What Can We Expect From a 2-Element Beam?

Part 5
Strategies for Improving Forward and Rearword Performance

L. B. Cebik, W4RNL

Strategies for Improving Performance

An end is not an end if folks ask questions and make suggestions. Several notes have suggested that there are strategies to improve the gain and/or the front-to-back ratio of a 2-element array. Indeed, there are. The gain and front-to-back performance given in earlier sections are the best obtainable within the design goals (maximum front-to-back ratio and resonance) for a 29 MHz Yagi model using 3/8" aluminum elements in a reflector-driven element arrangement. As noted, these elements scale to reasonable values for lower HF bands, but are not the final word on desirable element sizes. Limitations of both the antenna type and the method of study have been noted throughout.

Let's look at some of the strategies for improvement and divide the work into 2 parts: strategies that can improve front-to-back ratio and strategies that can improve gain. For the most part, and despite long- persisting claims, the two are separate, although one we shall note (near the end, of course), combines the two. Additionally, we shall look at only some samples of strategies, because the total number of ways to go about the process is limited only by the antenna designer's imagination. Finally, many of these samples require the use of other than 3/8" aluminum elements, so precise comparisons cannot be made with the models used to this point. However, some very interesting general trends can be noted.

Improving Rearward Performance

There are two chief ways to improve front-to-back performance of a 2- element array: phasing the two elements and altering standard 2-element geometry.

The ZL Special: I have done an extensive study of the ZL Special, so the following notes will be only a summary. See "Understanding and Modeling Small Beams: Part 5: The ZL Special," Communications Quarterly, (Winter, 1997), 72-90. The ZL Special became popular in the 50s after a series of articles by ZL3MH/ZL2QQ, George Prichard, with some quick test work by G2BCX. Claims of 7 dBd gain and 40 dB front-to-back ratios were common, mostly because the antenna outperformed many of the ill-designed 3-element Yagis of the period. It remained almost a constant claim that the antenna was a phased array 1/8 wavelength separated and using a twisted 45-degree phase line to give 135-degree phasing. It was Roy Lewallen who pointed out in the 1980s that is was not the impedance at the rear element that was critical, but the current, and this changed the analysis ball game, although it appears few have taken up the challenge.

Since current goes through a 360-degree cycle, not a 180-degree cycle like impedance along a transmission line, the proper analysis of a ZL Special must treat it as a -45-degree phased array. The minus sign is the product of the phase line twist. Once we make this shift in perspective, we can analyze the relationships of the current magnitudes and phases along the line such that they yield correct values for the spacing used and wind up with identical voltage magnitudes and phases at the junction with the feedline. For a given situation, line length, characteristic impedance, and velocity factor combine so that few values will satisfy the requirements, and fewer still if we stick to available commercial lines.

The spacing need not be precisely 1/8 wl, since every spacing between a very small one and something just under 1/4 wl has a current magnitude and phase requirement for the rear element that will yield maximum front-to- back ratio. In fact, for 1/8 wl spacing, the current phasing must be about -43-44 degrees, at 0.1 wl spacing, the current phasing must be about -34 degrees, and at 0.15 wl spacing, the current phase must be about -53 degrees.

The reason that I do not include gain as a feature of the ZL Special is that it never exceeds that of a 2-element Yagi designed for maximum front- to-back ratio by even 0.2 dB. However, the front-to-back ratio may reach beyond 50 dB at its peak.

There is no inherent performance difference between single dipole and folded dipole ZL Specials. Single dipole models often have very low feedpoint impedances (less than 10 Ohms) and require 70-Ohm parallel feedline, a hard to find commodity these days. Folded dipoles can have feedpoint impedances close to 50 Ohms (with a remnant inductive reactance component that a pair of capacitors in the feedline can cancel) and can use 300-ohm TV line for phasing. Most builders prefer to see their ZL Specials with slightly shorter forward elements, because that is what they are used to seeing in Yagi design--and some designs like the Swiss ZL Special effectively use this arrangement. However, in a phased array, the length of the forward element is a key factor in establishing the phase difference between the elements and can call for values that are slightly longer than the rear element. Remember: in a parasitical array, you are using antenna geometry to establish the phase relationships of the two elements; in a directly phased array, you are forcing the phase relationship by a device, and the geometry must meet the device requirements, if any are needed. They are needed for transmission-line phasing, but there is no rule that says one cannot create the phase relationship by independent networks, as has been done by ZL1LE.

Let's look at the sweeps of several antennas, using a 2-element Yagi as a reference. The ZL Specials will all use 5/8" aluminum single dipoles (not folded dipoles) with a 71-Ohm, .67 VF line. The feedpoint impedance for the ZL Special is always very low with this configuration, but we are interested in the gain and especially the front-to-back pattern. This pattern is not comparable to earlier ones, because it covers 28-29 MHz, with a design center frequency of 28.5 MHz. The Yagi has also been designed for this frequency range, with a 28.25 MHz design center. All antennas are at 35', close to 1 wl up. The Yagi is 2 1" aluminum elements, spaced 4.25' apart.

ZLSP1, like all the ZL Specials, is spaced 3.46' with an 16.04' forward element and a 16.4' rear element, simulating Yagi-type construction. ZLSP2 uses two equal 16.04' elements. ZLSP3 is optimized for maximum front-to- back ratio on the design center frequency, with an 8.000' forward element and a 7.897' rear element (all decimal places significant).

Antenna        28        28.25     28.5      28.75     29

Gain (dBi)     12.02     11.83     11.65     11.49     11.33
F-B (dB)       11.85     12.56     12.42     11.80     11.02
Feed Z         26.0-19   30.2-10   34.3-1.2  38.2+7    41.9+15

Gain (dBi)     11.22     11.36     11.50     11.64     11.78
F-B (dB)       15.89     17.26     18.26     18.39     17.44
Feed Z         9.4+6.0   9.8+8.0   10.1+11   10.5+14   10.9+17

Gain (dBi)     11.48     11.62     11.76     11.89     12.02
F-B (dB)       20.03     23.50     25.72     22.91     19.07
Feed Z         6.7+3.5   6.9+5.9   7.3+8.5   7.5+11    7.8+15

Gain (dBi)     11.61     11.75     11.88     12.01     12.14
F-B (dB)       21.52     28.00     40.53     24.97     19.37
Feed Z         5.3+1.7   5.6+3.9   5.8+6.3   6.1+9.0   6.3+12

The pattern of values is typical of phased arrays. Notice that the gain climbs with frequency, in contrast to the Yagi pattern of descending from the peak gain frequency. For some designs, the gain might have gone the other way. For reasonably well design ZL Specials, gain is a bit more stable than with comparable Yagis across a given frequency span.

For even the most casually designed ZL Special, front-to-back ratio is superior to that of a 2-element Yagi. Front-to-back ratio is dependent upon both the magnitude and the phase of the current on the rear element relative to the forward element, and the full-size Yagi is simply not geometrically capable of establishing both values parasitically. Yagis with shorter elements, although suffering reduced gain and bandwidth, come closer to achieving the proper current magnitude and phase for maximizing the front-to-back ratio.

The second ZL Special model uses equal length elements and achieves a very good and stable front-to-back ratio across the full MHz of 10 meters. The third ZL Special model has been carefully tweaked beyond the abilities of most shops to replicate (and to adjust for the difference between the modeling context and reality) to achieve a very high front-to-back ratio. Another decimal place in the dimensions would have bought another 10 dB of F-B ratio. However, notice how narrow banded the peak is, settling by the band edges to values very close to those of the equal-element model. Considering the continued drop in feedpoint impedance, it is questionable whether the last ZL Special model would be the correct design choice for most circumstances. Moreover, the front-to-back ratio applies for a very narrow rear window of degrees directly to the rear. Even at its peak, the overall front-to-rear ratio is closer to 20 dB, a figure similar to that of the equal-element model.

The Moxon Rectangle: What the ZL Special does with phasing lines, the Moxon rectangle does with geometry, that is, establish the correct rear element current magnitude and phasing for maximum front-to-back ratio. Derived from the VK2ABQ square, which is actually a rather poor performer, but with a germinal insight, the G6XN modification arose from practical considerations rather than a through understanding of what was going on. In fact. Moxon himself used the antenna with remotely tuned elements in order to flip the direction, and did not provide any solid basic information on its design. That led me to a considerable study of the antenna. See "Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and Moxon Rectangles," Communications Quarterly, (Spring, 1995), 55-70.

The Moxon rectangle bends the forward and rear elements of a Yagi toward each other, with a small but critical space between the ends. The precise dimensions are a matter of design goal choice. Broader bandwidth of the front-to-back ratio occurs with squarer versions, but at a higher feedpoint impedance (80 ohms or so). One can also build versions that are narrow from front to back, and hence a bit wider from side to side, and achieve a 50-Ohm feedpoint impedance, although the front-to-back ratio goes down toward the edges of a frequency sweep. Models can be built with anything from wire to aluminum tubing.

One #14 wire model I have built was 11.2' side-to-side and 6.6' front-to- back. The driven element was 16.6' long, with 2.7' bent back on either end. The reflector was 17.4' long, with 3.1' bent forward. This left a 0.8' space between element ends. The feedpoint impedance was about 79 ohms. A 1" aluminum tubing model I am currently working on calls for 12.24' side-to-side. The driven element is 15.6' long, with 1.68' fold- backs. The reflector is 16.84' long, with 2.3' fold-forwards, and a space between element ends of 0.52'. The feedpoint impedance is very close to 50 ohms.

The Moxon pattern approaches cardioid shape, with the greatest front-to- side null well beyond the 90-degree point. Typically, one can achieve 20 dB front-to-back across the entire rear quadrant at a 5/8 wl height and better than 24 dB around the rear curve at 1 wl up.

In one sense, the Moxon has a poorer forward gain than a 2-element Yagi or a ZL Special, about .5 dB down on average. However, that gain applies over a much wider beamwidth. A typical 2-element Yagi has a beamwidth between half-power (-3dB) points of abut 70 degrees. Moxon half-power point are typically 80 degrees or more apart, and the pattern circle extends beyond the 90-degree side direction. Hence, the proper application of a Moxon is where one wishes a broad forward hearing area and silence from the rear. It is ideal in the US for stations on the coast wanting to work the US without QRM from DX--or to work the DX across the water with silence from the US.

Let's look at a sweep of the 1" aluminum Moxon from 28 to 29 MHz at 35' up just to get a flavor for what it does.

Antenna        28        28.25     28.5      28.75     29

Reference Yagi
Gain (dBi)     12.02     11.83     11.65     11.49     11.33
F-B (dB)       11.85     12.56     12.42     11.80     11.02
Feed Z         26.0-19   30.2-10   34.3-1.2  38.2+7    41.9+15

1" Aluminum Moxon Rectangle
Gain (dBi)     11.78     11.62     11.44     11.26     11.08
F-B (dB)       13.64     18.56     24.21     22.05     17.75
Feed Z         35.3-16   44.3-6.9  53.6+.1   61.7+5    69.3+8.4
50-ohm SWR     1.67      1.21      1.07      1.27      1.43

Like the Yagi, the Moxon shows a slower increase in SWR above design center frequency. In fact, the SWR at 29.7 MHz with this model is about 1.7:1, and the front-to-back ratio is still nearly 12 dB. Even wire models show similarly wide operating bandwidths.

Because the geometry that yields the correct current magnitude and phase on the rear element to maximize front-to-back and front-to-rear ratio is frequency specific, the ratio falls off more rapidly than with the ZL Special. However, it remains superior to a standard 2-element Yagi across the entire frequency sweep. It does all this from an antenna about 3/4ths the size of a standard Yagi

Other designs have also been used to increase the front-to-back performance of the 2-element Yagi, but these two designs reveal what is at stake in making them work.

Improving Forward Performance

To improve the forward performance of 2-element parasitical beams, one can always use longer, higher gain elements. Or one may add an element.

However, for the standard reflector-driven element Yagi using half- wavelength dipoles, there are several minor routes to increasing forward gain

1. Fatter elements: Up to a certain point, one can improve the performance of a 2-element Yagi by increasing the size of the elements. The following table illustrates both the gains and the limits on them

Element        Gain      F-B ratio      Feed Z
inches         dBi       dB             R +/- jX Ohms
Full size; 0.16 wl spacing
0.375          6.12      10.86          46.67 - j0.35
0.75           6.15      10.89          46.01 _ j0.31
1.50           6.15      10.92          45.34 - j0.64
3.00           6.15      10.95          44.62 - j0.39

Fill size; 0.12 wl
0.375          6.25      11.19          32.47 + j0.23
0.75           6.31      11.23          31.33 - j0.98
1.50           6.31      11.27          31.08 - j0.52
3.00           6.30      11.31          30.74 - j0.99

Clearly, elements with diameters larger than 3/4" add virtually nothing more to the gain of the antenna. For the lower bands, the largest effective size element would be the scaled dimension from the one given for 10-meters.

2. Tapered elements: Increasing the size of the element in the high current region--close to its center--can also improve the performance of a Yagi. The following figures compare the maximum gain performance of a 2- element Yagi of very close spacing for a uniform element, an element of 2 sections, and an element of 3 sections each side of center.

Antenna             Gain      F-B ratio
                    dBi       dB
Uniform element     7.33      7.96
2-section element   7.36      7.49
3-section element   7.38      7.41

While the phenomenon is real, the marginal nature of the gains makes this strategy unfruitful unless there are other design reasons for using tapered element diameters.

3. Give up operating bandwidth and front-to-back ratio: In our exploration of full-size reflector-driven element Yagis, we saw that the closer the elements, the higher the gain of the antenna. We need only review the antennas spaced 0.08 (2.8') and 0.12 (4.1') wavelengths.

Frequency      28        28.5      29        29.5      30  MHz
0.08 wl spacing
Gain (dBi)     6.37      6.92      6.32      5.77      5.37
Gain (dBdr)    4.24      4.79      4.19      3.64      3.24
F-B (dB)       1.82      8.65      11.38     10.12     8.57
SWR            31.2      5.88      1.04      2.91      5.52

0.12 wl spacing
Gain (dBi)     6.98      6.74      6.25      5.82      5.48
Gain (dBdr)    4.85      4.61      4.12      3.69      3.35
F-B (dB)       5.46      9.79      11.19     10.37     9.18
SWR            7.12      2.33      1.01      1.81      2.76

Moreover, the highest gain obtainable with this configuration had poor front-to-back ratios.

Frequency      28        28.5      29        29.5      30  MHz
0.08 wl spacing
Gain (dBi)     7.15 R    6.01 R    7.02      6.59      6.02
Gain (dBdr)    5.02 R    3.88 R    4.89      4.46      3.89
F-B (dB)       10.29     0.72      6.29      10.61     10.54
SWR            40.6      16.4      1.01      6.87      14.2

0.12 wl spacing
Gain (dBi)     6.94 R    6.13      6.99      6.70      6.24
Gain (dBdr)    4.81 R    4.00      4.86      4.57      4.11
F-B (dB)       4.74      1.05      6.12      9.80      10.87
SWR            14.7      5.20      1.01      3.03      5.43

Nevertheless, if a higher gain is desired and the conditions of obtaining it acceptable, then a 2-element antenna may serve the purposes at hand.

4. Change configurations: A director plus driven element is capable of higher gain at close spacings than a reflector plus driven element. The following table provides figures for 0.08 and 0.12 wl models of such an antenna. Like the antennas for most of this exercise, the antenna is designed for maximum front-to-back ratio and for resonance.

Frequency      28        28.5      29        29.5      30  MHz
0.08 wl spacing
Gain (dBi)     5.04      5.72      6.55      7.29      6.83
Gain (dBdr)    2.91      3.59      4.42      5.16      4.70
F-B (dB)       8.68      12.85     20.25     10.12     2.53
SWR            3.20      2.17      1.04      3.61      14.21

0.12 wl spacing
Gain (dBi)     5.13      5.70      6.36      6.94      6.97
Gain (dBdr)    3.00      3.57      4.23      4.81      4.84
F-B (dB)       8.07      10.11     11.29     8.63      4.03
SWR            2.31      1.65      1.03      2.01      4.97

At the design center frequency, the director-driven element configuration exhibits a clear superiority over close-spaced reflector-driven element configurations with respect to both gain and front-to-back ratio. Moreover, unlike the reflector model which changes its direction just lower in frequency than the point of maximum gain, the director version remains stable in direction across the frequency sweep.

Unfortunately, the close-spaced director model has a 2:1 SWR operating bandwidth that is very narrow--perhaps 250 kHz at 10 meters. The frequency of maximum gain is about 29.65 MHz where the gain reaches 7.36 dBi, but with a front-to-back ratio of just 7.49. If gain is more important than either front-to-back ratio or operating bandwidth, and 2-elements is the construction limit, then this version may be useful.

The attempt to increase operating bandwidth by increasing the spacing of the antenna reveals the weakness of the director-driven element configuration. Although the operating bandwidth improves, it does so over the lower gain portion of the antenna's performance curve. Unlike the reflector models, where the SWR changes more rapidly below the design center frequency, the director model shows a rapid increase in SWR above the design center, in the higher gain portion of the curve. For high gain purposes, this tends to nullify the apparent increase in operating bandwidth. Moreover, the front-to-back figures are not superior to those of an equally spaced reflector model.

In the end, the pursuit of gain with a 2-element Yagi is always at the expense of something else: either or both operating band width and front- to-back ratio. More gain with respectable operating bandwidths and front- to-back ratios requires more elements, longer elements, or other antenna configurations, such as a stacked parasitical collinear extended double Zepp array.

This survey of strategies for improved forward and rearward 2-element performance is necessarily incomplete. But hopefully, it will alert you to both the opportunities and the pitfalls of the search.

Updated 5-8-97. 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.

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