Part 3: Dual Band Quad Beams With Common Feedpoints

Finally. . .we are ready to tackle dual-band quad beams with common feedpoints. Like the dual band beams in Part 2 that used separate feedpoints, our new beams will rest ultimately on the series of monoband beam designs that we examined in Part 1. They will also adhere to the basic limits surrounding the study by using no more than 2 bands per beam where the bands have at least a 1.3:1 frequency ratio. Hence, our new combination beams will include versions for 17 and 12 meters, for 15 and 10 meters, and for 20 and 15 meters.

**Fig. 1** provides a generalized sketch of the physical elements of the new set of beams. Like the versions using separate feedpoints, the new combinations will employ spider construction in order to maintain the spacing on each band used by the monoband beams. The angle between forward and rearward support arms is an average of the angles calculated from the collection of monoband quads. As noted in Part 2, very small variations in spacing make very little difference to performance compared to equally small variations in the element lengths.

Perhaps the one item in **Fig. 1** that requires further comment is the arrangement of the feedpoint. For each combination beam, the inner or higher frequency driver will use a square loop. All loop-shape distortion will involve the driver for the lower frequency of the pair. The design decision rests on a number of factors, not the least of which is relative simplicity compared to finding an intermediate position for the feedpoint that distorts both driver loops equally. In addition, experience suggests (but does not prove) that driver distortion has fewer negative effects on the lower frequency driver than on the inner or higher frequency driver.

To assess the quads that use a common feedpoint, we shall need some data at hand for reference. **Table 1** repeats the dimensions used on the same set of quads when using separate feedpoints. To the information presented in Part 2, I have added the circumference of the driver for each lower frequency quad.

All common-feed quad combinations sought to achieve the same goal used for the quads with separate feedpoints: restoration to the fullest extent possible of the performance of the monoband quads on which the designs rest. For immediate comparison of the physical results, **Table 2** provides the resulting dimensions for the common-feedpoint versions.

To obtain the circumference of any loop, we normally multiply the listed half-side length by 8. However, the models using a common feedpoint require us to add to the three linear sides the sloping and center sections of wire that creates the feedpoint. Hence, the circumference forms an odd value relative to the half-side lengths.

Certain general patterns show up in the physical dimensions. For each combination, the inner reflector for the higher-frequency band remains either fully or close to unchanged. However, every inner driver shows increased length relative to the inner drivers for the quads using separate feedpoints. Likewise, the outer reflectors for the lower frequency show virtually no change in length. As well, the circumferences of the outer drivers for the common-feedpoint quads are very close in overall length to the circumferences of the outer drivers for the versions using separate feedpoints. The inner drivers undergo the most extreme change of any element when converting from separate feedpoints to a common feedpoint, and the amount of change is significant. It ranges from a 6" to a 12" overall circumference increase, depending on the models involved. The lower band element exerts much more influence over the higher band driver, despite (or perhaps because of) the distortion in the lower-band driver shape. At the same time, both types of dual band quads use independent loops for reflector elements. In general, the interactions between the reflector elements do not change significantly when moving from separately fed drivers to drivers with a common feedpoint. You may wish to consult Part 1 for the dimensions of the original monoband quads to determine the total amount of variation, although changes in that variation apply mostly to the inner or higher-frequency driver elements.

We shall also need to compare the performance values for the common-feedpoint quads to corresponding figures for versions with separate feedpoints. **Table 3** collects the performance data for all of the 2-band quads into one table for convenient reference. We shall have occasion to refer to this table as we encounter each of the dual-band common-feedpoint quad assemblies.

The data that we shall develop on the new set of quads comes from NEC models. Although I habitually use NEC-4, all of the quad designs that we have so far explored work well with NEC-2. Nothing in the designs challenges NEC limitations. Hence, each quad so far has shown an Average Gain Test (AGT) score between 0.998 and 1.002, indicating a high reliability. I have also subjected the models to convergence tests. These tests altered the segmentation of each wire uniformly. For dual-band quads, I varied both the inner and the outer wire segmentation so as to maintain the same ratio of segments in corresponding wires relative to inner and outer loops. The goal was always to maintain to the degree possible an alignment between segment junctions. The results showed excellent convergence with relatively modest segmentation. Both the AGT and convergence tests are necessary but not sufficient conditions of model adequacy, but long use of wire quad models has resulted in relatively high reliability. (The reliability of the models presumes that physical implementations do not use construction methods that introduce corner fastening loops and other features that might detune an element relative to its model as a clean square.)

Given the high reliability of the models that we have used in Parts 1 and 2 of this exploration, we hope to achieve similar reliability for the common-feedpoint quads. However, the modeling itself presents a challenge.

**Modeling Common-Feedpoint Quads**

The only critical region of a dual-band quad model using a common feedpoint is the set of wires coming together at the feedpoint wire. The most common method used for developing the model appears in the upper section of **Fig. 2**.

The inner driver "bottom" wire consists of 3 modeled wires. The center wire consists of 3 segments, with the source or excitation placed on the center segment. The adjacent segments are the same lengths as the source segment, providing for equal currents on each side of the source segment. At the ends of this wire, we connect the remaining lengths of the inner driver wire. We segment each of these wires so that the segment lengths are as close as feasible to the segment lengths on the center wire.

The ends of the center wire also form junctions with the wires for the outer driver. We segment each of these added wires so that the segment lengths are as close as feasible to the lengths of segments in the center wire and in the inner driver wires. For many applications, this technique suffices to produce highly accurate models. The current division between the 2 driver loops does not occur until at least one segment away from the source segment.

In the case of the quad loops, the inner and outer driver wires form an angle. The angle appears to be fairly wide. In fact, if we were creating a a set of radials symmetrically arranged around a center junction, we might use much smaller angles and achieve high accuracy in the results from either NEC-2 or NEC-4. However, in the present situation, NEC-2 and NEC-4 shows considerable differences in the results that they report from a single quad model. Given a test model for 17 and 12 meters using this modeling scheme, NEC-2 reports a free-space gain at 18.118 MHz of 7.88 dBi and 7.74 dBi at 24.94 MHz. Changing the core to NEC-4 yielded gain reports of 7.19 and 7.06 dBi for the two frequencies. If we check the AGT values, NEC 2 produces values of 1.215 on 17 and 1.212 on 12. These values indicate that NEC-2 gain reports are about 0.85-dB too high. In the same conditions, NEC-4 produces AGT values of 1.037 and 1.038 for the two bands, still overestimating gain by about 0.16 dB. In addition to mis-reporting the gain, the source resistance will also be in error. To correct the source impedance, multiply the reported value by the basic AGT score.

The initial models of common-feedpoint quads present two challenges. First, we should be able to develop models with a more ideal AGT score, a value much close to 1.0 so that the gain reports require no adjustment. Second, the models should yield the same results under NEC-2 and NEC-4. Some years back, I worked out an alternative scheme for modeling feedpoints that essentially are in parallel with each other. The technique is applicable to common-feedpoint quads, as shown in the lower part of **Fig. 2**. We begin be retaining the structure of the inner driver wire, but we shall make no wire connections to it from the lower frequency or outer driver. Instead, we shall create parallel 3-segment wires, one for each driver. The sloping wires of the outer driver will connect to their own center wire. We should use enough spacing between the two center wires so that they do not interact significantly. We shall be able to tell the minimum correct spacing from AGT scores for the final model. We can begin with relatively close spacing and increase the spacing until the AGT values approaches 1.0 as closely as we need for a given modeling exercise.

The next step is to place a source or excitation on the center segment of one and only one of the center wires. Between the source segment and the corresponding center segment on the other center wire, create a transmission line with the NEC TL facility or command. Give the line a characteristic impedance somewhere in the ball park of the anticipated impedance values, although the actual value will not be at all critical. The key to establishing a parallel connection is to assign the transmission line as short a length as a given implementation of NEC will permit. Many programs permit lengths as short as 1e-10 meters if using the TL command directly. You may use the same specification in whatever unit may be in use, if the interface translates those units into meters internally. Some programs have certain minimum values for some or all length specifications. Whatever the lower limit, use it. The goal is to set up a line length that effects virtually no impedance transformation between one end and the other end of the line. Remember that the line length that you specify is independent of the physical distance between the center segments that you set up when establishing the two center wires.

Using this modeling system, both NEC-2 and NEC-4 return the same gain and impedance reports, with AGT scores very close to 1.0, for the test quad combination for 17 and 12 meters. We shall examine that model's performance in more detail shortly. For the moment, the development of a relatively reliable method of modeling common-feedpoint quads is our concern.

Despite the nearly ideal AGT score for the revised method of modeling the quads, we cannot claim that the model is as reliable as the monoband models or the dual-band models with separate feedpoints. In this instance, reliability refers to our ability to transfer the results to a physical implementation of the quad designs. The model does not correspond perfectly to the geometry of a typical common-feedpoint as constructed for use. Such common feedpoints normally consist of a center insulator where the wires join. The distance between the junctions of the two drivers is likely to be smaller than the length of the 3 segment center wires unless we use a very high number of segments per wavelength. Therefore, any physical implementation of a common-feedpoint quad should take the modeled data as a starting point for final field measurements and adjustments. However, the revised modeling system should come a good bit closer to field measurements than the initial modeling system.

**A 17-12-Meter 2-Element Quad Array Using A Common Feedpoint**

Because it involves a pair of narrow bands, the common-feedpoint 17-12-meter quad is the natural first experiment. The dimensions appear in **Table 2**. More pertinent to our interests here is **Table 4**, which provides the performance data. Compare the figures to those in **Table 3** for the 17-12-meter quad using separate feeders.

Compared to the separate feed model, the common feed 17-12-meter quad front-to-back curves appear to show an additional upward frequency shift. The 17-meter quad appears to reach peak value at the upper end of the band, while the 12-meter peak lies beyond the upper band limit. The gain levels are modest but well within expectations for a 2-element quad. Although the performance does not achieve the full monoband potential, the numbers and the patterns are fully appropriate for these bands. **Fig. 3** provides a gallery of free-space E-plane patterns for both bands to confirm this fact.

The impedance behavior of the common-feed dual band quad holds a surprise: the mid-band feedpoint impedances are very similar for the two bands. The impedances specifically leave remnant reactances due to an interesting potential for the array. A single 75-Ohm match-line can serve both bands in providing a satisfactory match to a 50-Ohm main feedline. The model calls for a 145" (electrical) length, although in practice, a builder may have to experiment with the length that yields the best 50-Ohm SWR curves on both bands. The modeled line is about 0.22 wavelength on 17 meters and about 0.31 wavelength on 12 meters. The matching line is an abbreviated form of series matching, for which Regier's work provides the most general solutions. The worst-case 50-Ohm SWR is 1.32:1, a value that meets the most stringent SWR requirements on the amateur bands.

The ability to have a common feedpoint and a single match-line--along with the fully adequate performance on both bands--makes the dual-band 17-12-meter quad a prime candidate for actual construction and use. However, remember that the common-feed models require slight distortions of the physical geometry in order to meet modeling constraints. Therefore, one cannot approach such a project is if the model formed a final template.

**A 15-10-Meter 2-Element Quad Array Using A Common Feedpoint**

The proper assessment the band-edge performance of the common-feedpoint quad requires that we examine models designed to cover wider bands. The 15-10-meter common-feedpoint quad provides one of two tests of the performance curves. **Table 5** gives us the summary data on the model's performance on both bands for comparison with data for the separate feedpoint models in **Table 3**.

On 15 meters, the rate of gain decrease across the band is identical to the rate for the separate feed model. **Fig. 4** shows the gain and front-top-back curves for 15 meters. Relative to the separate-feedpoint model, the common-feedpoint version appears to show an added shift of the 180-degree front-to-back curve upward in the band, even though the gain curves for the two types of quads are very similar. The peak front-to-back value occurs just above the mid-band frequency.

**Fig. 5** provides a gallery of free-space E-plane patterns for both the separate- and the common-feedpoint models on 15 meters. The clearest evidence of front-to-back upward frequency shift is the set of rear lobes that occur at 21 MHz. The common-feedpoint lobes are larger in all ways than those for the separate-feedpoint quad.

In **Fig. 6**, we see the post-match impedance curves for the 15 meter portion of the quad. The 110" (electrical length) 75-Ohm match-line is about 0.20 wavelength at the 15-meter design frequency. The result is an SWR curve that reaches its minimum value very low in the band. However, the upper band limit shows a maximum value that is under 1.7:1. Although we might change the length for a better match on 15, we have selected the length that yields the best compromise values for both 15 and 10 meters. The technique may not be ideal for the widest amateur upper-HF bands, but it is serviceable.

As the widest of the bands within our survey, the first MHz of 10 meters presents the greatest challenge to the common-feedpoint dual-band quad. The rate of gain decrease across the 10-meter band is actually lower than it is using separate feedpoints. The curves appear in **Fig. 7**. Once more, the common-feedpoint quad shows additional upward frequency shifting of the front-to-back curve relative to the separate-feedpoint model. The peak values of the 180-degree front-to-back ratio occurs at about 28.55 MHz.

The upward frequency drift of the performance curves shows itself most vividly in a comparison of the 28-MHz free-space E-plane patterns for both the separate- and the common-feedpoint models in **Fig. 8**. The band-edge front-to-back value of the common-feedpoint model is under 13 dB, and the pattern shows significant devolution compared to the 28-MHz pattern for the separate-feedpoint quad. In contrast, at 29 MHz, the separate-feedpoint model shows no signs of a 180-degree null, but the common-feedpoint model has a null that approaches 3 dB.

Although the pre-match feedpoint impedance values of both 15 and 10 meters are similar in value, the post-match impedances show interesting differences. The post-match impedance performance curves appear in **Fig. 9**. At 28.4 MHz, the 110" 75-Ohm match-line is about 0.26 wavelength. Once more the minimum 50-Ohm SWR occurs quite low in the band, with 29 MHz showing a value of 1.91:1--just barely within the usual amateur 2:1 standard. The 3.5% bandwidth of 10 meters provides a considerable challenge for a compromise match-line length. However, in principle, the system does work. The quad design is subject to enough variables in the translation into a physical antenna that one could not certify the system with out extensive field adjustment of the element lengths and the line length.

The 15-10-meter dual-band common-feed quad has its main function as a study model for observing the performance of the antenna under wide-band conditions. 10 meters provides the major challenge for the performance of the inner quad loops. There are potential outer band loops that must cover a wider bandwidth than the 2.1% offered by 15 meters.

**A 20-15-Meter 2-Element Quad Array Using A Common Feedpoint**

To confirm the general tendencies in wide-band performance of dual-band common-feedpoint quads, we may model a version for 20 and 15 meters. This combination places the challenge for coverage on 20 meters, the outer quad in the pair. As well, the frequency ratio is higher for this pair of quads: 1.5:1. **Table 6** provides the summary data about the performance of the pair.

As shown in **Fig. 10**, the rate of gain decrease across 20 meters is slightly lower for the common-feedpoint quad than for the version using separate feedpoints. However, the front-to-back curve slips further upward in frequency so that the peak value occurs at about 14.25 MHz. This slippage results in a continuing trend toward unequal front-to-back ratios at the band edges relative to the monoband model on which both dual-band quad beams rest.

The gallery of free-space E-plane patterns in **Fig. 11** shows the degradation of the common-feedpoint rear lobe structure at the low end of 20 meters. The 180-degree front-to-back ratio has fallen below 10 dB, a value that is considered low even for a 2-element driver-reflector Yagi. It is not clear whether one may further refine the design to move the front-to-back curve lower in the band and still retain adequate forward gain and a usable feedpoint impedance. Remember that among the 2-element quad performance characteristics, the front-to-back ratio undergoes the greatest change over any bandwidth. Normally, one can more easily obtain a feedpoint impedance curve meeting any of the normal limits than one can obtain a broad front-to-back curve that meets any of the usual standards.

The pre-match feedpoint impedance values on 20 meters (**Table 6**) are comparable to those for any of the other bands, with allowances for the bandwidth when comparing values. A 170" 75-Ohm match-line is about 0.20 wavelength at 14.14 MHz. It provides an adequate set of impedances for a 50-Ohm feedline, although the upper band edge shows an SWR of 1.8:1. As in the case of the 15-10-meter combination, the 20-meter minimum SWR value occurs quite low in the band.

The rate of gain decline on 15 meters in the present combination is lower than when we use separate feedpoints. Although the gain at the low end of 15 meters--as shown in **Fig. 13**--is lower than for the separate feedpoint version, the gain values at the upper end of the band are nearly the same. The front-to-back ratio curve shows its anticipated upward shift. The separate-feedpoint version of the array showed a peak front-to-back value near mid-band. With a common feedpoint, the peak value occurs at about 21.3 MHz. As well, the peak value does not reach 30 dB. Obtaining very high and narrow bandwidth values of front-to-back ratio is not operationally very significant. However, it is a measure of the degree to which multi-band and common-feedpoint interactions among wires decrease performance peaks.

The gallery of free-space E-plane patterns in **Fig. 14** provides a glimpse at the types of azimuth patterns that one might obtain over ground. Our interest is in comparing the patterns for separate feedpoints with those for a common feedpoint. As in the other wide-band dual-band quads in this part, the pattern at the lower edge of the band (here, 15 meters) shows the greatest change of shape relative to patterns for the monoband and separate-feedpoint 15-meter beams. The front-to-back ratio at 21 MHz is down by about 3 dB relative to the separate feedpoint model. Overall, even though the common-feedpoint quad uses a design frequency of 21.19 MHz, performance appears to be best in the SSB portion of the 15-meter band.

The pre-match impedance spread resembles the curves for all of the other bands. The total change in resistance is lower than on 20 meters, while the total change in reactance is about the same. However, on 20 meters, we needed a 170" 75-Ohm line to achieve a manageable 50-Ohm SWR curve across that band. This same line length on 15 meters is about 0.31 wavelength, somewhat longer than ideal for use as a single match-line for a common-feedpoint quad. Nevertheless, as shown in **Fig. 15**, the SWR curve fits, with a maximum value of 1.85:1. The peak value occurs at the low end of the band, and the 50-Ohm SWR never drops below about 1.2:1. Because 20 and 15 meters show peak SWR values at opposite ends of the band, any physical implementation of such a system is likely to require extensive field adjust to work.

Like the 15-10-meter combination, the 20-15-meter common-feedpoint quad model is most useful in displaying the wide-band behavior of this type of quad. Perhaps the 17-12-meter version is the one most apt for construction, especially since coverage of those bands very often is an afterthought and uses beams of lesser capability than antennas for 20, 15, and 10 meters.

**Conclusion to the Series**

Our efforts to model dual-band common-feedpoint quads have produced a number of results, most of which may be smaller in scope than one might have imagined prior to the step-by-step process that we have gone through to arrive at these models. As we did in Part 2, we retained the spacing of the basic monoband quads and used spider construction so that the angle formed between the reflectors and drivers in a multiband quad remained constant. In all cases, we simply adjusted element lengths to obtain the closest approach possible to monoband performance. Throughout, we used quads with a frequency ratio of at least 1.3:1.

Part 2 showed that the largest physical adjustments to the dimensions of monoband quads occur by virtue of simple proximity of one quad to the next. Despite the use of separate drivers for each of the 2 bands in each assembly, we had to change some of the element lengths to restore performance. The three dual-band quads that meet the basic requirements for this exploration all show the same patterns in physical and performance modifications relative to their monoband origins. The size of outer reflector increases, while outer drivers diminish. Inner reflectors require no change, whereas inner drivers shrink. The resulting performance patterns tend to shift gain and front-to-back curves slightly upward in the band, while allowing the pre-match feedpoint impedances to be near resonance on the original design frequencies. Both feedpoint impedances decrease, the outer by about 10 Ohms, the inner by about 25 to 30 Ohms.

The modification of these models for a common feedpoint required only small dimensional changes. For each combination, the inner reflector for the higher-frequency band remains either fully or close to unchanged. However, every inner driver shows increased length relative to the inner drivers for the quads using separate feedpoints. Likewise, the outer reflectors for the lower frequency show virtually no change in length. As well, the circumferences of the outer drivers for the common-feedpoint quads are very close in overall length to the circumferences of the outer drivers for the versions using separate feedpoints. The inner drivers undergo the most extreme change of any element when converting from separate feedpoints to a common feedpoint, and the amount of change is significant. It ranges from a 6" to a 12" overall circumference increase, depending on the models involved. The lower band element exerts much more influence over the higher band driver, despite (or perhaps because of) the distortion in the lower-band driver shape. At the same time, both types of dual band quads use independent loops for reflector elements. In general, the interactions between the reflector elements do not change significantly when moving from separately fed drivers to drivers with a common feedpoint.

Adding a common feedpoint for a dual-band quad does affect the performance to some degree. The upward shift in the performance curves for gain and the front-to-back ratio continues the progression that we first saw in 2-band quads with separate feedpoints. One result on wider amateur bands, such as 20, 15, and 10 meters, is a degradation of the rear lobe confinement at the low end of each band. In contrast, the near resonant feedpoint impedance at the design frequencies turned out to be very nearly the same for both bands of operation. The value of the resistive component is the value associated with the outer quad of separate-feedpoint dual-band quads. Although interesting, this result has limited utility if the impedance requires transformation in order to match the characteristic impedance of the main feedline. In the course of developing the common-feedpoint models, we saw that a single match-line length might serve 2 bands manageably, if not ideally.

The single match-line for a 50-Ohm main feedline is not a necessary condition of common-feedpoint quad operation. It is possible to feed the quads with a balanced, shielded parallel line composed of series-connected lengths of 50-Ohm cable. As the SWR curves for the two wide-band models show in **Fig. 16**, only 10 meters is wide enough to press the limits of the curve, even though the design frequency impedance is close to 120 Ohms. The direct feed system has the advantage of being applicable to common-feed multi-band quads covering 3 or more bands, so long as the impedance curves on each band are similar to those shown for the dual-band models.

The models that we chose as our baseline are not necessarily the best designs to implement for a multi-band quad using either separate or common feedpoints. I selected them because they presented the widest operating bandwidth of any 2-element quads using common wire elements. They offered us the best chance of seeing the dimension and performance changes that 2-band operation might create, while still maintaining recognizable performance curves. Along the way, the feedpoint impedance was not the limiting factor. The front-to-back ratio remains the quad's most changeable parameter as we scan any of the wider upper-HF amateur bands. If we wish full band coverage of 20, 15, or 10 meters, then we must decide if a relatively low front-to-back ratio at one band edge or the other is a satisfactory condition. If we only wish to cover a portion of these wider bands, then the 2-element quad becomes competitive with a 3-element short boom monoband Yagi and highly competitive with multi-band Yagis using considerably longer booms.

*Updated 02-01-2007. © L. B. Cebik, W4RNL. This item appeared in* AntenneX*, November, 2006. 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.*