.99 dBi                 9.48 dBi
+&lt;2:1 swr bandwidth:           6.44 mhz                 4.31 mhz
+&gt;20 dB F-B Bandwidth:         3.27 MHz                 2.77 MHz
+
+3.  Wire Diameter:                           0.25"
+                              Wide-Band                High-Gain
+Reflector Circumference:      89.256"                  88.552"
+Driver Circumference:         83.056"                  83.752"
+Director Circumference:       75.568"                  79.240"
+Refl-Driver Spacing:          13.521"                  14.150"
+Driver-Dir Spacing:           21.760"                  18.024"
+Total Boom Length:            35.281"                  32.174"
+Feedpoint Impedance:          71.7 Ohms                50.2 Ohms
+Free-Space Gain:              9.07 dBi                 9.57 dBi
+&lt;2:1 swr bandwidth:           7.43 mhz                 4.84 mhz
+&gt;20 dB F-B Bandwidth:         3.96 MHz                 3.28 MHz
+
+4.  Wire Diameter:                           0.5"
+                              Wide-Band                High-Gain
+Reflector Circumference:      90.960"                  90.032"
+Driver Circumference:         83.624"                  84.272"
+Director Circumference:       75.040"                  79.104"
+Refl-Driver Spacing:          13.693"                  14.133"
+Driver-Dir Spacing:           21.194"                  17.869"
+Total Boom Length:            34.887"                  32.002"
+Feedpoint Impedance:          71.5 Ohms                49.0 Ohms
+Free-Space Gain:              9.13 dBi                 9.63 dBi
+&lt;2:1 swr bandwidth:           8.72 mhz                 5.63 mhz
+&gt;20 dB F-B Bandwidth:         4.95 MHz                 4.03 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Let's begin with the wide-band arrays. <b>Fig. 7</b> shows the frequency sweep of gain across the 2-meter band for each array in the left column of <b>Table 3</b>. For wide-band operation, the peak gain occurs below the lower limit of the operating passband. Hence, gain decreases across the band. However, the decrease is significantly lessened as we increase the element diameter, with the 0.5" element model showing just over a 0.05 dB change. When maximum operating bandwidth is the primary consideration, increasing the element diameter draws the point of maximum gain closer to being within the operating passband so that the gain curve is at its shallowest.</p>
+  <center>
+    <img src="2mq-7.gif" width="647" height="522" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 180-degree front-to-back curve in <b>Fig. 8</b> reveals that the operative design technique--as used with the 2-element quad--was to place maximum front-to-back at or very near to the design frequency. However, the addition of the 3rd element limits the maximum value of front-to-back ratio as well as the bandwidth over which the value exceeds 20 dB. Although any of the curves might well be usable for many purposes, in terms of the design standards of this exercise, only the 0.5" element version of the antenna achieves 20 dB across the entire band.</p>
+  <center>
+    <img src="2mq-8.gif" width="647" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As with the 2-element quads, the SWR bandwidth of the arrays is considerably wider than the front-to-back bandwidth, as shown in <b>Fig. 9</b>. The more rapid rise in SWR below the design frequency is evident for all versions of the array. However, all of the curves would be acceptable. In fact, referring to <b>Table 3</b>, any of these antennas would be matchable directly to a 75-Ohm main feedline.</p>
+  <center>
+    <img src="2mq-9.gif" width="648" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 10</b> provides--among the models given in <b>Table 3</b>--a worst-case look at the patterns of the 0.0625" element diameter model for the entire 2-meter band. In practical terms, the gain would be accounted as reasonably stable, even if not as good as that of the 0.5" model. As well, the rear quadrants--although not up to the 20 dB standard at the band edges--remain quite well controlled and predictable. The nearly 9 dBi free-space gain is rarely achieved in common short-boom 4-element Yagis.</p>
+  <center>
+    <img src="2mq-10.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p>If we turn to the high-gain versions of the antenna, we should expect more gain and a narrower operating bandwidth. In fact, the design of these arrays turned out to be something of a surprise for the designer. As shown in <b>Fig. 11</b>, the peak gain appears within the operating passband, although it gradually shifts toward the high end of the band with the fattest- element version of the array. For the 0.5" diameter model, the gain is about a half dB higher than for the wide-band version, with excellent gain stability across the band.</p>
+  <center>
+    <img src="2mq-11.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In terms of front-to-back ratio, graphed in <b>Fig. 12</b>, the peak front-to-back ratio approaches that of the wide-band array and almost achieves the 20-dB standard with 0.5" diameter elements. Since peak gain was the primary criterion, the exact placement of the front-to-back peak was left a bit more variable, but it occurs in all cases between 145.5 and 146.0 MHz.</p>
+  <center>
+    <img src="2mq-12.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The limiting factor in the high-gain arrays is the SWR curve. shown in <b>Fig. 13</b>. The second surprise of the design exercise was that fact that these arrays all yielded impedance values close to 50 Ohms. The 0.0625" element model fails to achieve a 2:1 50-Ohm SWR curve for the entire 2-meter band. However, the larger-diameter models fit safely within the limits, although with higher band-edge SWR values than for the wide-band models.</p>
+  <center>
+    <img src="2mq-13.gif" width="646" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 14</b> provides a set of free-space azimuth patterns across the band for the 0.0625" model--allowing a comparison with the wide-band version of the array shown in <b>Fig. 10</b>. Whether these patterns are suitable for particular applications is a user judgment.</p>
+  <center>
+    <img src="2mq-14.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The maximum design-frequency gain of the high-gain models is about 9.6 dBi (free-space), which approaches the gain of a standard 5-element Yagi (about 10 dBi). The wide-band version achieves about 9.1 dBi for the same 0.5" element diameter, with a proportionally wider operating bandwidth. The most interesting aspect of this seemingly small set of differentials is that they require very different dimensional profiles to maximize each set of design goals. <b>Fig. 15</b> shows the side profiles of the two arrays, while <b>Table 3</b> shows in detail the differences in actual dimensions.</p>
+  <center>
+    <img src="2mq-15.gif" width="365" height="520" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Nonetheless, each type of array follows a natural progression similar to that of the 2-element arrays. It is possible to optimize a series of each type of array using wire sizes ranging from 3.16E-5 through 1E-2 wavelengths and then to subject the results to regression analysis. The regression equations can than be programmed into any setting for calculations of array dimensions and properties that hold good for 3 to 300 MHz. The same limitations regarding skin effect and array gain that applied to 2-element quads also apply to these arrays. <b>Appendix 2</b> provides a GW Basic listing for the wide-band array design, while <b>Appendix 3</b> supplies a similar listing for the high-gain version. Note that GW Basic recognizes only natural logs so that a multiplier must be added to convert the value to a common log--which is used by the regression analysis. If the program is translated to a spreadsheet that already knows the difference between common and natural logs, the multiplier can be omitted.</p>
+  <p>As with the 2-element arrays, the designs are resonated within +/-1 Ohm reactance at the design frequency. However, the driven element can be adjusted to place resonance within a MHz of the design frequency with minimal effect on the other antenna properties. Alterations to the director and reflector loop sizes have greater consequences for performance. Thus, to move the center point for the peak front-to-back ratio or SWR curve lower in the band, it is recommended that one choose a slightly lower design frequency.</p>
+  <h3>Very-High-Gain 3-Element Quad Beams</h3>I must confess at this point to having arrived at the limit of completely systematic work on 3-element quad designs. The remainder of these notes will address more suggestive conclusions that are insufficiently confirmed to be completely reliable. Nonetheless, they will indicate some directions of development for further design work. In many ways, this is the most interesting arena of quad design, since once quad dimensions are reduced to a set of usable equations for automated design, they become rather dull.
+  <center>
+    <img src="2mq-16.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The first interesting anomaly we might address is the possibility of a 3-element quad having even more gain than the standardized model--and on a short boom. The design is based on a high-gain Yagi which has a design frequency free-space gain of about 8.1 dBi, with about 24 dB front-to-back ratio and a resonant feedpoint impedance of about 25 Ohms. By optimizing the loop sizes of the comparable quad, I was able to achieve with 3/16" diameter elements and a 27" boom length nearly 9.9 dBi gain with over 32 dB of 180-degree front-to-back ratio. <b>Fig. 16</b> shows the free-space azimuth patterns for the array over the 2-meter band. With a worst-case front-to-back value of better than 15 dB, this array looks promising.</p>
+  <center>
+    <img src="2mq-17.gif" width="644" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 17</b> shows the gain curve and front-to-back curve across the 2- meter band for this array. The front-to-back rate of change is not unusual, but the rate of gain change across the band is very steep, ranging from 9.57 dBi at 144 MHz to 9.94 dBi at 147 MHz. However, for most of the band, the forward gain exceeds the best gain of the 0.5" high-gain model in the series just examined.</p>
+  <center>
+    <img src="2mq-18.gif" width="648" height="501" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The limiting factor of this design appears in the SWR curve, shown in <b>Fig. 18</b>. The 2:1 SWR curve is under 2 MHz wide, less than half the band. Moreover, the resonant impedance is about 22.7 Ohms. Interestingly, the resistive component of the impedance changes by less than 0.5 Ohms across 2 meters. However, the reactance varies by nearly 67 Ohms from one end of the band to the other. The array is thus most useful for narrow band applications, since achieving a match over such a wide range of reactance would present a very significant challenge. <b>Table 4</b> lists the properties of the array that we have been discussing.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Table 4:  Design Data for a High-Gain Short 3-Element Quad
+
+Element Diameter:             0.1875"
+Reflector Circumference:      86.688"
+Driver Circumference:         86.064"
+Director Circumference:       81.888"
+Refl-Driver Spacing:          12.388"
+Driver-Dir Spacing:           14.275"
+Total Boom Length:            26.663"
+Feedpoint Impedance:          22.7 Ohms
+Free-Space Gain:              9.89 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>One reason for working with this array--besides its narrow-band potentials for some applications--was to test the possibility of applying to quads certain Yagi techniques to broaden the operating bandwidth and to control the feedpoint impedance. Called "Optimized Wide-Band Antennas" (OWA) by their developer, Jim Breakall, WA3FET (with preceding work by Tom Schiller, N6BT, and even further back, incipient OWA properties in DL6WU long Yagis), the techniques have proven highly effective with Yagis of almost any size over 2 elements. The key is the addition of a new first director that, in conjunction with reflector spacing, sets the feedpoint impedance stably over a wide operating passband, while the remaining elements set the pattern characteristics of the array. I have designed a number of such arrays ranging from 4 to 7 elements, each of which has a flat 50-Ohm feedpoint impedance that is under 1.3:1 SWR across the wider ham bands in both HF and VHF versions. For each array, the essential operating characteristics of 3-6 element Yagis of the same boom length have been replicated, but with the desired feedpoint characteristics.</p>
+  <p>The question thus arose as to whether these techniques might be applied to quad designs using parameters initially derived from Yagis. The answer is a highly qualified affirmative, but with a very strong reservation--at least so far. <b>Table 5</b> lists the 4-element OWA quad trial design dimensions and properties.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Table 5:  Design Data for an "OWA" 4-Element Quad
+
+Element Diameter:                  0.25"
+Reflector Circumference:           87.952"
+Driver Circumference:              84.136"
+Director 1 Circumference:          76.960"
+Director 2 Circumference:          76.640"
+Refl-Driver Spacing:               11.965"
+Driver-Dir 1 Spacing:              12.287"
+Dir 1-Dir 2 Spacing:                8.085"
+Total Boom Length:                 32.337"
+Feedpoint Impedance:               42.7 Ohms
+Free-Space Gain:                   9.60 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="2mq-19.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 19</b> shows the set of free-space azimuth patterns for the array across 2 meters. As is evident, the rear quadrants are well controlled, although the forward gain has not yet been restored to the peak value attained from the model before "OWA" treatment. <b>Fig. 20</b> affirms this failure to achieve peak gain as well as showing that the rate of gain change across the band is consistent with the untreated model. The front- to-back curve is similar to the original.</p>
+  <center>
+    <img src="2mq-20.gif" width="645" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The gain in performance appears in the SWR curve of <b>Fig. 21</b>, which shows the 50-Ohm SWR performance of the array. However, both the gain and the SWR curves are similar to those of 0.25" diameter 3-element high-gain model shown earlier--with the earlier model having a more stable gain across the band.</p>
+  <center>
+    <img src="2mq-21.gif" width="648" height="507" border="2" vspace="5" hspace="9">
+  </center>
+  <p>If the present attempt at applying OWA techniques to a 3-element Yagi-Spaced quad is indicative (and perhaps design evidence is not yet sufficient to assert this with confidence), attempting to apply OWA techniques runs into a conflict that is endemic to quads. The optimal coupling between quad elements requires greater spacing than for Yagis. Hence, the spacing of the new "OWA" element is forced a greater distance from the driver to obtain impedance control. In the end, the resultant spacing yields a quad that would obtain similar results in terms of both gain and feedpoint impedance without the OWA element. In essence, the director of the high-gain 3-element quad performs both pattern control and impedance control duties--as well as it can. Although too soon to be said with authority, it is likely the case that obtaining further wide-band performance from a quad simply requires the addition of properly spaced directors.</p>
+  <h3>4-Element Quad Array Design</h3>The foray into 4-element quad array design is fraught with further complications. The additional director multiplies the number of variables. However, we may be able to indicate some useful directions for design effort--and possibly some limitations that may be inherent in long quads.
+  <p>A useful place to begin would be with a sample or two of existing design. I have selected two widely disseminated design, although they appear in disguise. Models of each of them required that I frequency scale the design in order to produce any usable results. Hence, one is redesigned 1.5 MHz below its original design frequency, while the other is 2 MHz below its original design frequency. <b>Table 6</b> summarizes the design and performance data for the two designs.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            Table 6:  Design Data for Two 4-Element Quad Arrays
+
+                              Version A:          Version B:
+Element Diameter:             #14 AWG             #18 AWG
+Reflector Circumference:      87.696"             85.264"
+Driver Circumference:         83.448"             83.136"
+Director 1 Circumference:     80.960"             80.712"
+Director 2 Circumference:     78.554"             78.272"
+Refl-Driver Spacing:          15.152"             16.320"
+Driver-Dir 1 Spacing:         12.460"             13.187"
+Dir 1-Dir 2 Spacing:          12.452"             11.192"
+Total Boom Length:            40.064"             40.699"
+Feedpoint Impedance:          42.4 Ohms           42.4 Ohms
+Free-Space Gain:              10.18 dBi           10.05 dBi
+
+                      Performance Data:  144-148 MHz
+
+Version A:
+Frequency Free-Space     Front-to-      Feed Impedance 50-Ohm SWR
+  MHz     Gain dBi       Ratio dB       R +/- jX Ohms
+ 144       9.68           7.99          31.6 - j 32.9       2.50
+ 145       9.99          10.25          34.9 - j 12.8       1.60
+ 146      10.18          12.81          39.0 + j  6.4       1.33
+ 147      10.27          15.61          43.5 + j 24.3       1.71
+ 148      10.30          18.43          47.7 + j 40.4       2.24
+
+Version B:
+Frequency Free-Space     Front-to-      Feed Impedance 50-Ohm SWR
+  MHz     Gain dBi       Ratio dB       R +/- jX Ohms
+ 144       9.55           7.89          35.6 - j 39.0       2.50
+ 145       9.86          10.04          38.6 - j 17.3       1.60
+ 146      10.05          12.42          42.4 + j  3.7       1.20
+ 147      10.14          14.85          46.7 + j 23.7       1.63
+ 148      10.17          16.86          50.8 + j 42.4       2.27
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The similarity of the final designs is a function of their design premises: to use thin wire and a short boom. There should be little wonder that the performance is similar for each array, since there is so little difference in the design, despite their independent sources.</p>
+  <p>The two designs have boom lengths about 6" longer than the average 3-element quad, and their design frequency gain level is only about 0.4 dB higher than the best of the high-gain series of 3-element quads. The point of maximum front-to-back ratio is well above the passband of the array (that is, above 148 MHz). Finally, the neither antenna manages to provide less than 2:1 SWR across 2-meters.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 7:  Design Data for a Wide-Band 4-Element Quad
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.                                 2.
+Wire Diameter:           0.0625"        Wire Diameter:           0.125"
+Reflector Circumference: 86.658"        Reflector Circumference: 87.360"
+Driver Circumference:    82.448"        Driver Circumference:    82.728"
+Refl-Driver Spacing:     13.218"        Refl-Driver Spacing:     13.218"
+Dir 1 Circumference:     78.024"        Dir 1 Circumference:     77.952"
+Refl-Dir 1 Spacing:      38.885"        Refl-Dir 1 Spacing:      38.885"
+Dir 2 Circumference:     75.264"        Dir 2 Circumference:     75.192"
+Refl-Dir-2 Spacing:      68.338"        Refl-Dir-2 Spacing:      67.947"
+Feedpoint Impedance:     60.6 Ohms         Feedpoint Impedance:     58.5 Ohms
+Free-Space Gain:         10.23 dBi      Free-Space Gain:         10.40 dBi
+&lt; 2:1 swr bandwidth:     4.11 mhz       &lt; 2:1 swr bandwidth:     4.50 mhz
+&gt;20 dB F-B Bandwidth:    2.53 MHz       &gt;20 dB F-B Bandwidth:    2.90 MHz
+
+3.                                 4.
+Wire Diameter:           0.25"          Wire Diameter:           0.5"
+Reflector Circumference: 88.448"        Reflector Circumference: 89.976"
+Driver Circumference:    83.072"        Driver Circumference:    83.424"
+Refl-Driver Spacing:     13.218"        Refl-Driver Spacing:     13.218"
+Dir 1 Circumference:     77.782"        Dir 1 Circumference:     77.760"
+Refl-Dir 1 Spacing:      38.885"        Refl-Dir 1 Spacing:      38.885"
+Dir 2 Circumference:     74.992"        Dir 2 Circumference:     74.352"
+Refl-Dir-2 Spacing:      67.446"        Refl-Dir-2 Spacing:      66.953"
+Feedpoint Impedance:     57.3 Ohms         Feedpoint Impedance:     55.0 Ohms
+Free-Space Gain:         10.52 dBi      Free-Space Gain:         10.61 dBi
+&lt; 2:1 swr bandwidth:     5.06 mhz       &lt; 2:1 swr bandwidth:     5.59 mhz
+&gt;20 dB F-B Bandwidth:    3.39 MHz       &gt;20 dB F-B Bandwidth:    4.01 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="2mq-22.gif" width="646" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p>However, it is possible to design 4-element quads with better than 10 dB free-space gain across the entirety of 2-meters. <b>Table 7</b> provides the specifications for 4 such quads with our standard range of element diameters. As shown in <b>Fig. 22</b>, even the thinnest element provides good gain across the band, although the 0.5" diameter version supplies an additional 0.4 or more dB gain.</p>
+  <center>
+    <img src="2mq-23.gif" width="647" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p>These wide-band 4-element quads are only relatively wide--that is, for the class of 4-element quads. In <b>Fig. 23</b>, we can see that only the 0.5" version of this design provides better than 20 dB 180-degree front-to-back ratio for the entirety of 2 meters, although the thinnest element version provides better than 15 dB front-to-back ratio across the band. The SWR curves in <b>Fig. 24</b> reveal that 3 of the 4 arrays meet the 2:1 SWR standard. Since (as shown in <b>Table 7</b>) the resonant impedances are all close to 50 Ohms, these curves will reflect performance with a standard 50-Ohm cable as well.</p>
+  <center>
+    <img src="2mq-24.gif" width="646" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Very often gain and 180-degree front-to-back ratios come at the expense of general pattern shape. However, the designs we are presently discussing have well controlled patterns. The free-space azimuth patterns for the 0.5" diameter element version of the array appear in <b>Fig. 25</b> to verify this claim. The forward lobe is especially consistent from one end of the band to the other, while the rear lobes remain quite well controlled.</p>
+  <center>
+    <img src="2mq-25.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The arrays that we have sampled emerged from a small GW Basic program, which is listed in <b>Appendix 4</b>. The optimized samples that provided the basis for the regression analysis are extensions of the 2- and 3-element wide-band quads that we earlier discussed.</p>
+  <center>
+    <img src="2mq-26.gif" width="646" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The collection of quad designs with which we have been working reveals some interesting trends. <b>Fig. 26</b> graphs the design-frequency gains of all four programmed quad designs for each of the sample 2-meter element diameters. Although the relative gain figures for 2-, 3-, and 4-element quads are interesting, the relative slope of the curves is the key attention-getter. Note that the more elements we add to the quad design, the more dependent the quad becomes on the element diameter. Making multi- element quads of thin wire at VHF and up is one way to lose a significant part of any design's potential.</p>
+  <center>
+    <img src="2mq-27.gif" width="646" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 27</b> reveals another fact of life about quads: the greater the number of elements, the narrower the SWR bandwidth of the array. Above a certain number of elements (I do not yet know the exact number), the only way to achieve a wide SWR bandwidth may be to stagger parasitic elements. However, in every case of stagger-tuned elements, the gain falls below maximum. Hence, the multi-element quad may be self-limiting relative to competeing designs wherever operating bandwidth is a significant consideration.</p>
+  <p>If we permit a narrower operating bandwidth, then we can derive considerably more gain from a 4-element quad. For significantly higher gain from a 4-element quad, we must turn to a design with fat elements and wide spacing. <b>Table 8</b> lists the structural parameters of one such design.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 8:  Design Data for a High-Gain 4-Element Quad
+
+Element Diameter:             0.5"
+Reflector Circumference:      89.120"
+Driver Circumference:         83.760"
+Director 1 Circumference:     77.760"
+Director 2 Circumference:     74.080"
+Refl-Driver Spacing:          13.200"
+Driver-Dir 1 Spacing:         25.937"
+Dir 1-Dir 2 Spacing:          30.715"
+Total Boom Length:            69.840"
+Feedpoint Impedance:          43.1 Ohms
+Free-Space Gain:              10.98 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Three items should be immediately apparent from <b>Table 8</b>. First, the design uses large-diameter elements: 1/2" in this case. Second, the boom is quite long--about 2" shy of 6'. Third, the design frequency gain is nearly a full dB higher than for the short-boom models with which we began our foray into 4-element quads. The question remaining is whether we have made sufficient improvements to justify the added mechanical requirements of a quad over a Yagi.</p>
+  <p>To partially answer this question, I shall present the design data for 3 OWA Yagis for 2 meters: a 6-element design using 3/16" elements, a 7-element design using 0.1" elements, and another 7-element design using 1/4" elements. Comparative physical and performance data may prove instructive--at least provisionally.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   Table 9:  Design Data for 3 OWA Yagis
+
+Antenna                  6 0.1875" El        7 0.1" El      7 0.25" El
+Reflector Length              40.520"        41.180"        41.200"
+Driver Length                 39.962"        39.634"        39.400"
+Director 1 Length             37.376"        37.338"        36.800"
+Director 2 Length             36.310"        36.660"        36.100"
+Director 3 Length             36.310"        36.730"        36.100"
+Director 4 Length             34.960"        36.542"        35.900"
+Director 5 Length              ----          34.856"        34.200"
+Refl-Driver Spacing:          10.130"         8.570"         8.942"
+Driver-Dir 1 Spacing:          4.192"         4.923"         4.658"
+Dir 1-Dir 2 Spacing:          10.974"        12.016"        12.030"
+Dir 2-Dir 3 Spacing:          11.356"        15.484"        15.253"
+Dir 3-Dir 4 Spacing:          16.936"        20.848"        20.538"
+Dir 4-Dir 5 Spacing:           ----          22.488"        22.079"
+Total Boom Length:            54.218"        84.329"        83.500"
+Feedpoint Impedance:          50.0 Ohms      45.7 Ohms      44.3 Ohms
+Free-Space Gain:              10.23 dBi      11.47 dBi      11.55 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>As shown in <b>Table 9</b>, the boom lengths of the Yagis bracket our improved 4-element quad array. The 70" quad boom lies roughly evenly between the 54" 6-element Yagi boom and the 84" 7-element Yagi booms. As well, the 4-element quad gain also lies between the Yagi numbers. However, before we make judgments using date from just the design frequency, let's survey the entirety of the 2-meter band for all 4 antenna designs.
+  <center>
+    <img src="2mq-28.gif" width="647" height="524" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 28</b> shows the free-space gain figures for the 4 antennas--3 Yagis and a quad. Apparent is the greater stability of the Yagi gain, as the quad changes gain by over 0.4 dB across the band. By way of contrast, the Yagis show a maximum gain change of about 0.2 dB. How significant this factor is will be a user judgment.</p>
+  <center>
+    <img src="2mq-29.gif" width="645" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 180-degree front-to-back figures appear in <b>Fig. 29</b>. Although the 6-element OWA Yagi shows the highest peak front-to-back ratio, the band-edge values for all three Yagis are very similar and are above 20 dB. In contrast, the 4-element quad achieves a 20 dB front-to-back ratio for only about 3/4 of the passband. Once more, the relatively narrow-band operating characteristic of the quad emerges.</p>
+  <center>
+    <img src="2mq-30.gif" width="648" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <p>All of the antennas achieve 50-Ohm SWR values of under 2:1 across 2 meters, as shown in <b>Fig. 30</b>. All three OWAs have values of under 1.25:1 across the band, with the 7-element 0.25" element version achieving under 1.2:1 across 2 meters. All three Yagis can be tweaked for this performance. The quad comes nowhere near this performance, although it does stay within the &lt;2:1 standard. Whether the OWA curves are significantly preferable to the quad curve may rest on a user judgment of the significance of line losses within the total antenna-feedline system.</p>
+  <center>
+    <img src="2mq-31.gif" width="470" height="390" border="2" vspace="5" hspace="9">
+  </center>
+  <p>It is interesting also to investigate pattern shape for various antennas that one might consider using. <b>Fig. 31</b> compares the free-space azimuth patterns for the quad with those for the 0.25" element 7-element OWA Yagi. The Yagi displays better control of rear quadrant radiation across the band. However, the long Yagi also shows some "neck bulges," that is, emergent secondary lobes. Similar lobes are just appearing within the quad pattern, but are far less prominent. To an antenna designer who is not under the press of commercial deadlines, the existence of all such pattern bulges is a sign that further development work is in order. Such emergent lobes are not always eliminable, but the purist tries anyway. This last note is a way of saying that the work is still in progress and far from complete.</p>
+  <h3>Some Very Tentative Conclusions</h3>The conclusions to be drawn from this investigation may be obvious, but are perhaps worth noting anyway.
+  <p>1. For quad design at VHF, using large-diameter elements can be beneficial in achieving close to the full theoretical gain of a quad over a Yagi with a similar number of elements. Thin-wire elements narrow the operating bandwidth and reduce gain by significant amounts.</p>
+  <p>2. Traditional short-boom monoband quad designs fail to realize full quad gain and bandwidth by overlooking the naturally higher mutual coupling of quad elements--a factor that dictates longer boom lengths for optimal performance (relative to arrays with linear elements).</p>
+  <p>3. Quads up through 3 elements are certainly capable of performance that is superior to that of Yagis with the same number of elements and relevantly similar boom lengths. However, above 3 elements, the need for added boom length to achieve optimum inter-element coupling may set a limit on the utility of quads wherever operating bandwidth is an equal concern with gain.</p>
+  <p>4. Quads--even short-boom quads--may still excel for narrow-band applications. However, achieving full performance from a narrow-band quad requires the use of sizable element diameters. Otherwise, the simplicity of VHF Yagi construction may prevail, especially with the availability and simplicity of OWA designs.</p>
+  <p>5. When it comes down to simple and cheap utility antennas with some gain and directivity, the Yagi-quad decision becomes more a matter of what materials are available and less upon the purist considerations that have gone into these notes. Coat hangers, scrap wire, wood, and PVC have yielded generations of utility antennas of either the Yagi or the quad type.</p>
+  <p>6. The work is far from done.</p>
+  <pre>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 1:
+    A GW Basic Program to Calculate Dimensions of a 2-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 2-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U&gt;3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1&lt;-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1&gt;-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00336#:BD=.04966518519#:CD=.2731955556#:DD=.6716364021#:ED=1.644147937#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.003173333333#:BR=.0508237037#:CR=.3081977778#:DR=.8663851852#:ER=2.040064444#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AS=-.003#:BS=-.03551851852#:CS=-.1553055556#:DS=-.2902116402#:ES=-.02540079365#
+240 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+250 AZ=1.976333333#:BZ=30.84751852#:CZ=172.4909722#:DZ=419.5162831#:EZ=519.8747579#
+260 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+270 AG=-.06333333333#:BG=-.7203703704#:CG=-3.010277778#:DG=-5.381375661#:EG=3.738769841#
+280 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+290 AW=1.688666667#:BW=23.76837037#:CW=124.9339444#:DW=295.8872328#:EW=281.2755159#
+300 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+310 AF=-.00266666667#:BF=.388#:CF=4.790666667#:DF=19.55485714#:EF=28.76628571#
+320 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+330 AN=-.08333333333#:BN=-.9462962963#:CN=-3.943055556#:DN=-7.582671958#:EN=-5.23234127#
+340 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+350 WL=299.7925/F:PRINT "Wavelength in Meters =";WL
+360 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+370 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+380 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+390 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+400 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+410 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+420 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+430 PRINT "Approximate Resonant Feedpoint Impedance =";ZR;"Ohms"
+440 PRINT "Approximate Free-Space Gain =";GN;"dBi"
+450 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+460 PRINT "Approximate &gt;20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+470 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+480 INPUT "Another Value = 1, Stop = 2: ";P
+490 IF P=1 THEN 10 ELSE 500
+500 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 2:
+A GW Basic Program to Calculate Dimensions of a Wide-Band 3-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U&gt;3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1&lt;-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1&gt;-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00064:BD=.01044148148#:CD=.06484444444#:DD=.1886626455#:ED=1.232080635#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0009333333333#:BR=.01915555556#:CR=.13983333333#:DR=.4587492063#:ER=1.64042381#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.0012#:BI=-.0209037037#:CI=-.13021111111#:DI=-.3498137566#:EI=.5941126984#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=-.0033#:BS=-.03927777778#:CS=-.1724583333#:DS=-.3239603175#:ES=-.04951547619#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.004866666667#:BP=-.06262962963#:CP=-.29347222222#:DP=-.6174457672#:EP=-.2289269841#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=-2.227066667#:BZ=-26.75247407#:CZ=-115.9142556#:DZ=-217.8183323#:EZ=-79.59203175#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.07#:BG=-.7877777778#:CG=-3.350833333#:DG=-6.143888889#:EG=5.104166667#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=-.05847333333#:BW=-.5028392593#:CW=-.4586494444#:DW=6.080227037#:EW=17.61091389#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11695666667#:BF=1.717985556#:CF=9.6510925#:DF=25.23848992#:EF=27.78167988#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 AN=-.04666666667#:BN=-.5414814815#:CN=-2.302777778#:DN=-4.364074074#:EN=-3.092777778#
+380 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+390 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+400 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+410 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+420 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+430 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+440 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+450 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+460 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+470 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+480 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+490 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+500 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+510 PRINT "Free-Space Gain =";GN;"dBi"
+520 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+530 PRINT "Approximate &gt;20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+540 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+550 INPUT "Another Value = 1, Stop = 2: ";P
+560 IF P=1 THEN 10 ELSE 570
+570 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 3:
+A GW Basic Program to Calculate Dimensions of a High-Gain 3-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "Alternate Design",,,"L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U&gt;3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1&lt;-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1&gt;-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.000266666667#:BD=.00506666667#:CD=.03633333333#:DD=.1221904762#:ED=1.183285714#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0037333333333#:BR=.05362962963#:CR=.29275555556#:DR=.7424529101#:ER=1.814412698#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.00266666667#:BI=-.033244444444#:CI=-.1550666667#:DI=-.3222793651#:EI=.7283809524#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=.00033333333#:BS=.004837037037#:CS=.02552777778#:DS=.05643756614#:ES=.2191230159#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.002333333333#:BP=-.03128148148#:CP=-.15586111111#:DP=-.3417669312#:EP=-.05499206349#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=4.4029#:BZ=53.43954444#:CZ=239.2408583#:DZ=462.3614437#:EZ=373.3035655#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.15#:BG=-1.768518519#:CG=-7.763055556#:DG=-14.78592593#:EG=-.609722222#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=.16666666667#:BW=2.265925926#:CW=11.706111111#:DW=27.93058201#:EW=28.88753968#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11933333333#:BF=1.671777778#:CF=8.9885#:DF=22.45931746#:EF=23.68797619#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+380 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+390 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+400 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+410 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+420 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+430 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+440 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+450 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+460 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+470 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+480 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+490 PRINT "Free-Space Gain =";GN;"dBi"
+500 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+510 PRINT "Approximate &gt;20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+520 INPUT "Another Value = 1, Stop = 2: ";P
+530 IF P=1 THEN 10 ELSE 540
+540 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 4:
+A GW Basic Program to Calculate Dimensions of a Wide-Band 4-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 4-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U&gt;3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1&lt;-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1&gt;-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=-.00018:BD=-.002359259259#:CD=-.01090277778#:DD=-.01971296296#:ED=.1174938889#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED:DE=DE*8
+210 AR=.0002666666667#:BR=.004237037037#:CR=.02554444444#:DR=.07158756614#:ER=.2119230159#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER:RE=RE*8
+230 AI=-.0002#:BI=-.002525925926#:CI=-.01182777778#:DI=-.02473915344#:EI=.1008246032#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI:IR=IR*8
+250 AT=-.0006#:BT=-.009059259259#:CT=-.04912777778#:DT=-.1152343915#:ET=.01678174603#
+260 TT=(AT*(D1^4))+(BT*(D1^3))+(CT*(D1^2))+(DT*D1)+ET:TT=TT*8
+270 SP=.1635:IP=.481
+280 ATT=.0026666666667#:BTT=.036888888889#:CTT=.177#:DTT=.3386587302#:ETT=1.046738095#
+290 TTP=(ATT*(D1^4))+(BTT*(D1^3))+(CTT*(D1^2))+(DTT*D1)+ETT
+300 AZ=1.2#:BZ=13.92592593#:CZ=60.777777778#:DZ=113.9177249#:EZ=132.618254#
+310 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+320 AG=-.1#:BG=-1.184444444#:CG=-5.228333333#:DG=-9.831507937#:EG=4.045238095#
+330 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+340 AW=-.06663333333:BW=-.6539148148:CW=-1.677836111:DW=1.361137831:EW=9.502790079
+350 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+360 AF=-.03#:BF=-.27666667#:CF=-.4475#:DF=2.348809524#:EF=7.853214286#
+370 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+380 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+390 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+400 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+410 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+420 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+430 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+440 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+450 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+460 PRINT "Director 1 Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+470 PRINT "Director 1 Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+480 PRINT "Director 1-Reflector Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+490 PRINT "Director 2 Side =";(TT/4);" WL or";(TT/4)*WF;"Feet or";(TT/4)*WL;"Meters"
+500 PRINT "Director 2 Circumference =";TT;" WL or";TT*WF;"Feet or";TT*WL;"Meters"
+510 PRINT "Director 2-Reflector Space =";TTP;" WL or";TTP*WF;"Feet or";TTP*WL;"Meters"
+520 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+530 PRINT "Free-Space Gain =";GN;"dBi"
+540 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+550 PRINT "Approximate &gt;20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+560 INPUT "Another Value = 1, Stop = 2: ";P
+570 IF P=1 THEN 10 ELSE 580
+580 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 04-21-2001. &COPY; L. B. Cebik, W4RNL. This article first appeared in</i> Proceedings of the 2001 Southeastern VHF Society Conference <i>(ARRL, 2001), pp. 116-156. 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="quadlist.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40">Go to Quad List</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#quad'>Quad</a>, <a href='../topics.html#vhf-uhf'>VHF / UHF</a></p><br>
+</body>
+</html>

content/quad/3bq.html

@@ -0,0 +1,136 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Quad, HF Upper">
+  <title>3-Band, 2-Element Spider-Supported Quad Beam</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>A 3-Band, 2-Element Spider-Supported Quad Beam</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>One of the most difficult tasks in designing a multi-band 2-element quad beam is obtaining full band coverage. This problem has two dimensions. One dimension involves obtaining at the antenna an SWR that is less than 2:1 relative to the impedance of the main feedline all across each of the bands covered by the beam. The second dimension covers other important operating parameters, such as adequate gain and front-to-back ratio across each band.</p>
+  <p>The design that we shall show covers only the widest amateur upper-HF bands: 20, 15, and 10 meters. For the narrower bands, 17 and 12 meters, one may use a dual-band quad with a common feedpoint, as shown in Part 3 of the recent series of articles analyzing the element interactions and the use of a common feedpoint. The present beam uses separate feedpoints and restricts coverage to only 3 bands in order to obtain between adjacent bands the largest feasible frequency ratios. The result is relevantly similar band-to-band performance and a set of manageable feedpoint resistance and reactance values. By judicious use of a 75-Ohm matching line on each band, the 50-Ohm SWR values will be under 2:1 across all passbands.</p>
+  <p>The design specifically excludes the narrow bands, even though we might have thrown in loops for them. In the latter portion of our discussion, we shall examine a pair of 5-band designs previously analyzed in Volume 1 of <i>Cubical Quad Notes</i>. The exercise will clearly indicate why a 3-band limit within the upper HF range is desirable for a 2-element quad.</p>
+  <p><b>The Physical Design</b></p>
+  <p>The tri-band quad sketched in <b>Fig. 1</b> derives from the same set of monoband 2-element quads that we have used as the basis for dual-band quad behavior. In fact, it is simply a refined version of the sample tri-band, 2-element quad shown in Part 2 of "Sneaking Up on 2-Element Common-Feed Quads." The design frequencies for the 3 bands are 14.14, 21.19, and 28.4 MHz. At these frequencies, the monoband quads are set for resonance (within +/-j 1 Ohm) and for peak 180-degree front-to-back ratio. At the design frequency, the free-space forward gain is 7.04 dBi on all frequencies. The designs derive from calculations based on a large collection of models and regression analysis. The programs appear in Volume 2 of <i>Cubical Quad Notes</i> and require the designer only to input the element diameter and the design frequency. The model outline sketch on the left shows the positions of the 3 separated feedpoints, but not the match-line needed to feed the array with a 50-Ohm main cable. Of course, only one feedpoint would be active at any one time, so the array requires a remote switch on the mast or 3 separate feedlines to the shack.</p>
+  <center>
+    <img src="3bq-1.gif" width="481" height="340" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In adapting these monoband designs for a tri-band quad, I am using spider construction. It requires non-conductive support arms that "lean" forward and backward about 31 degrees relative to a vertical line created by the mast is it reaches the hub (and virtually passes through to continue that line). This angle is the average of the angles for each of the 3 bands. Since AWG #14 copper wire has a different diameter on each band if we measure it in wavelengths, the angle varies slightly from band to band. However, the small discrepancy in driver-to-reflector spacing will make no practical difference in the performance. The loop lengths are much more sensitive to changes. If a builder wishes to use the specified spacing between elements, he or she may attach a fiberglass or similar rod between the forward and rearward support arms near to the elements for each band.</p>
+  <p><b>Table 1</b> provides the required dimensions for the tri-band 2-element quad. All dimensions are in inches. The side lengths are for full sides. Modelers may need to divide those numbers by 2 in order to center a NEC or MININEC model at the center of the coordinate system. Later, all performance numbers will use free-space values. The gain of the array over ground will increase by about 5 or more dB (depending upon the actual height), but the front-to-back ratio will remain unchanged. If the array is at least 1 wavelength above ground, the impedance will be virtually unchanged from the free-space value. Even at lower heights, the quad is less prone to ground-induced impedance changes than a beam using linear elements. The quad loop is actually two dipoles spaced about 1/4 wavelength vertically, with the ends brought together at the zero-current points. When measured as a function of the elevation angle of the main lobe and the same angle for a dipole or 2-element Yagi, the working height of a quad is about 2/3 of the distance from the bottom to the top horizontal wires. For non-critical purposes, the centerline or the hub height will do as the conventional marker of antenna height.</p>
+  <center>
+    <img src="3bq-t1.gif" width="460" height="241" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The dimensional table lists the sizes of the foundational monoband quads as well as the dimensions used in the tri-band version. For each band, the driver-to-reflector spacing remains unchanged. On 20 meters, the tri-band driver is longer than the monoband driver, but the tri-band reflector is shorter. On 10 meters--the innermost set of loops--the tri-band driver is shorter than the monoband driver, but the tri-band reflector is longer. In the recent study of dual-band interactions ("Adjacent-Band Quad Behavior"), I noted that when an element set undergoes interactions with both an inner and an outer set of elements, the middle set is not influenced equally. Hence, the effects on both the middle driver and reflector are not simply canceled out. In the case of the present tri-band design, the 15-meter driver and reflector are both shorter than in the monoband design on which they rest.</p>
+  <p>Each driver requires a match-line consisting of a length of 75-Ohm cable. The 20-meter quad uses a relatively precise 1/4 wavelength. On 15 meters, 1/4 wavelength is about 139", while on 10 meters, 1/4 wavelength or close to 104". The prescribed lengths for 15 and 20 are both shorter. When we examine the modeled performance data for the quad, we shall better understand why the lines use less than a full quarter wavelength of impedance transformation. Since the quad uses square rather than diamond construction, the match-lines (or even directly connected main feed lines) require support. I recommend the use of a UV-protected rope running from the hub through each feedpoint. You may then tape or otherwise clamp the match-lines to the rope, since coaxial cable is not designed to support loads--not even its own weight for very far. Of course, there is no rule that requires a coaxial match-line. Parallel 75-Ohm transmission line--if available or if you can fabricate it--will work as well. However, at the remote switch or the transition to a 50-Ohm coaxial feed line, you will need a 1:1 balun or ferrite-bead choke to suppress (or, more correctly, attenuate) common-mode currents. Such a device is good practice at the remote switch even if you use coaxial cables for the match-lines.</p>
+  <p>The dimensions for the tri-band quad are more finicky than those for a monoband quad (but less finicky than the dimensions for a 5-band quad). Therefore, you will wish to use careful construction methods to avoid the need for nearly endless field adjustments. The support arms should be non-conductive. As well, the method for attaching the elements to the arms at the element corners should make use of non-conductive materials or hardware. Metal clamps or loops can create 1-turn inductors at the element corners. The 4 required for each element may be enough to significantly detune the element. There are methods of compensating for such methods of fastening, but they tend to be long and tedious. If you are constructing quads commercially, going through the compensation process once for each new design may well be worth the effort to obtain a desired set of corner fixtures. However, for a one-of-a-kind antenna that grows out of one's workshop, giving some extensive forethought to designing an effective means of arm-to-element attachment that involves only non-conductive materials may actually shorten the construction time considerably.</p>
+  <p><b>TriBand Performance</b></p>
+  <p>The goal of the design was to obtain--to the degree possible--all of the performance potential offered by the monoband quads that form the basis for each element set. Studies in element interaction suggest that we may not be able to succeed completely. However, we may be able to develop a very good tri-band quad. As a yardstick, a short-boom Yagi will show about 7+ dBi free-space gain. Here, a short boom is about 8' on 10 meters and 16' on 20 meters. (A long-boom 3-element Yagi might develop just over 8-dBi free-space gain, where a long-boom on 20 is about 24' and on 10 is about 12'.) A 2-element driver-reflector Yagi may be able to manage about 6 dBi free-space gain. The 2-element Yagi front-to-back ratio will run between 10 and 12 dB across any of the wider amateur upper HF bands. However, a well-designed short-boom 3-element Yagi may achieve 20 dB across 20 and 15 meters and at least 17-18 dB across 10 meters. Although it is possible to design a 2-element driver-reflector Yagi for direct connection with a 50-Ohm cable, most higher-performance Yagis below 6 elements require a matching network to raise a lower feedpoint impedance to the usual 50-Ohm cable impedance. In general, a 2-element quad can match the gain of a short-boom (but not a long-boom) 3-element Yagi, but the quad suffers fairly narrow bandwidth for its front-to-back performance. Under the best conditions, a monoband quad will show band-edge front-to-back ratio values somewhere between 12 and 18 dB, depending on the passband width. For this reason, I have used an initial monoband quad design with the broadest possible bandwidth for both the front-to-back and impedance performance.</p>
+  <p>Element interactions in a multi-band beam will limit our ability to achieve full monoband performance. However, Gain is not one of those limitations. As shown by the graph in <b>Fig. 2</b>, the gain curves are normal or above normal for 2-element monoband quads. The design frequency is at the 40% marker on the steps up each of the bands. At that point, the monoband gain is about 7.04 dBi, and even the 20 meters elements achieve this level. The more inward loop sets manage slightly higher gain levels. However, the difference in not sufficient to be operationally noticeable. We may note in passing that the closer a set of elements is to the outer position, the steeper is the slope of gain decrease with rising frequency.</p>
+  <center>
+    <img src="3bq-2.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Like all 2-element driver-reflector parasitic structures, the gain decreases as the frequency increases. The rate of descent of even the steepest curve is not far from the monoband curve. (Any parasitic array with at least one well-designed director will show a reverse curve, that is, one that increases in gain with rising frequency. For example a typical short-boom Yagi would show a curve that is virtually the reverse of the quad gain curves, but with very similar band-edge gain values.)</p>
+  <p>One reason for tweaking the dimensions of the tri-band beam elements was to place the front-to-back peak as close as feasible to the design frequency on each band. The curves in <b>Fig. 3</b> measure the success of that move. I wanted to find out if centering the front-to-back peak at the design frequency would yield relatively equal band-edge values, as the process did for the monoband quads. The band-edge front-to-back values are only slightly less equal than for the monoband beams on which this design rests.</p>
+  <center>
+    <img src="3bq-3.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For comparative purposes, the monoband 20 meter quad achieves about 16-dB front-to-back values at the band edges. The tri-band 20 meter elements fall from 1 to 2 dB below that value. The 15-meter monoband quad shows about 18-dB at the band limits. The 15-meter elements of the tri-bander are again about 1-2 dB lower. On 10 meters, the monoband quad reached a very high peak level, with about a 14-dB front-to-back ratio at 28 and 29 MHz. The inward position of the 10-meter elements in the triband quad prevents us from achieving the very high peak front-to-back value, but the band-edge values are 2 to 3 dB higher than for the monoband model.</p>
+  <p>We must add two notes to these reports of modeled performance. First, the actual peak front-to-back ratio--as a 180-degree value--will not be as operationally significant as it is dramatic in the graphs. Not only is the peak a narrow-bandwidth phenomenon, it is also a dimple in the overall rearward gain levels of the array. Second, the values appear in the graphs due to simple changes in the modeled array geometry. It is also unlikely that one will be able to precisely place the peak value with respect to frequency. (The best way to tell is to perform tests with a nearby patient friend, with the quad pointed directly away from that station.) The final construction-ending test is the adequacy of the front-to-rear overall performance, especially at the band edges.</p>
+  <p>The band-edge patterns are quite unlike those at the design frequency or at the nearby band center. To show the range of likely patterns, <b>Fig. 4</b> presents a gallery of free-space E-plane (azimuth) patterns for each of the bands, using the band limits and the band center as snapshot frequencies.</p>
+  <center>
+    <img src="3bq-4.gif" width="600" height="600" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The patterns show both good and not quite so good things about 2-element quad performance in a tri-band array. The very good aspect of the gallery views is the fact that the patterns for each band are very similar for corresponding positions in each band. The design constraints brought to the project have resulted in a quad that performs in a very similar manner on each of the included bands. Less than very good is a fundamental limitation in the rearward lobes of a quad when used on a wider amateur band. Note that the lines that indicate the strongest rearward gain have similar values at the lower band edge and at mid-band: very roughly 15 dB below the main forward lobe. However, at the upper band edge, the worst-case front-to-back ratio is down to about 12 dB or so, even though the 180-degree value is somewhat higher. We would find the same pattern of rearward lobes, even using monoband quads.</p>
+  <p>The next step in our review of tri-band quad performance takes us into the region of the feedpoint impedance. The monoband quads showed design-frequency resonant impedance values between 130 Ohms at 20 meters to 136 Ohms at 10 meters. Those values allow us to use a standard 1/4 wavelength 75-Ohm match-line on any of the monoband quads to obtain a good match to a 50-Ohm main feed cable and still have an acceptable SWR across each of the bands.</p>
+  <center>
+    <img src="3bq-5.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 5</b> shows what happens to the feedpoint impedances in terms of resistance and reactance before we add any matching devices or networks. Again, the 40% marker represents the approximate design frequency for each band. At this point, we can see the crossing reactance lines at about j0 Ohms. As we learned in the study of adjacent-band quad behavior, it does not matter whether a multi-band loop set occupies an outer or an inner position. The feedpoint resistance will decrease. The 20-meter value is about 123 Ohms. Perhaps the new information offered by the tri-band quad is that as we add set of loops, the resistance decreases further as we move toward the innermost set. On 15 meters, the resonant impedance is only about 106 Ohms, and on 10 meters, it has decreased to 94 Ohms. We shall look at these values once more in the last part of these notes when we compare tri-band performance to 5-band performance.</p>
+  <p>The reactance curves are rather modest for 20 and 15 meters, partly as a function of having other element sets inward from them and partly because the bands are between 2.1% and 2.5% wide. In contrast, the 10-meter reactance curve undergoes the greatest excursion and virtually in a linear progression. The size of the excursion of reactance is a joint function of the added bandwidth (3.5% wide) and the fact that the 10-meter elements are the most inward of the bands included in this array.</p>
+  <p><b>Fig. 6</b> shows the resistance and reactance at the shack-end of the match-line prescribed for each band. On 20-meters, we can employ a 1/4 wavelength 75-Ohm line, which is about 209" at the design frequency. A corresponding 15-meter line would be about 139" long. However, a transmission line effects an impedance transformation at any length. By judicious line length selection, we can often achieve a more desirable set of resistance and reactance values across a given band. Note that the use of a 130" line on 15 yields band-edge resistance values that are very similar to those we obtain on 20 meters with the full 1/4 wavelength line. At the same time, the reactance curve for 15 meters is actually flatter than the one for 20 meters.</p>
+  <center>
+    <img src="3bq-6.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p><i>Important Note</i>: The line lengths noted here are electrical lengths translated into inches. Multiply the listed electrical length by the velocity factor of the line actually used to arrive at the necessary physical line length. For most purposes, you may use 0.66 as the velocity factor for 75-Ohm lines with a solid dielectric and 0.8 for lines with a foam dielectric. However, for best precision, it may be useful to measure the velocity factor of the line used.</p>
+  <p>On 10 meters, we have less than an ideal situation. A quarter wavelength line does not yield an acceptable range of impedances, largely due to the wider range of reactance values that we encounter on this band. However, an electrical length of 95" will yield acceptable SWR values. As shown in <b>Fig. 6</b>, the resistance range is very similar to the range resulting from the 20- and 15-meter match-lines. However, the reactance curve is considerably wider than those for 15 and 20.</p>
+  <p>For most operators, the final measurement is simply the 50-Ohm SWR at the junction of the matchline and the main feed cable. (I am avoiding all temptation to show values that might result from taking measurements 50, 75, 100 or more feet down an actual cable with its loss factors included. These shack-end SWR values will always be lower than the values at the point where the 50-Ohm cable is closest to the antenna.) <b>Fig. 7</b> shows the modeled SWR curves. The match-lines use the NEC-provided lossless cable for the match-line. However, since each match-line is 1/4 wavelength or less, the lossless values are a very good approximation of reality.</p>
+  <center>
+    <img src="3bq-7.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 50-Ohm SWR curves 20 and 15 meters are very satisfactory, with the peak value just over 1.4:1. The 15-meter curve shows a lowest value that is higher than the lowest 20-meter value because the 15-meter match-line is a bit shorter than 1/4 wavelength. Had we used a perfect 1/4 wavelength line, the curve would have still been acceptable, but one end of the band would have shown a much higher value than the other.</p>
+  <p>On 10 meters, we departed the farthest from 1/4 wavelength, and the resulting SWR curve has a low value of about 1.2:1, At the band edges, the SWR is 1.8:1 or slightly higher. The result is an acceptable, but certainly not an outstanding 50-Ohm SWR curve. However, in the world of multi-band 2-element quads, covering the entire first MHz of 10 meters with under 2:1 50-Ohm SWR is itself a bit rare, especially if we wish to achieve any performance across this wide band.</p>
+  <p>The tri-band spider quad based on wide-band monoband quad designs achieves its goals of providing close to monoband performance across all three included bands. Gain is standard. The front-to-back curves are what we might expect from a 2-element quad, and the band-edge values hold up better than in most designs. The use of match-lines for the separate feedpoints on each band allows us to obtain very good 50-Ohm SWR curves on 20 and 15, with an acceptable curve on 10 meters.</p>
+  <p>We have a left over question that is more than trivial. Why not include all 5 upper HF amateur bands in the array? There is a very straightforward answer, but it may not be completely believable without a demonstration. Therefore, let's spend a little time exploring the performance of some typical 5-band spider quads.</p>
+  <p><b>3 Bands or 5 Bands</b></p>
+  <p>In Volume 1 of <i>Cubical Quad Notes</i>, I reviewed the performance of two different but related 5-band 2-element quad beams. Both used spider construction and thus had the general layout shown in <b>Fig. 8</b>. The figure shows the positions of all of the feedpoints, but only 1 would be active at a time. The difference between the two beams rested on the spacing between elements. The narrow version used an element spacing of 0.125 wavelength. The wide version used a spacing of 0.174 wavelength or 6' at 10 meters.</p>
+  <center>
+    <img src="3bq-8.gif" width="300" height="340" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Both quad beams differed from the present design not only in spacing, but as well in the design frequency used for the wider amateur bands. The design frequency for all bands was the mid-band frequency: 14.175, 18.118, 21.225, 24.94, and 28.5 MHz. If I were interested in redesigning these arrays using the prescribed spacing today, I likely would lower the design frequency on each wider band to ensure equalized front-to-back ratios at the band edges.</p>
+  <p>However, our use of these older designs is not to produce a buildable design. The narrow version is attractive in some building circles because it results in a more compact array with arm supports that require less of an angle relative to a vertical line drawn from the mast upward. The required angle is about 25.5 degrees or about 51 degrees between the driver and reflector support arms. The wide version is actually slightly wider than the 3-band quad that we have reviewed in these notes. Relative to a vertical line, the arm angle is a bit over 33 degrees, or 66 degrees total between driver and reflector support arms. Indeed, the wide version will be useful in showing differences between 3- and 5-band quads without having to replicate the newer design in a 5-band version.</p>
+  <center>
+    <img src="3bq-t2.gif" width="389" height="321" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Table 2</b> provides the dimensions for the 2 older 5-band designs. The chart shows both the side length and the circumference of the loops--as well as element spacing--so that you may directly compare the numbers to the corresponding dimensions for the 3-band quad in <b>Table 1</b>. Let's examine the basic free-space performance of these arrays as background for the critical conclusions that we shall draw from them.</p>
+  <p><i>A 5-Band 2-Element Quad Using 0.125-Wavelength Element Spacing</i></p>
+  <p>The use of narrow spacing allows the quad array to achieve slightly higher gain levels than the 3-band version. The differentials average about 0.15 dB, which may not be operationally significant. The gain curves for the 3-wide bands of the array appear in <b>Fig. 9</b>. I have omitted the narrow bands from the performance review. More complete data appear in the original discussion.</p>
+  <center>
+    <img src="3bq-9.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although the front-to-back peaks do not occur precisely at mid-band, as shown in <b>Fig. 10</b>, we can glean something about band-edge performance from the curves. Across the upper HF range, the band-edge front-to-back performance averages from 10 dB at 20 meters to about 15 dB at 10 meters. The corresponding values for the tri-band design at 14 and 17 dB, respectively. The difference is a joint function of the narrower element spacing and the proximity of the loop sets in a 5-band quad beam.</p>
+  <center>
+    <img src="3bq-10.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>One temptation that accompanies a 5-band quad design is to use direct feeding. The impedances suggest that a 75-Ohm feedlines might be satisfactory for the array. <b>Fig. 10</b> shows the 75-Ohm SWR curves of the array for each of the wider bands.</p>
+  <center>
+    <img src="3bq-11.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The results are not satisfactory from the perspective of full band coverage. On 20 meters, we manage to cover about 90% of the band, and with some juggling of the 20-meter driver, we likely would obtain full band coverage. The SWR curve for 15 meters with resonance at mid-band yields only about 75% coverage. However, the low SWR at the upper end of the band suggests that judicious redesign of the 15-meter driver might extend that coverage. However, 10 meters provides only about 30% band coverage. We shall see the reasons for this difficulty after examining the wide 5-band quad array.</p>
+  <p><i>A 5-Band 2-Element Quad Using 0.174-Wavelength Element Spacing</i></p>
+  <p>Wider element spacing provides some improvement in the performance values. The wide 5-band array emerged before the development of idealized 2-element monoband models and hence uses a spacing just wider than optimum. However, as the curves in <b>Fig. 12</b> reveal, the gain values do not differ greatly from those of the tri-band model. The 5-band 20-meter curve is steeper than in the tri-band case, while the 5-band 10-meter gain curves is somewhat flatter. Both results stem from the closer proximity of loop sets in the 5-band model.</p>
+  <center>
+    <img src="3bq-12.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As shown by <b>Fig. 13</b>, the front-to-back performance again fails to place peaks precisely at the mid-band design frequencies. However, band-edge performance is fairly balanced. The 10-meter band-edge values average 19 dB--higher than for the tri-band version. However, the 20-meter band-edge values remain low, averaging about 11 dB. Thus, at the band edges, the band-to-band range of 180-degree front-to-back ratios is about 8 dB, compared to about 3 dB for the tri-band model. The results suggest (but do not definitively prove) that it may be more difficult to obtain even band-to-band 2-element quad performance when covering 5 bands with a lower frequency ratio between adjacent loop sets.</p>
+  <center>
+    <img src="3bq-13.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Direct 75-Ohm feeding of the wide 5-band quad is tempting. In fact, <b>Fig. 14</b> shows that we obtain quite satisfactory 75-Ohm SWR curves on both 20 and 15 meters. 10 meters remains the most difficult case, with only about 75% band coverage with less than a 2:1 75-Ohm SWR ratio.</p>
+  <center>
+    <img src="3bq-14.gif" width="722" height="481" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The wider 5-band quad achieves satisfactory gain values. Within general limitations of 2-element quad design, we might also rate the front-to-back performance as adequate at the band edges. However, the feedpoint impedances remain problematical. To see why, let's compare in a simple table (<b>Table 3</b>) the minimum and maximum resistance values for all three 2-element quad designs. For good measure, we shall also show the range of reactance values that accompany the resistance values across each of the wide upper HF amateur bands.</p>
+  <center>
+    <img src="3bq-t3.gif" width="325" height="305" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The first step is to compare the narrow and the wide 5-band quads. Since the frequency ratio between adjacent loops is the same for both beams, any differences are functions of the element spacing. The average differential in the feedpoint resistance between these two beams is 15 to 20 Ohms, with the higher average on 10 meters. Accompanying the lower feedpoint resistances for the narrow beam is a higher range of reactance values across each of the bands. Narrow element spacing therefore has an obvious negative impact on the ability of the array to cover all of each band. The 5-band arrays also show a systematic lowering of the feedpoint resistance as we increase the frequency band. The inner loops show a systematic lowering of the feedpoint resistance relative to more outward loops. Hence, when we combine this effect with the larger reactance excursion for the inner loops, we obtain large difficulties in covering 10 meters with narrow spacing.</p>
+  <p>The table allows us to make a second comparison, this time between the wide 5-band quad array and the tri-band design that we featured earlier. Note the descending values of feedpoint resistance for the 3-band model: about 90, 80, and 70 Ohms for 20, 15, and 10 meters, respectively. Every multi-band quad shows a reduction in the feedpoint resistance regardless of loop position in the presence of loops for other bands. The lower the frequency ratio between loops, the greater the reduction in feedpoint resistance. The tri-band quad uses frequency ratios between 1.34:1 and 1.5:1.</p>
+  <p>In contrast, the 5-band wide quad uses frequency ratios between bands that average about 1.2:1. As a result, even the 20-meter minimum feedpoint resistance is lower than for the tri-band beam: about 80 Ohms compared to the tri-band value of 90 Ohms. The impedance value declines more rapidly as we move up in the HF region. On 10 meters, the differential between tri-band and 5-band minimum feedpoint resistance values is double that of 20 meters: about 70 Ohms vs. abut 50 Ohms for the 5-band model. For reference, the reactance ranges for the wide 5-band model and the tri-band model are comparable. You may repeat the exercises that we just ran using the maximum resistance values, although the minimum values are perhaps more critical.</p>
+  <p>The net result is that, as we move up the bands of a 5-band 2-element quad array, the feedpoint resistance drops much more rapidly than it does for a tri-band array that omits 17 and 12 meters. On 10 meters, the low resistance accompanied by a wide reactance range results in matching difficulties that are difficult to overcome. In most cases, we must de-rate the 10 meter coverage and even then rely on line losses of the main feedline to achieve a 2:1 SWR across the smaller portion of 10 meters. The comparisons provided by the numbers in <b>Table 3</b> provide a demonstration of a quite general phenomenon. Given pre-set upper and lower frequency limits, the more bands that we pack into a multi-band 2-element quad array, the lower the frequency ratio between adjacent loop sets. As we lower the frequency ratio, the feedpoint resistance drops more rapidly, even though the reactance range may not change very much. The higher the ratio between reactance and resistance, the more difficulties we encounter in effecting a match to a main feedline of a specified characteristic impedance, with or without matching devices or networks.</p>
+  <p>The tri-band quad begins with higher feedpoint resistance values on all band. Hence, we require some form of matching. A 75-Ohm (or similar) match-line that is 1/4 wavelength--or shorter as necessary--allows us to match the quad on each band to a 50-Ohm main feedline. As well, we may achieve full band coverage on all 3 bands with an SWR value of less than 2:1 (without relying upon losses in the main feedline). In a nutshell, this small demonstration shows why I chose to design a tri-band 2-element quad beam rather than stretch for a 5-band model that would fail to provide full-band coverage on 20 through 10 meters.</p>
+  <p><b>Conclusion</b></p>
+  <p>These notes have described and analyzed the structure and performance of a tri-band 2-element quad beam for the wider upper-HF amateur bands of 20 through 10 meters. The design rests upon wide-band monoband quad beams and adjusts the dimensions to obtain as close to monoband performance on each band as feasible. In fact, the beam comes very close to replicating monoband performance. The array allows us to match the individual feedpoints to a 50-Ohm main feedline by the use of 75-Ohm lines of prescribed lengths, some of which are less than the usual 1/4 wavelength. The array presumes the use of a remote switch or separate feedlines for each band. The structure uses spider construction to sustain the required spacing between the driver and the reflector on each band.</p>
+  <p>My choice of a tri-band quad array rather than a 5-band beam results from previous studies of what happens to the feedpoint resistance as we add bands and consequently reduce the frequency ratio between adjacent loops sets. The more bands that we add to a multi-band quad, the lower the ratio becomes. The result is both a general lowering of all feedpoint resistance values and a greater differential between the feedpoint resistance values for 20 and 10 meters. Since the reactance ranges tend not to change by any great amount, the high ratio of reactance to resistance tends to reduce matched coverage of 10 meters, regardless of whether or not we use a matching device or network. By sustaining a higher frequency ratio between adjacent loop sets in a tri-band model, we may overcome the matching issue.</p>
+  <p>All of these notes presume that the general parameters of quad operation over the wide amateur bands are acceptable. A 2-element quad shows good gain with the typical driver-reflector parasitic-assembly decrease in gain with increasing frequency. However, the 180-degree front-to-back ratio shows considerable variability, with a relatively high mid-band peak but band-edge values that are only somewhat higher than the ones that we obtain from a 2-element driver-reflector Yagi. Finally, full-band matching is achievable with an appropriate matching line, but only if we begin with a basic design optimized for wide band coverage.</p>
+  <p>Cubical Quad Notes Vol 1 - 3 available in PDF book format on the <a href="../bookant.html">Books Page</a>.</p>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center>
+  <p><i>Updated 04-01-2007. &COPY; L. B. Cebik, W4RNL. This item appeared in</i> AntenneX<i>, March, 2007. 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" width="591" height="3">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> <b>Return to Amateur Radio Page</b></a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#quad'>Quad</a></p><br>
+</body>
+</html>

content/quad/3l3bq.html

@@ -0,0 +1,108 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Quad, HF Upper">
+  <title>A 3-Band, 3-Element Quad?</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Why Not Use a 3-Band, 3-Element Quad?</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Although we can find a number of designs for 3-element monoband quad beams, we would have a difficult time uncovering tri-band or 5-band versions of them. There are both physical and electrical reasons for this lacuna in the range of available quad multi-band designs. We should spend at least a brief time discovering what the reasons are.</p>
+  <p><b>Monoband 3-Element Quads</b></p>
+  <p>Among 3-element quad beams, we can find both good and mediocre designs. In Volume 2 of <i>Cubical Quad Notes</i>, I offered computer programs for two types of 3-element monoband quads. One version stressed the widest obtainable bandwidth for both the front-to-back ratio and the SWR curve. The other version gave up bandwidth (but not altogether) in exchange for the maximum gain that we might obtain from 3 quad loops, commensurate with a reasonable front-to-back ratio at the design frequency. Both programs (along with a NEC-Win Plus NEC model that incorporated the equations) required only two input variables: the element (wire) diameter in the units in use and the design frequency. <b>Fig.1</b> shows the outlines of the two beam types to provide an idea of their proportions.</p>
+  <center>
+    <img src="3l3bq-1.gif" width="330" height="340" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The wide-band version is about 19% longer than the high gain model. Despite the greater length, the wide-band driver is closer to the reflector than the corresponding element on the high-gain version. The wide-band director is also considerably smaller in circumference than the high-gain director.</p>
+  <p>The wide-band version may be the easier antenna to mount. If you draw a centerline through the elements to represent a boom, then the mid-point of the boom will fall just beyond the "r" in the word "driver." However, since there would be two elements and their support arms left of the midpoint, the actual position for the boom-to-mast plate would fall somewhere within the word "driver." Alternatively, some builders have placed additional weights inside the director end of the boom to provide a mast position closer to the boom mid-point.</p>
+  <p>The situation is a bit more precarious with the high-gain version of the antenna. Here, the mid-point of the imaginary boom line falls close to the "d" in "driver." Since support arms tend to be flexible and an element wire extends across the face of the support mast or tower, builders tend to use counter weights inside the director boom end to arrive at a balance point that maximizes the flexing space for the driver support arms and wire.</p>
+  <p>Because the data will be significant when we explore the electrical properties of attempted tri-band 3-element quads, let's quickly review the potential performance of both types of monoband quads. Since all bands provide similar performance, except for bandwidth issues, we can illustrate performance by reference to the widest of the upper HF bands, 10 meters. <b>Table 1</b> provides the dimensions for both antennas. All dimensions are in inches, and the table lists full side lengths and loop circumferences. The spacing dimension is referenced to the reflector.</p>
+  <center>
+    <img src="3l3bq-t1.gif" width="623" height="230" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The modeled performance in free space for both beams represents close to the best obtainable for 3-element quads of each type. <b>Table 3</b> samples the performance at the band edges and at the design frequency. Note that the worst-case and the 180-degree front-to-back ratios are the same at the band edges and differ only in the middle portion of the band, where the rear lobe shows a characteristic "dimple." Also notable is the difference in beamwidth between the two designs. As gain increases, beamwidth decreases.</p>
+  <center>
+    <img src="3l3bq-t2.gif" width="451" height="354" border="2" vspace="5" hspace="9">
+  </center>
+  <p>We may correlate the main performance data in the table to the gain and 180-degree front-to-back curves for both models in <b>Fig. 2</b>. The high-gain version of the 3-element quad allows one to structure the design so that the maximum forward gain occurs at the design frequency, with lesser values at the band edges. Obtaining a high-gain curve of this shape with a Yagi is not normally possible. The high-gain quad model obtains in its 3 elements about the same gain as a long-boom 4-element Yagi. However, unlike Yagis that usually manage close to a minimum front-to-back ratio of 20 dB across the band, the quad shows the typically narrow-band nature of its front-to-back curve. The high-gain model manages 20-dB front-to-back ratio for only about 35% of the 10-meter band.</p>
+  <center>
+    <img src="3l3bq-2.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The wide-band version of the 3-element quad trades gain for a more acceptable feedpoint impedance range. The trade-off results in a gain level that is about 0.55-dB lower than the high gain model at the design frequency. The design frequency free-space gain level is close to the value obtained from a short-boom 4-element Yagi. In addition, the wide-band model shows peak gain at the low end of the band, with a decreasing gain curve toward the high end. However, the minimum gain value is about 8.2 dBi, about 1.5-dB higher than the minimum value for a 2-element monoband quad on 10 meters. Interestingly, the front-to-back curves for both the wide-band and the high-gain versions of the antenna are very similar. Differences would fall below the operationally noticeable level.</p>
+  <p>The graph also contains a pair of marks at each end--along the upper edge. Since the curves for all 3-element quads derived from the equation models would be very similar, the marks show the curve limits for the 20-meter and the 15-meter amateur bands. You may extrapolate the likely gain and front-to-back values for each band by using these limiting marks. The impedance data in <b>Fig. 3</b> contains the same marks for similar extrapolations.</p>
+  <center>
+    <img src="3l3bq-3.gif" width="744" height="407" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The wide-band resistance curve centers at about 75 Ohms. Although the resistance change across the band is higher than the corresponding change for the high-gain model, the reactance shows a much lower total change from 28 to 29 MHz. Hence, the wide-band models shows a 75-Ohm SWR curve that covers about 900 kHz of the band with less than a 2:1 value. The same curve on 20 and 15 meters would show band-edge values well below 2:1.</p>
+  <p>The resonant impedance for the high-gain model is closer to 50 Ohms, allowing within the limits of the antenna a direct connection to the typical main feedline (with a common-mode current attenuator, of course). However, the total range of reactance across the band limits the 2:1 50-Ohm SWR operating bandwidth to about 600 kHz or about 60% band coverage. Since 20 meters is about 70% of the bandwidth of 10 meters, the curve would not quite allow 2:1 SWR use of that band. However, the curve would just about fit 15 meters, since it is about 60% of the bandwidth of 10 meters.</p>
+  <p>The monoband data will prove useful in evaluating the potential performance of any attempted tri-band 3-element quad. Tri-band 2-element quads managed to produce performance levels on each band that are similar to monoband values for each band. The key electrical question will be whether or not we can expect similar results from a tri-band 3-element quad.</p>
+  <p><b>Tri-Band 3-Element Quads: the Physical Questions</b></p>
+  <p>Typically, there are two ways of constructing a multi-band quad: the spider and the planar methods. The spider method uses the distance between elements as measured in wavelengths as a constant. Therefore, the physical spacing between elements varies from one band to the next. <b>Fig. 4</b> shows a possible arrangement of elements for a tri-band quad in which the drivers form a plane and the reflectors and directors vary their distance in inches, feet, or meters as we change frequency band. The model uses the wide-band version of the monoband quad as the basis for the elements shown.</p>
+  <center>
+    <img src="3l3bq-4.gif" width="481" height="340" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The alternative construction method uses planar support arms for each elements. <b>Fig. 5</b> shows the general outline for such a quad in terms of the element placement. Since the element spacing would be optimal for only one of the 3 bands--at most--the element spacing values will vary according to the design compromises used to create the structure.</p>
+  <center>
+    <img src="3l3bq-5.gif" width="481" height="340" border="2" vspace="5" hspace="9">
+  </center>
+  <p>At this juncture, we shall overlook performance questions to concentrate on the physical challenges presented by each design direction with constructing a tri-band 3-element quad. If we add support arms to the spider quad in <b>Fig. 4</b>, we obtain a sketch resembling the side view shown in <b>Fig. 6</b>.</p>
+  <center>
+    <img src="3l3bq-6.gif" width="472" height="304" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The optimal angles for the parasitic support arms exceed what is wise (or perhaps, even what is possible) using the wide-band quad as a model. Quad support arms must be relatively light and strong, a combination that gives the arms considerable flexibility. When we exceed certain angles (that vary with the arm structure), flexibility turns into sag that tension rods between pairs of forward and rearward arms cannot overcome. We can modify the structure somewhat, perhaps be using the high-gain design with its shorter overall front-to-back dimension. However, even this design would show support-arm angles that threaten serious sag, especially if we add an ice load to the array. The next strategy might be seriously to reduce the spacing between elements. However, this tactic will either reduce the operating bandwidth or reduce the performance level below 3-element expectations.</p>
+  <center>
+    <img src="3l3bq-7.gif" width="432" height="412" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 7</b> shows the fundamental difficulty with all planar 3-element quads. The compromises called for in the electrical performance of this type of multi-band array tend to place the driver very close to the support mast. Typical reflector-to-driver spacing values for upper HF multi-band quads are from 8' to 10'. However, driver-to-director spacing values use the same range. Support arm structures are lightweight and flexible. However, they still have some weight. Hence, even if we use different spacing values for the forward and rearward elements, we must adjust the mast-to-boom connection to compensate for the double X-structure on one side of the mast. The net effect is to put the driver elements in jeopardy of contacting the mast or tower during normal wind loads.</p>
+  <p>For the reasons outlined, we find few 3-element tri-band quad designs available. Most builders prefer to move from 2 to 4 elements. Virtually all 4-element quad designs use planar construction. Hence, the load on each end of the boom, relative to the mast or tower, is equal. The reflector and driver elements go to the rear, while the directors ride in front. It is still important to mount the quad at its center of mass rather than using the boom-length center point. However, even that adjustment leaves several feet of space between the mast and the nearest set of element wires.</p>
+  <p><b>Tri-Band 3-Element Quads: the Electrical Questions</b></p>
+  <p>There is more to dis-recommend a multi-band 3-element quad than just the mechanical details. Someone might well be able to overcome the physical constraints if the 3-element quad offered near-monoband performance on all bands, even if only in a 3-band version. However, we are unlikely to see such an antenna because the 3-element design--when multi-banded--presents some electrical problems.</p>
+  <p>To test the tri-band 3-element quad, I created a number of models using both planar and spider construction. All of the planar models failed to have either the gain or the bandwidth of the wide-band monoband 3-element quad. Since it is not possible in a finite lifetime to exhaust all of the possibilities, I cannot claim the survey to be exhaustive, although it has so far proven both exhausting and futile. Among spider models, the version of the antenna shown in <b>Fig. 4</b> and in <b>Fig. 6</b> proved to provide the best performance. <b>Table 3</b> samples that performance at the design frequencies. The table also lists the design-frequency monoband performance on all 3 bands to ease the task of making comparisons.</p>
+  <center>
+    <img src="3l3bq-t3.gif" width="492" height="307" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The table clearly shows that we encounter a lower feedpoint resistance as we increase the frequency. However, the rate of decrease is lower than for 2-element tri-band quads. The reduced rate rests on a combination of factors, including the planar arrangement of the drivers and the fact that each driver has two elements that exert influence on the feedpoint impedance. Were it not for other factors, we might use this beam without further adjustment to the driver lengths.</p>
+  <p>Unfortunately, as we increase frequency, we also see a decline in the array gain. In fact, the 10-meter gain falls within the range that we can achieve with only 2 elements in a tri-band quad. As well, we also find a decrease in the front-to-back ratio. These numbers are not simply the product of a front-to-back peak that is on a different frequency. Rather, the decrease in front-to-back ratio is part of the same set of effects that yields the lower gain on each band above 20 meters. In fact, 20 meters is the only band on which we see near-normal (monoband) gain, and this fact provides a clue to what is happening.</p>
+  <center>
+    <img src="3l3bq-8.gif" width="600" height="280" border="2" vspace="5" hspace="9">
+  </center>
+  <p>We can visualize the problem by examining <b>Fig. 8</b>, which shows the relative current magnitudes when we operate the array on 15 meters and on 10 meters. On the left, we find fairly high peak currents on the 15-meter elements, since the operating frequency is 21.2 MHz. There is one additional active element: the 20-meter director. Its current magnitude is over 1/3 the value of the 15-meter director current magnitude. Likewise, on 10 meters or 28.42 MHz, we find fairly high values of current magnitude on the 10-meter elements. As well, the 15-meter director is active at a current magnitude that is more than 1/2 the current magnitude of the 10-meter director.</p>
+  <p>Current magnitude is not the sole determiner of what occurs with these elements. We must also consider the phase angle of the current. In the monoband versions of these 3-element quads, we find a relative current magnitude on the reflector that varies between 0.81 and 0.86 across 20 meters. The corresponding current phase varies from 126 to 153 degrees. The director current varies from 0.23 to 0.36 in magnitude, with a phase angle range of from -133 to -151 degrees. At the design frequency, the current magnitudes and phase angles are about at the average of these ranges (0.85 at 140 degrees for the reflector and 0.29 at -140 degrees for the director).</p>
+  <p>In the tri-band design, at 14.15 MHz, the reflector values are 0.84 at 131 degrees and 0.27 at -149 degrees--well within the range shown for the monoband beam. However, at 21.2 MHz, the tri-band reflector current is down to 0.68 at 133 degrees, while the director current is 0.31 at -150 degrees. The reflector relative current magnitude is low. At the same time, the 20-meter director shows current values of 0.11 at -11.6 degrees. At 28.42 MHz, the 10-meter reflector current is 0.64 at 148 degrees. The 10-meter director current values are 0.36 at -135 degrees. While the combinations are not optimal, the key value is the low reflector relative current magnitude. At this frequency, the 15-meter director shows current values of 0.20 at 20 degrees.</p>
+  <p>If the parasitic element current magnitude and phase angle values are not radically out of line (with the possible exception of the 10- and 15-meter reflector magnitudes), then we may still be at a loss to explain why the forward gain drops so much, rather than just a little. The answer lies in understanding how currents and element functions go together. Clearly, reflector currents show a positive phase angle, while director currents show a negative phase angle in 3-element arrays. Although the exact number will change according to the precise design, the monoband ranges of magnitudes and phase angles give us ballpark values for any 3-element parasitic array. We should not neglect the driver current, which in all cases of this modeled sequence is 1.0 at 0 degrees. Essentially, phase angle values near zero yield a driver element, and the two directors with unintended activity are closer to zero degrees than to values appropriate to reflectors or directors. In effect, the parasitically active directors for the next higher band are radiating energy, but without the direct influence of the parasitic elements that have been cut for the band in use.</p>
+  <p>The energy must go somewhere. For the subject design, the energy tends to go "up" and "down" relative to the wires in the loop as much as it goes forward and backward. In other words, we end up with wider beamwidth values, not only in the E-plane, but as well in the H-plane. Re-examine the data in <b>Table 3</b>. The tri-band 20-meter beamwidth values are nearly the same as the ones we derived for the monoband beam. In fact, all three monoband 3-element quads have almost identical beamwidth values. However, when we move to 15 meters, the E-plane shows a 4.5-degree wider beamwidth, while the H-plane value increases by about 8 degrees. At 10 meters, relative to the monoband values, the E-plane beamwidth increases by about 13 degrees, while the H-plane beamwidth increases by over 20 degrees. <b>Fig. 9</b> provides a gallery of H-plane patterns that show clearly the increasing beamwidth as we operate the 3-element tri-band quads on the upper bands.</p>
+  <center>
+    <img src="3l3bq-9.gif" width="600" height="410" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The exact degree of pattern deformation, relative to a standard derived from the monoband pattern, will vary with the multi-band quad design. However, every planar and spider 3-element quad design that I have examined has shown the same basic phenomena. At 15 meters, the 20-meter director is active, and at 10 meters, the 15-meter director is active. In both cases, being active means having a current magnitude of at least 10% the value of the driver. The activity is sufficient to prevent the quad from reaching its monoband performance levels on the upper two band. Regardless of the precise design, the upper bands of a 3-element multi-band quad in some cases barely reach 2-element performance levels.</p>
+  <p>Planar 3-element, 3-band designs are at a further disadvantage. 2-element designs exhibit only slow changes of performance with variations in reflector-to-driver spacing. However, the driver-to-director spacing (and element circumference) in a 3-element quad reacts to smaller changes in spacing. Hence, a 3-element tri-band quad tends more readily to show that fact that the element spacing is optimal at best on only one of the 3 bands and often not on any of them. As a consequence, tri-band planar designs using 3 elements tend not to achieve a very significant gain over a 2-element quad. Optimized quad designs for the widest bandwidths easily show about 8.5 dBi free-space gain at mid-band. Optimized high-gain monoband quads top 9.0 dBi. A planar quad rarely achieves 7.8 dBi on any band.</p>
+  <p>I sampled tri-band 3-element planar quads using 3 different popular spacing values for boom lengths of 18' to 20'. One sample used 10' from reflector to driver and 8' from driver to director, while a second reversed those two numbers. A final sample used 10' for both the reflector-driver and driver-director spacing values. Although it may be possible to refine the performance further, <b>Table 4</b> shows the range of values at mid-band for the group of designs.</p>
+  <center>
+    <img src="3l3bq-t4.gif" width="542" height="171" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The element spacing value range favors 15 meters over the other 2 bands. Hence, the overall 180-degree front-to-back ratio level is higher on that band. As well, the lowest gain value is higher than for either of the other bands. The planar design also suffers in beamwidth in both the E- and the H-planes. Optimized monoband designs showed about a 66-degree E-plane beamwidth and a 79-degree H-plane beamwidth. As the table shows, all of the beamwidth values for the tri-band planar design are higher. In addition, the values increase with increasing operating frequency. Finally, the H-plane beamwidth shows considerable growth as the operating frequency increases. Given the associated physical challenges of a 3-element planar multi-band quad construction, most builders have concluded that there is no great sense in deriving 2-element performance from 3 elements.</p>
+  <p><b>Conclusion</b></p>
+  <p>The only definitive point that these notes establish is that multi-band 3-element quads present both physical and electrical challenges that most quad builders find perhaps too daunting. Whether there are any sure-fire ways to overcome both sets of challenges, I frankly do not know. To this point, I have discovered none. Apparently, most quad builders have not found these ways either, since 3-element multi-band quads are far more rare than 4-element multi-band quads.</p>
+  <p>With 4 elements, a quad presents no major mounting problems other than the weight of the elements and their support arms. As well, the presence of the second director overcomes to a large measure the pattern distortions that tend to prevent 3-element quads from reaching monoband performance on the upper bands. Nevertheless, 4-element quads present their own challenges--and sometimes the means to overcome them. Virtually all 4-element quads use planar construction. The result will inevitably be that some bands have compromise performance values that emerge from using a boom length that is either too short or too long for optimal wide-band performance. At the same time, the presence of three parasitic elements per band allows the builder to offset some loop dimensions to increase the operating bandwidth with an acceptable SWR value. The challenge lies in finding the correct combination that yields operating bandwidth and reasonable performance that is worth the construction and adjustment effort. Many quad builders have found the benefit-cost ratio favorable in 4-element designs while finding the ratio unacceptable for 3-element multiband quad designs.</p>
+  <p>Cubical Quad Notes Vol 1 - 3 available in PDF book format on the <a href="../bookant.html">Books Page</a>.</p>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center>
+  <p><i>Updated 04-01-2007. &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" width="591" height="3">
+  </center>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> <b>Return to Amateur Radio Page</b></a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#quad'>Quad</a></p><br>
+</body>
+</html>

content/quad/40q.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Quad, Loading, HF Lower">
+  <title>Full and Shrunken 40-Meter Quads</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/quad.gif" align="left" width="91" height="91" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Notes on Full and Shrunken 40-Meter Quads</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>
+  Most commercial 40-meter Yagis use half size elements plus a method of loading the elements to achieve some gain and front-to-back ratio on a limited portion of the 40-meter band. Half-size elements, even when spaced optimally at about 20 feet, limit the available gain relative to a full- size 2-element Yagi. However, shortening the elements does increase the available front-to-back ratio relative to a full-size beam.
+  <p>The limitations of shortened 40-meter Yagis has raised some interest in the possibilities of a 40-meter quad. The following notes are extrapolations from studies published in <i>Communications Quarterly</i>, Summer, 1997 (pp. 71- 92) (<a href="../mu/mu7a.html">link</a>). The full study focused on 10 meter models and test antennas, with nearly automatic extensions of the ideas to 20 meters. However, a number of variables has required some extensive remodeling for 40-meters.</p>
+  <p>40-meters is a wide band. 300 kHz at 40 is electrically the equivalent to 600 kHz at 20 or 1.2 MHz at 10. Hence, it is inherently more difficult sustaining the performance of any type of array across the band, in addition to maintaining an inclusive operating bandwidth. Therefore, for virtually any multi-element antenna design, there will be a region of the band at which performance is peak and other parts of the band where the antenna may be operated with lesser gain and front-to-back ratio.</p>
+  <p>This restriction applies equally to quads as to Yagis, either full or half size. Moreover, reduced-size or shrunken quads will be subject to the same types of reduced bandwidth for each of the major antenna performance characteristics of greatest concern to radio amateurs: gain, front-to-back ratio, and SWR bandwidth.</p>
+  <p>Let's look at four quad possibilities: a full size model and three versions of shrunken models, and then compare their performance potentials as derived from models. All gain figures are free space gains in dBi.</p>
+  <p>In the process of comparing these antenna models, I shall by pass mechanical questions. The quad is requires a significant mechanical support structure. Companies, such as Cubex, to name just one, make support structure hardware available. Whether the resulting assembly is adequate to various climates will have to be a builder decision.</p>
+  <h3>Full-Size 40-Meter Quad</h3>A full-size 2-element quad for 40 meters has the width of a half-size 40- meter Yagi--about the same width as a full-size 20-meter beam. However, the vertical space requirement and the consequential support structure is very significant. The quad forms a box about 36' top and side, with a front-to-back spacing of about 20 feet.
+  <center>
+    <img src="40q-4.gif" width="521" height="384" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The figure shows the wire dimensions for a full size quad optimized for maximum performance at the lower end of the band. The modeled wire size for this and all models is #14 copper. If you use a fatter wire, do not expect element shortening. As Bob Haviland pointed out, as you increase the wire diameter of the quad or almost any other closed-geometry antenna, element length increases.</p>
+  <p>The 20' spacing represents a separation of about 0.14-0.15 wavelength, which is a good compromise among the major performance characteristics of the antenna. Shorter spacings are possible with a consequent narrowing of the operating bandwidth. Larger element spacing tends to increase the ungainliness of the assembly almost exponentially.</p>
+  <p>For all quad models, peak gain occurs below 7 MHz. As gain increases, the front-to-back ratio decreases. For all the models shown, a minimum band- edge front-to-back ratio of 9-10 dB was used as a design limit.</p>
+  <p>Frequency sweeps of the model show a maximum front-to-back ratio of over 29 dB at 7.1 MHz, where the gain is about 6.9 dBi. Gain is higher at lower frequencies, reaching 7.4 dBi at 7 MHz. Above the design center, both gain and front-to-back ratio show a regular decline down to 5.9 dBi and 10.2 dB at 7.3 MHz.</p>
+  <p>Since the feedpoint impedance of the antenna fluctuates around the 100-ohm mark, the antenna was designed for use with a 1/4 wavelength 75-ohm matching section. With the section in place, the antenna has a 50-ohm SWR of less than 2:1 across the band.</p>
+  <h3>Square Inset-Loaded Shrunken Quad</h3>One method of shrinking a quad is to use voltage-node loading. This method eliminates inductor losses and maintains current levels in the wire elements where they are the highest. However, the design has some limitations.
+  <p>First, the current is still high at the corners of a full size quad. Shrinking the loop changes the polarization of the formerly corner current to vertical, where is tends to cancel with fields from the opposite side of the loop. Hence, we can expect lesser gain from every shrunken quad.</p>
+  <center>
+    <img src="40q-5.gif" width="538" height="378" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As the figure shows, we can reduce the dimensions of the quad significantly, that is, by 20 to 25%. However, in the square configuration, we are limited by the need for dimensional space for the insets. Further shrinking can be obtained by spreading the inner ends of the insets, thus decreasing their length. However, further shrinkage will be accompanied by further gain reductions.</p>
+  <p>With the dimensions shown (retaining the 20' spacing), maximum front-to- back ratio occurs between 7.05 and 7.1 MHz and peaks above 17 dB. Gain in this region is between 6 and 6.4 dBi, climbing to about 6.8 dBi at the lower band edge.</p>
+  <p>As with the full-size quad, gain and front-to-back ratio decline from 7.1 to 7.3 MHz, dropping to 4.6 dBi and 6.1 dB, respectively, at the upper band edge. Obviously, peak antenna performance appears over a narrower bandwidth with the smaller antenna.</p>
+  <p>The shrunken quad presents a feedpoint impedance apt for a 75-ohm feedline. Therefore, the antenna was designed for this feedline, with expectations of an appropriate transformation either at the antenna feedpoint or at the shack. 2:1 SWR bandwidth just about covers the entire band.</p>
+  <h3>Diamond Inset-Loaded Shrunken Quad</h3>The builder can obtain further decreases in overall antenna circumference by using a diamond configuration. Unlike the square configurations, where the reflector is purposely made larger than the driven element, the diamond configurations use loops of the same size, varying only the load sizes. A builder can use either scheme with either configuration with very little change in performance characteristics.
+  <center>
+    <img src="40q-6.gif" width="580" height="409" border="2" vspace="5" hspace="9">
+  </center>
+  <p>With an overall reduction of circumference to the 70% of full-size mark, the diamond configuration is at the verge of that point in antenna design where further size reductions are accompanied by much larger decreases in performance, especially with respect to gain and operating band width. Moreover, the maximum cross-arm dimensions and hence both the horizontal and vertical space required by the quad approach the horizontal and vertical dimensions of the square full-size quad. However, the diamond shrunken quad provides more space for the insets, and the configuration will be much lighter and possibly better at shedding ice and snow than wither of the square models.</p>
+  <p>The maximum front-to-back ratio of this configuration peaks just above 7.05 MHz at above 17 dB, with a gain of about 6 dBi. Lower band edge gain is close to 6.5 dBi. Gain and front-to-back ratio taper up the band to upper band-edge figures of 3.95 dBi and 4.51 dB, respectively.</p>
+  <p>Like the square inset-loaded quad, the antenna is apt for 75-ohm coax feed, and the 2:1 SWR operating band width covers just about the entire band.</p>
+  <h3>Diamond "Capacity-Hat" Loaded Shrunken Quad</h3>An alternative to inset loading at a voltage node is so-called capacity-hat loading. Instead of an inset, one brings a wire from the left and right corners inward and then branches it in parallel to the main wire to lengths that resonate each loop at the frequencies needed for optimal parasitical performance.
+  <center>
+    <img src="40q-7.gif" width="601" height="420" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As the figure shows, the cap-hat loaded diamond is mechanically equal to the inset-loaded diamond model. The cap-hat wires perform essentially the same function as the insets: to provide the wire length necessary to reach resonance at the desired frequency without adding significantly to the radiation fields. Hence, we would expect performance figures to be equally similar.</p>
+  <p>We shall not be disappointed. Maximum front-to-back ratio once more peaks at about 18 dB at 7.05 MHz where the gain is 6.1 dBi. Gain climbs to 6.4 dBi at the band edge. Gain and front-to-back ratio decreases toward 7.3 MHz, where they are 4.1 dBi and 5.4 dB, respectively.</p>
+  <p>Insets and cap-hats present the builder with construction challenges of different but comparable sorts. The square and diamond inset models require parallel wires reaching toward (but not reaching and certainly not overlapping) the antenna boom. Lightweight spacers, perhaps 1/2" nominal CPVC, can maintain spacing while UV rated synthetic rope can serve as the insulated link to the hub support. There is no reason why the insets cannot be as much as 15 degrees off-plane without unduly affecting the front-to-side ratio of the antenna pattern. The spread cap-hat wires can be insulated and spaced from the main element wires by similar means: CPVC.</p>
+  <p>The dimensions shown are modeled dimensions and will required field alteration to account for the variables of quad construction. Unlike aluminum tubing, which is relatively rigid in length, quads are subject to changes in length depending on the tension applied by the builder during construction. The results may be changes to the insets or the cap-hat spread wires. The amount of metal, if any, in the spreaders may also require small changes in wire length. In short, wire quad dimensions are never as assured as aluminum tubing dimensions.</p>
+  <h3>Performance Comparisons</h3>To get a better picture of how the antennas modeled above compare with each other, lets look at some graphs of modeled performance across the 40-meter band.
+  <h4>Gain</h4>
+  <center>
+    <img src="40q-1.gif" width="644" height="519" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The individual models, when graphed across the band, show that gain is largely a function of percentage of full-size. The full-size quad not only has a higher forward gain than the shrunken models, but the rate of decrease is slower across the band. At the design center--about 7.05-7.1 MHz, the gain approaches that of a short boom or a wide-band 3-element Yagi and exceeds the gain of a full-size 2-element Yagi by over a half dB. (The forward gain of a full-size 2-element quad is still a dB short of the gain of a long-boom optimized 3-element Yagi.)</p>
+  <p>The 78% square inset-loaded quad shows good gain across the band relative to the smaller quads and relative to a full size 2-element Yagi. The 2 diamond 70% quads compete well with a full size 2-element Yagi and are superior to half-size Yagis. However, the shrunken quads do show a tendency to more rapidly decrease their gain across the band relative to a full size quad. However, the lowest figures remain about 2 dB better than a dipole.</p>
+  <h4>Front-to-Back Ratio</h4>
+  <center>
+    <img src="40q-2.gif" width="645" height="519" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Because the full-size quad has inherently a better front-to-back ratio, it is possible to design its peak further into the 40-meter band and still have about 13 dB at the band edge. This design tactic provide better than a 10 dB front-to-back ratio at the upper end of 40 meters, despite the rapid drop in the ratio above 7.1 MHz.</p>
+  <p>All three shrunken models show front-to-back ratio curves that would be indistinguishable in practice. The square 78% model has its peak between 7.05 and 7.1 MHz, which is invisible on this sweep at 0.05 MHz intervals. However, that peak is not significantly above those of the diamonds. with a design limit that set the front-to-back ratio at 9-10 dB at the lower edge of the band, this ratio is sustained only to abut 7.15 MHz for all three models. If a builder desires to center the performance peak within the phone end of the band, he must change element dimensions. However, the antenna may become inoperative at the low end of the band if centered between 7.2 or 7.25 MHz.</p>
+  <h4>2:1 SWR Operating Bandwidth</h4>
+  <center>
+    <img src="40q-3.gif" width="645" height="518" border="2" vspace="5" hspace="9">
+  </center>
+  <p>All four antenna models show a wide operating bandwidth, covering all of 40 meters. However, one should understand that the upper half of the band is achieved at significantly lower antenna performance figures.</p>
+  <p>The full-size model SWR curve is for a 50-ohm SWR basis. The model was constructed with 1/4 wavelength 75-ohm matching section cut for 7.1 MHz. The 50-ohm SWR never exceeds 1.76 across the band.</p>
+  <p>All three shrunken models are inherently 75-ohm antennas, and the SWR curves are based on 75 ohms. The use of 7.05 MHz as a design center is apparent in all of the curves.</p>
+  <p>The resonant frequency, at which the antenna shows near-zero reactance, must be set low in the band. To a degree higher than virtually any other antenna design, quads show a very rapid rise in SWR below resonance and a very slow rise in SWR above resonance. The rapid rise in SWR below design frequency is a combination of a rapid drop in the resistive component and a rapid rise in reactance. Above the resonant frequency, both the resistive and reactive components of the feedpoint impedance rise very slowly. This fact can mislead a user into believing that his antenna is performing very well, when, indeed, the low SWR is accompanied by mediocre gain and front- to-back ratio.</p>
+  <p>Consequently, it is never good practice to build a quad without making at least some measurement of the front-to-back ratio across the band in addition to impedance measurements. One can make fairly extensive changes in the driven element without affecting antenna performance. However, changes in the reflector will change the resistive and reactive components of the feedpoint impedance. Hence, for most cases, it is better to begin by establishing the reflector length with respect to front-to-back ratio pattern across the band and then adjust the driven element for the desired SWR characteristics. If the change in the driven element is quite large, it may take one more round of reflector-then-driven-element adjustment to settle on the final dimensions.</p>
+  <p>All of the designs presented can be improved with respect to almost every characteristics. I developed them, not as the last word in 2-element 40- meter quad design, but as typical models on which to base expectations and to make design decisions for one's individual situation.</p>
+  <p>For further information on quads, see at least the following references:</p>
+  <ul>
+    <li>
+      <p>William I. Orr, W6SAI, <i>All About Cubical Quad Antennas</i></p>
+    </li>
+    <li>
+      <p>Bob Haviland, W4MB, <i>The Quad Antenna</i></p>
+    </li>
+    <li>
+      <p>John Koszeghy, K2OB, <i>High Performance Cubical Quad Antennas</i></p>
+    </li>
+  </ul><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 12-30-97. &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><br>
+  <br></p>
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+  <title>An 80/40 Quad Design</title>
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+  <h1 style="text-align: center;">An 80/40 Quad Design</h1>
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+  <p style="text-align: center; font-weight: bold;"><a href="8040quad.pdf">An 80/40 Quad Design</a></p>
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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
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+  <title>The Birdcage Antenna</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/quad.gif" align="left" width="91" height="91" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">The Birdcage Antenna</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>
+  The folded X-beam derives its existence from the G4ZU Birdcage antenna. W2EEY viewed the X-beam as half a Birdcage.(1) Although this is historical fact, the logic of antennas goes the other way round: the Birdcage is a double folded X-beam. For reference, Figure 1 provides a free space pattern of an X-beam tuned for maximum front-to-back ratio.
+  <center>
+    <img src="bc1.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>We may legitimately ask, how much better does the whole Birdcage work compared to an X-beam? When Dick Bird, G4ZU, published his work in 1960, he made some fairly extravagant claims for the antenna, claims that led him to patent it.(2) At this distance and with the calculating power made available by NEC and its offspring, we may decide that the claims for his antenna (and those of many hams who built one) reflect more accurately the low state of home-brew Yagi and quad construction of the time than they do contemporary comparative performance. Models of the Birdcage show little advantage over the X-beam and exaggerate some of its limitations.</p>
+  <p>Bird graphically demonstrated what he took to be the principles of the Birdcage by beginning with the bi-directional pattern of the dipole. Folded into a Vee, the antenna would show, according to his sketches, a strong lobe out the open end and a weak lobe off the apex. Add a Vee reflector (pointed the other way to make an X), double the assembly a quarter wave above or below, bend the X-arms vertically to meet each other as phasing lines, and the Birdcage is born. Figure 2 shows the outline of the Birdcage, with identification of each relevant dimension.</p>
+  <center>
+    <img src="bc2.gif" width="470" height="463" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Unfortunately, the seeming flaw in the reasoning begins with the Vee itself. Short Vees do not cancel the radiation off the backsides of the elements (the outsides of the V). Thus are born the uneliminable quartering lobes of the X-beam and even larger lobes for the Birdcage.</p>
+  <p>Birdcages come in two forms: with a reflector and with a director. Table 1 shows 10-meter models of each beginning with a self-resonant Birdcage with equal-size elements derived from data given in 1960's literature.(3)</p>
+  <pre>Table 1.  Modeled Dimensions of the Birdcage Antenna
+
+Dimensions     DE Arm (A)     Parasitic (C)       Vertical (B and D)
+               L (ft)         L (ft)              L (ft)
+Basic
+ Birdcage      5.05           5.05                8.666
+
+DE and Refl
+ Resonated     4.95           5.26                8.666
+
+DE and Dir
+ Resonated     5.16           4.91                8.666
+
+Note:  all models used #14 copper wire in free space at 28.5 MHz on NEC-4.
+</pre>
+  <p>Figure 3 shows the performance in free space of the basic Birdcage--a nice 4-leaf clover.</p>
+  <center>
+    <img src="bc3.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>G4ZU favored the reflector version, which is perhaps the worse performer of the two possible versions. With a forward gain in free space of under 6 dBi and a front-to-back ratio of about 8 dB, the beam is not the equal of a 2-element Yagi or even of the X-beam. Figure 4 shows its performance in free space.</p>
+  <center>
+    <img src="bc4.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The director version that parallels the development of the X-beam provides more gain and front-to-back ratio: 6.3 dBi and 17 dB, respectively. Figure 5 shows its performance in free space. The direction is reversed, since I simply re-dimensioned the reflector to form a director.</p>
+  <center>
+    <img src="bc5.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As shown in Table 2, the figures for the directed Birdcage surpass both the X-beam and the 2-element Yagi by a small bit, while the reflected Birdcage leaves much to be desired.</p>
+  <pre>Table 2.  A Comparison of Antenna Performance
+Antenna             TO Angle  Gain      Front-to-      Feedpoint
+ Type               (degrees) (dBi)     Back (dB)      R &ntilde; jX (Ohms)
+A.  Free Space
+Birdcage: DE + Ref  --         5.8       8.0           34 -  0
+Birdcage: DR + Dir  --         6.3      16.9           40 +  4
+Folded X-Beam       --         5.3      39.1           37 -  3
+B.  Height = 5/8 wl
+Birdcage: DE + Ref  22        10.5       8.0           31 -  3
+Birdcage: DR + Dir  22        11.0      17.1           40 +  3
+Folded X-Beam       23        10.5      21.8           35 +  0
+2-El Yagi           23        11.3      10.9           34 -  5
+2-El Quad           22        11.7      18.3           97 -  3
+C.  Height = 1 wl
+Birdcage: DE + Ref  13        11.3       8.6           32 -  2
+Birdcage: DR + Dir  14        11.8      17.0           39 +  2
+Folded X-Beam       14        10.8      31.7           33 -  1
+2-El Yagi           14        11.7      13.5           35 +  0
+2-El Quad           13        12.4      17.9           92 +  8
+Note:  TO angle=the angle of maximum radiation at which azimuth readings of
+calculated gain and front-to-back ratio were obtained.  All calculations
+via NEC-4.
+</pre>
+  <p>The pattern of the Birdcage in either version does not meet today's standards of front-to-side ratio or front-to-rear ratio. The quartering rear lobes of the X-beam become virtual side lobes of the Birdcage and are only down from the main lobe by some 4 to 5 dB in the either version. There is little QRM-rejection potential, especially in the reflector version. Over real ground, the pattern devolves into a mound of whip cream. However, over real ground, the director version tends to push its side lobes to the rear, and the pattern begins to resemble that of the folded X-beam.</p>
+  <p>Like the folded X-beam, the Birdcage retains its most optimal pattern only over a small portion of the band of design. The reflector version rapidly grows a tail below design frequency, while the director version grows its tail above design frequency. The SWR bandwidth is also narrow, less than 0.5 MHz at 10 meters for a 2:1 SWR. However, the complex structure of the Birdcage is less amenable to a tunable parasitic element than is the simpler X-beam.</p>
+  <p>All in all, the additional complexities of the Birdcage are not warranted by a significant increase in performance over the X-beam. Gain aside, the side and rear performance of the antenna falls far short of other compact designs. Consequently, while that antenna has a great name and an appealing look, performance models do not recommend the investment of time and resources in this antenna. In some ways, it is a shame to discover this: G4ZU contributed extensively to amateur practice in the field of antennas. Although the Birdcage antenna has had its day, Dick's other work--and his example--will long endure.</p>
+  <center>
+    <h4>Notes</h4>
+  </center>(1) John Schultz, W2EEY, "The G4ZU X Beam for 20," CQ (June, 1965), pp. 26- 28, 102.
+  <p>(2) Dick Bird, G4ZU, "The G4ZU 'Bird Cage' Aerial," CQ (April, 1960), pp. 40-42, 117.</p>
+  <p>(3) See George Cousins, VE1TG, "The Tri-Band Birdcage," CQ (July, 1963), pp. 30-33. Another brief reference to the antenna occurs in Orr and Cowan, Cubical Quad Antennas, 3rd Ed. (Lakewood, NJ: Radio Amateur Callbook, 1993), p. 102, where it is shown with a reflector and referred to as a variation of the quad.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-18-97 &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><br>
+  <br></p>
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