40 + 30 = 50 (Not 70)
The Rudiments of a Design Idea

L. B. Cebik, W4RNL (SK)

A number of requests over the years have taken this direction: can you design a combination 40 meter and 30 meter beam on a single boom--making everything give full-size performance but still be compact--relative to the bands involved?

That request is a tall order. Full size Yagi elements for 40 meters run over 70' in length. Most commercial Yagis for 40 meters use various methods of element shortening to reduce the raw physical load created by full size elements. Linear and inductive loading are the two most popular approaches. However, there are a number of 3 and 4 element full size Yagis on the job. (Very often, the 4th Yagi element functions less to increase gain and more to permit a wide operating bandwidth.)

30-meter elements are more modest at lengths approaching 45-50'. As well, the band is narrow enough (50 kHz) to permit the use of narrow-band, high performance driver-director Yagis. A beta match usually suffices to bring the low feedpoint impedance up to standard coax levels. (Of course, we should not overlook the relatively compact phased array for 30 meters developed by N7CL.)

It would be nice if a combined 40 and 30 array could have elements that extended no further outward than the +/-25' required for 30-meter elements. There is a way of achieving this goal, but it is not likely to be an easy one to implement in a physical design. There are some adjustments that require field implementation, and they can be a bit daunting. As well, supporting the number of elements in the final array, along with their peculiarities, will also require engineering beyond the scope of this design exercise. However, for whatever it may be worth, here is a design that will cover all of both bands with only a 50' side-to-side width.

These note can only be the rudiments of a design and not a finished product. Because I do not have the facilities or tower to build and test the array, I cannot complete all of the mechanical details that will also have an impact on the electrical design. At best, I can only locate some of the many points where the individual designer and builder will have to make decisions and refine the outlines given here.

The basic design consists of a Moxon rectangle for 40 meters with a 2-element driver-director Yagi for 30 meters. The 30-meter driver is slaved to the 40-meter Moxon fed element. Fig. 1 shows a general outline sketch of the array.

The maximum side-to-side width of the array is 50'. The boom length is 26' (plus whatever excess is necessary for proper element support). There are a total of 4 elements, with the Moxon elements having end tails that point toward each other. The Moxon element arrangement will present physical problems that we shall take up later.

Fig. 1 labels each dimension, and the following table provides numbers that go with the labels. However, the dimensions are based on NEC-4 models of the array using 1" diameter aluminum elements throughout. I chose the modeling diameter based upon the equivalent uniform diameter of elements from a number of 40-meter arrays on file. Although such arrays begin with large diameter tubing--sometimes up to 3"--they step downward rapidly and end up with 0.5" and even 0.375" element diameters at the outer ends. We shall go into the meaning of this situation for practical antenna construction before we are done. First, some basic dimensions.

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40-30-Meter Moxon-Yagi Combination Dimensions

Note: all dimensions are in feet and correspond to designations shown in Fig. 1.

Dimension Length in Feet
A 50.00'
B 7.21'
C 1.73'
D 9.47'
E 18.41'
F 0.64'
G 6.95'
H 26.00'
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Before we look into the dimensions and their implications for refinement and construction, let's first see if this is a design in which you would be interested by virtue of its performance. The 40-meter performance is strictly Moxon-rectangle standard. One of the reasons for using fatter elements (instead of wire) is to increase the operating passband width, not just in terms of SWR, but as well, to include a spreading of the gain and front-to-back profiles.

Fig. 2 provides azimuth and elevation plots for the 40-meter array at the edges and middle of the band. The antenna height is 70' or about 1/2 wavelength on 40. I would not recommend using the array below 70' or else you will have to make some adjustments to center the SWR curve. Like every Moxon rectangle, the beamwidth tends to be wider than that of most Yagis.

Fig. 3 provides band edge and center patterns for 30 meters, which are mostly a function of the forward two elements. However, the 40-meter elements also function in a minor way as reflectors to increase the overall performance. (We determine this in part by the current levels on the Moxon elements and also by the increase in performance over a stand-alone 2-element driver-director Yagi of the same spacing.) A 2-element driver director Yagi with closely spaced elements (less than 0.08 wavelength) yields quite high gain and a good front-to-back ratio, but only over a narrow bandwidth. Being "slaved" to the Moxon rectangle (or any other fed array) tends to further reduce the operating bandwidth. Only the narrowness of 30 meters permits good performance (for an array of this type) across the entire band.

To translate the patterns into more definite numbers, the following table gives the principal operating predictions from the model.

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40-30-MHz Array Operating Potential at 70'

Freq. Gain 180-Deg/Worst-Case Feedpoint Z 50-Ohm
MHz dBi Front-to-Back dB R +/- jX Ohms SWR
40 Meters: TO/Elevation Angle of Maximum Radiation: 26 degrees
7.0 11.29 13.32--13.32 41.3 - j22.1 1.68
7.1 11.14 20.37--20.37 67.3 - j12.9 1.49
7.2 10.90 15.99--15.73 85.3 - j16.8 1.80
7.3 10.66 12.17--12.17 91.7 - j21.2 1.97
30 Meters: TO/Elevation Angle of Maximum Radiation: 19 degrees
10.0 11.50 16.35--14.25 84.0 + j10.4 1.72
10.125 12.05 24.76--18.18 42.9 + j 3.1 1.18
10.15 12.17 22.47--19.43 32.3 + j 8.7 1.63
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The take-off angles for the two bands, of course, are functions of the fact that, with respect to a wavelength, the antenna is higher on 30 meters than on 40 meters. Only part of the extra 30-meter gain is attributable to the increased height. Most of it stems from the fact that a closely spaced driver-director Yagi in fact has more gain than the Moxon rectangle or a comparably spaced driver-reflector Yagi.

The key influences of the arrays on each other show up in the impedance reports. The slaved 30-meter driver keeps the Moxon feedpoint reactance capacitive in this array, when an independent Moxon might well show a shift from capacitive to inductive reactance across the band. The slaved 30-meter driver also affects the feedpoint impedance on the 40-meter element during 10-MHz operation, creating a dip in the inductive reactance at mid-band, but not going into the capacitive region. Expect impedance curves in an actual antenna that may even vary from these, according to the finally selected dimensions used in the array.

Fig. 4 provides both 50-Ohm SWR curves on one graph. It is unlikely that one can change the 30-meter curve much, except to move it a bit up and down the narrow band. The Moxon 40-meter curve might well show improvement with careful adjustment of some of the dimensions.

One cannot simply buy a batch of 1" diameter tubing and construct this array. The first task for any builder is to determine the stepped-diameter schedule to be used. For the 4 elements, the first portions up to 25' from center can all be identical, assuming that the smallest diameter tubing used allows sufficient strength to support the tails.

Once you have selected a mechanically sound element taper schedule, the best procedure is then to convert the uniform 1" diameter element lengths into lengths suitable for the stepping schedule. It is very likely that you will have to lengthen all side-to-side dimensions with the tubing that you use. Elements that taper downward from center to outer end usually require greater length than uniform diameter elements. The differential may amount only to a few inches, but it will be enough to detune both portions of the array considerably if not taken into account.

There are handbook formulas for making the transformation of element lengths. However, one of the most convenient methods is to create a model on a NEC program and adjust the element tip lengths until you arrive at uniform-diameter equivalents that match the initial design. If the equivalent uniform element diameter is between 0.8 and 1.2 inches, the original dimensions will not require much adjustment. However, feel free to customize the design to your own desires. Both EZNEC and NEC-Win Plus have provisions for creating uniform-diameter substitute elements for unloaded symmetrical elements using a tapering schedule.

In the Moxon portion of the array, perhaps the most critical dimension is the gap between element tails. The Moxon makes use of 2 forms of elements coupling to achieve its patterns and impedance: mutual coupling between the element portions parallel to each other and end coupling between the tails. The degree of end coupling depends upon 2 factors: the space between the tail ends and the diameter of the elements at that point. The initial design makes use of 1" diameter tail ends, but a tapered-element schedule is likely to use smaller diameter tubing for the tail ends. Therefore, to achieve the same coupling with smaller tubing, the tails will need to be brought closer together--without significantly changing the overall final design length of the reflector element (including the parallel and tail sections). Incidentally, one cannot use the tapered-diameter correction facility in NEC-2 programs with the Moxon rectangle, since the elements are not linear. However, one can use sundry work arounds to arrive at adequate construction guidance (including obtaining a NEC-4 program).

To keep the tails aligned, it is very useful to use a section of non-conductive tubing that just fits inside the two tail end tubes. Since the goal is alignment rather than mechanical support, the tubing can be relatively light, such a CPVC or similar. We shall turn to mechanical support soon.

The slaved 30-meter driver must be very close (0.64' in the model) to the 40-meter Moxon driver to achieve the desired feedpoint impedance. Several factors suggest that the element spacing will not be identical to the initial model used here. First, using a tapered diameter schedule will alter the coupling slightly along the length of both elements. Second, the model is reaching the limits for giving accurate reports with closely spaced elements of different lengths, even though the segment ends are closely aligned throughout the mode. This is a NEC limitation. Therefore, expect to make adjustments to the spacing of the slaved driver and to its length as well. At 30 meters, one can make several inches worth of adjustment without having to restore the director to the initial design spacing from the driver. However, finding the right combination of element spacing and length to achieve an acceptable 50-Ohm SWR curve on the main driver from 10.0 to 10.015 MHz can be laborious. Adjustments work best when the initial setting is somewhere close to ideal. When the elements are spaced too far apart, the progression of results for small adjustments seems to move in the opposite direction than when inside the ballpark. Hence, once can work for hours, being led all of the time in the wrong direction. When adjustments only seem to make matters worse, return to the starting point and begin again, but in the opposite direction as used during the first run.

Elements as large as those used in the array will tend to oscillate in the wind. Because the Moxon elements, with their tails, are constrained by the non-conductive tail links, the 40-meter assembly will have wind-motion characteristics quite unlike the 30-meter elements, with their free ends. Collisions between the 30-meter slaved driver and the 40-meter fed driver will be inevitable. Therefore, some means of holding the 30-meter slaved driver and the 40-meter Moxon driver in alignment is likely more a necessity than something merely desirable.

Besides holding the drivers in alignment, we also need a means of supporting the 40-meter tails. The tail assemblies on a large Moxon rectangle place significant strain on the two elements supporting them. One method of support is to use tubing sizes large enough that the weight of the tails is no especial problem. Alternatively, one might develop a supplemental support system for the entire array that can reduce element stress and keep the elements aligned.

Fig. 5 shows the basic outline of such a scheme. Somewhere (sensible, from a mechanical perspective) above the main boom, install a shorter stiff boom on the mast. This boom will be used to hold one end of a series of stays, that is, non-conductive support lines for the elements.

At a mechanically sensible point outward on each side of center, place a non-conductive support arm (tube?) so that it is beneath each element. By a series of notches and/or ties, fastened to each element to the arm. Because there will still be differences in the way elements react to the wind, the tie system should be set to fix the spacing but to let the individual elements slide a bit. On one or more elements, fix the arm in both directions so that the stay-system does not pull the arm inward.

At points near the out ends of the arms, connect and fasten the stays. If the arm material is too flexible, you may add a third set of stays perpendicular to the mast. The support system then depends on the equalization of tension on the stays.

Without a set of specific load figures, derived from a program like YagiStress and customized to the particular element diameter schedule chosen for the array, it is impossible to recommend any particular set of dimensions for the support-arm-and-stay system. Indeed, there are many variations on this theme that one might apply to the array. However, the basic message is that this is a major collection of aluminum tubing that has considerable weight and wind area. Adequate support is a necessity if the design and construction effort goes for naught during the first stiff breeze.

As we noted at the beginning, these notes only begin the design process; they do not complete it. I have tried to locate many of the areas that will need detailed attention before one can begin to gather materials, let along start actual construction.

Nonetheless, the design principle is sound, having been applied to light arrays for the upper HF region. It does show that a combination 40-30-Meter array is possible with quite decent full-band performance for a 26' boom. Until I have facilities and space to try out the design with an actual set of elements on a tower that will give me the minimal height for adequate performance, these notes will have to do. Unfortunately, I do not have time at present to customize the design for specific taper schedules, but you can do the job yourself with any of the low-end NEC-2 programs with a facility for providing uniform-diameter equivalents. Even when the customizing has been completed within the design system, expect to do considerable adjustment on the physical product of this work.

For those who wish to model the array, the following EZNEC model description should suffice to create a model in any of the leading programs.

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40-30-M Moxon-Yagi Array Frequency = 7.1 MHz.

Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1

--------------- WIRES ---------------
Wire Conn. --- End 1 (x,y,z : ft) Conn. --- End 2 (x,y,z : ft) Dia(in) Segs
(40-meter elements)
1 -25.000, 11.200, 70.000 W2E1 -25.000, 18.406, 70.000 1.00E+00 7
2 W1E2 -25.000, 18.406, 70.000 W3E1 25.000, 18.406, 70.000 1.00E+00 45
3 W2E2 25.000, 18.406, 70.000 25.000, 11.200, 70.000 1.00E+00 7
4 -25.000, 9.472, 70.000 W5E1 -25.000, 0.000, 70.000 1.00E+00 9
5 W4E2 -25.000, 0.000, 70.000 W6E1 25.000, 0.000, 70.000 1.00E+00 45
6 W5E2 25.000, 0.000, 70.000 25.000, 9.472, 70.000 1.00E+00 9
(30-meter elements)
7 -24.000, 19.050, 70.000 24.000, 19.050, 70.000 1.00E+00 43
8 -22.900, 26.000, 70.000 22.900, 26.000, 70.000 1.00E+00 41

-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 23 2 / 50.00 ( 2 / 50.00) 1.000 0.000 V

Ground type is Real, high-accuracy analysis
Conductivity = .005 S/m Diel. Const. = 13
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