In the first part of the case study, we looked at the 4 Ss of designing by modeling: Starting Point, Specifications, Strategy, and Segmentation. Essentially, we began with a design by ON7NQ and built upon it on the way to developing the following antenna model, shown as a wire assembly:
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W4RNL 4.5-Element, 5-Band Quad Model
Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
Wire Conn. --- End 1 (x,y,z : in) Conn. --- End 2 (x,y,z : in) Dia(in) Segs
1 W4E2 0.000,-108.50,-108.50 W2E1 0.000,108.500,-108.50 8.09E-02 15
2 W1E2 0.000,108.500,-108.50 W3E1 0.000,108.500,108.500 8.09E-02 15
3 W2E2 0.000,108.500,108.500 W4E1 0.000,-108.50,108.500 8.09E-02 15
4 W3E2 0.000,-108.50,108.500 W1E1 0.000,-108.50,-108.50 8.09E-02 15
5 W8E2 0.000,-84.250,-84.250 W6E1 0.000, 84.250,-84.250 8.09E-02 13
6 W5E2 0.000, 84.250,-84.250 W7E1 0.000, 84.250, 84.250 8.09E-02 13
7 W6E2 0.000, 84.250, 84.250 W8E1 0.000,-84.250, 84.250 8.09E-02 13
8 W7E2 0.000,-84.250, 84.250 W5E1 0.000,-84.250,-84.250 8.09E-02 13
9 W12E2 0.000,-72.700,-72.700 W10E1 0.000, 72.700,-72.700 8.09E-02 11
10 W9E2 0.000, 72.700,-72.700 W11E1 0.000, 72.700, 72.700 8.09E-02 11
11 W10E2 0.000, 72.700, 72.700 W12E1 0.000,-72.700, 72.700 8.09E-02 11
12 W11E2 0.000,-72.700, 72.700 W9E1 0.000,-72.700,-72.700 8.09E-02 11
13 W16E2 0.000,-61.200,-61.200 W14E1 0.000, 61.200,-61.200 8.09E-02 9
14 W13E2 0.000, 61.200,-61.200 W15E1 0.000, 61.200, 61.200 8.09E-02 9
15 W14E2 0.000, 61.200, 61.200 W16E1 0.000,-61.200, 61.200 8.09E-02 9
16 W15E2 0.000,-61.200, 61.200 W13E1 0.000,-61.200,-61.200 8.09E-02 9
17 W20E2 0.000,-55.000,-55.000 W18E1 0.000, 55.000,-55.000 8.09E-02 7
18 W17E2 0.000, 55.000,-55.000 W19E1 0.000, 55.000, 55.000 8.09E-02 7
19 W18E2 0.000, 55.000, 55.000 W20E1 0.000,-55.000, 55.000 8.09E-02 7
20 W19E2 0.000,-55.000, 55.000 W17E1 0.000,-55.000,-55.000 8.09E-02 7
21 W24E2 60.000,-60.300,-60.300 W22E1 60.000, 60.300,-60.300 8.09E-02 9
22 W21E2 60.000, 60.300,-60.300 W23E1 60.000, 60.300, 60.300 8.09E-02 9
23 W22E2 60.000, 60.300, 60.300 W24E1 60.000,-60.300, 60.300 8.09E-02 9
24 W23E2 60.000,-60.300, 60.300 W21E1 60.000,-60.300,-60.300 8.09E-02 9
25 W28E2 60.000,-52.900,-52.900 W26E1 60.000, 52.900,-52.900 8.09E-02 7
26 W25E2 60.000, 52.900,-52.900 W27E1 60.000, 52.900, 52.900 8.09E-02 7
27 W26E2 60.000, 52.900, 52.900 W28E1 60.000,-52.900, 52.900 8.09E-02 7
28 W27E2 60.000,-52.900, 52.900 W25E1 60.000,-52.900,-52.900 8.09E-02 7
29 W32E2 120.000,-106.50,-106.50 W30E1 120.000,106.500,-106.50 8.09E-02 15
30 W29E2 120.000,106.500,-106.50 W31E1 120.000,106.500,106.500 8.09E-02 15
31 W30E2 120.000,106.500,106.500 W32E1 120.000,-106.50,106.500 8.09E-02 15
32 W31E2 120.000,-106.50,106.500 W29E1 120.000,-106.50,-106.50 8.09E-02 15
33 W36E2 120.000,-82.800,-82.800 W34E1 120.000, 82.800,-82.800 8.09E-02 13
34 W33E2 120.000, 82.800,-82.800 W35E1 120.000, 82.800, 82.800 8.09E-02 13
35 W34E2 120.000, 82.800, 82.800 W36E1 120.000,-82.800, 82.800 8.09E-02 13
36 W35E2 120.000,-82.800, 82.800 W33E1 120.000,-82.800,-82.800 8.09E-02 13
37 W40E2 120.000,-70.700,-70.700 W38E1 120.000, 70.700,-70.700 8.09E-02 11
38 W37E2 120.000, 70.700,-70.700 W39E1 120.000, 70.700, 70.700 8.09E-02 11
39 W38E2 120.000, 70.700, 70.700 W40E1 120.000,-70.700, 70.700 8.09E-02 11
40 W39E2 120.000,-70.700, 70.700 W37E1 120.000,-70.700,-70.700 8.09E-02 11
41 W44E2 120.000,-59.100,-59.100 W42E1 120.000, 59.100,-59.100 8.09E-02 9
42 W41E2 120.000, 59.100,-59.100 W43E1 120.000, 59.100, 59.100 8.09E-02 9
43 W42E2 120.000, 59.100, 59.100 W44E1 120.000,-59.100, 59.100 8.09E-02 9
44 W43E2 120.000,-59.100, 59.100 W41E1 120.000,-59.100,-59.100 8.09E-02 9
45 W48E2 120.000,-52.200,-52.200 W46E1 120.000, 52.200,-52.200 8.09E-02 7
46 W45E2 120.000, 52.200,-52.200 W47E1 120.000, 52.200, 52.200 8.09E-02 7
47 W46E2 120.000, 52.200, 52.200 W48E1 120.000,-52.200, 52.200 8.09E-02 7
48 W47E2 120.000,-52.200, 52.200 W45E1 120.000,-52.200,-52.200 8.09E-02 7
49 W52E2 216.000,-97.500,-97.500 W50E1 216.000, 97.500,-97.500 8.09E-02 15
50 W49E2 216.000, 97.500,-97.500 W51E1 216.000, 97.500, 97.500 8.09E-02 15
51 W50E2 216.000, 97.500, 97.500 W52E1 216.000,-97.500, 97.500 8.09E-02 15
52 W51E2 216.000,-97.500, 97.500 W49E1 216.000,-97.500,-97.500 8.09E-02 15
53 W56E2 216.000,-79.900,-79.900 W54E1 216.000, 79.900,-79.900 8.09E-02 13
54 W53E2 216.000, 79.900,-79.900 W55E1 216.000, 79.900, 79.900 8.09E-02 13
55 W54E2 216.000, 79.900, 79.900 W56E1 216.000,-79.900, 79.900 8.09E-02 13
56 W55E2 216.000,-79.900, 79.900 W53E1 216.000,-79.900,-79.900 8.09E-02 13
57 W60E2 216.000,-69.750,-69.750 W58E1 216.000, 69.750,-69.750 8.09E-02 11
58 W57E2 216.000, 69.750,-69.750 W59E1 216.000, 69.750, 69.750 8.09E-02 11
59 W58E2 216.000, 69.750, 69.750 W60E1 216.000,-69.750, 69.750 8.09E-02 11
60 W59E2 216.000,-69.750, 69.750 W57E1 216.000,-69.750,-69.750 8.09E-02 11
61 W64E2 216.000,-59.900,-59.900 W62E1 216.000, 59.900,-59.900 8.09E-02 9
62 W61E2 216.000, 59.900,-59.900 W63E1 216.000, 59.900, 59.900 8.09E-02 9
63 W62E2 216.000, 59.900, 59.900 W64E1 216.000,-59.900, 59.900 8.09E-02 9
64 W63E2 216.000,-59.900, 59.900 W61E1 216.000,-59.900,-59.900 8.09E-02 9
65 W68E2 216.000,-52.500,-52.500 W66E1 216.000, 52.500,-52.500 8.09E-02 7
66 W65E2 216.000, 52.500,-52.500 W67E1 216.000, 52.500, 52.500 8.09E-02 7
67 W66E2 216.000, 52.500, 52.500 W68E1 216.000,-52.500, 52.500 8.09E-02 7
68 W67E2 216.000,-52.500, 52.500 W65E1 216.000,-52.500,-52.500 8.09E-02 7
69 W72E2 312.000,-98.000,-98.000 W70E1 312.000, 98.000,-98.000 8.09E-02 15
70 W69E2 312.000, 98.000,-98.000 W71E1 312.000, 98.000, 98.000 8.09E-02 15
71 W70E2 312.000, 98.000, 98.000 W72E1 312.000,-98.000, 98.000 8.09E-02 15
72 W71E2 312.000,-98.000, 98.000 W69E1 312.000,-98.000,-98.000 8.09E-02 15
73 W76E2 312.000,-79.900,-79.900 W74E1 312.000, 79.900,-79.900 8.09E-02 13
74 W73E2 312.000, 79.900,-79.900 W75E1 312.000, 79.900, 79.900 8.09E-02 13
75 W74E2 312.000, 79.900, 79.900 W76E1 312.000,-79.900, 79.900 8.09E-02 13
76 W75E2 312.000,-79.900, 79.900 W73E1 312.000,-79.900,-79.900 8.09E-02 13
77 W80E2 312.000,-69.650,-69.650 W78E1 312.000, 69.650,-69.650 8.09E-02 11
78 W77E2 312.000, 69.650,-69.650 W79E1 312.000, 69.650, 69.650 8.09E-02 11
79 W78E2 312.000, 69.650, 69.650 W80E1 312.000,-69.650, 69.650 8.09E-02 11
80 W79E2 312.000,-69.650, 69.650 W77E1 312.000,-69.650,-69.650 8.09E-02 11
81 W84E2 312.000,-59.300,-59.300 W82E1 312.000, 59.300,-59.300 8.09E-02 9
82 W81E2 312.000, 59.300,-59.300 W83E1 312.000, 59.300, 59.300 8.09E-02 9
83 W82E2 312.000, 59.300, 59.300 W84E1 312.000,-59.300, 59.300 8.09E-02 9
84 W83E2 312.000,-59.300, 59.300 W81E1 312.000,-59.300,-59.300 8.09E-02 9
85 W88E2 312.000,-52.000,-52.000 W86E1 312.000, 52.000,-52.000 8.09E-02 7
86 W85E2 312.000, 52.000,-52.000 W87E1 312.000, 52.000, 52.000 8.09E-02 7
87 W86E2 312.000, 52.000, 52.000 W88E1 312.000,-52.000, 52.000 8.09E-02 7
88 W87E2 312.000,-52.000, 52.000 W85E1 312.000,-52.000,-52.000 8.09E-02 7
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In order to evaluate the design--while still in its modeling stage--let's review the performance of the smaller ON7NQ design.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeled Performance: ON7NQ 3.5-element, 5-Band Quad NEC-4; Full Segmentation Freq. Gain Front/Back Impedance 50-Ohm MHz dBi dB R +/- jX SWR 14.0 8.42 11.83 37.6 - j 18.5 1.66 14.175 8.29 15.06 44.3 + j 4.4 1.17 14.35 8.06 9.76 34.8 + j 36.5 2.50 18.068 8.47 21.80 42.7 - j 5.1 1.21 18.118 8.42 25.52 43.5 - j 0.3 1.15 18.168 8.36 20.90 43.2 + j 4.6 1.19 21.0 8.43 15.28 49.7 - j 20.1 1.49 21.225 8.52 20.98 46.4 - j 0.0 1.08 21.45 8.47 10.24 36.2 + j 30.7 2.16 24.89 9.26 22.72 35.1 - j 2.1 1.43 24.94 9.22 18.92 41.1 + j 2.3 1.27 24.99 9.18 16.70 47.6 + j 4.8 1.12 28.0 9.01 18.40 43.8 - j 31.6 1.96 28.2 9.35 25.89 45.3 - j 11.0 1.29 28.4 9.62 30.72 51.3 + j 6.8 1.15 28.6 9.85 22.80 58.7 + j 9.6 1.27 28.8 9.73 12.38 31.1 + j 8.1 1.68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
For comparison, here are the modeled performance figures for the larger design.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeled Performance: W4RNL 4.5-element, 5-Band Quad NEC-4; Full Segmentation Freq. Gain Front/Back Impedance 50-Ohm MHz dBi dB R +/- jX SWR 14.0 8.81 15.02 33.7 - j 20.8 1.88 14.175 8.58 16.76 51.9 + j 10.0 1.22 14.35 8.14 9.95 57.8 + j 34.0 1.89 18.068 9.23 22.01 36.1 - j 1.8 1.39 18.118 9.18 21.24 39.2 + j 5.7 1.32 18.168 9.10 17.38 42.3 + j 12.5 1.38 21.0 9.49 15.33 41.5 - j 15.6 1.47 21.225 9.47 17.04 57.0 + j 7.5 1.21 21.45 9.54 19.13 31.3 + j 10.0 1.70 24.89 10.27 21.79 38.6 + j 5.3 1.33 24.94 10.28 19.82 40.3 + j 9.1 1.35 24.99 10.24 16.77 41.9 + j 14.4 1.43 28.0 9.59 12.15 40.8 - j 27.4 1.88 28.2 10.15 17.00 49.3 - j 12.7 1.29 28.4 10.60 20.51 47.1 - j 2.8 1.09 28.6 10.85 19.77 42.6 + j 18.1 1.52 28.8 10.51 29.75 64.9 + j 12.1 1.40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design Evaluation
In this morass of data are some significant figures. First, note that, to a very large degree, the performance curves of the larger array on each band tend to replicate the curves of the smaller array, but with a higher gain. The replication strongly suggests that--with a few exceptions--the array has yielded about all of the performance of which it is capable. But how well did it meet its specifications?
1. Gain: at least 0.7 dB greater than the existing array
Although the improvement in gain is not a constant for any individual band, the following average gain advantage/band list suggest the performance improvement provided by the extra set of directors.
Performance Improvement: 3.5 Elements vs. 4.5 Elements Band Gain Improvement 20 Meters 0.25 dB 17 0.75 15 1.03 12 1.04 10 0.90
Only 20 meters fails to show a considerable gain increase. The reasons will be explained in the discussion of "Coverage."
2. Front-to-Back Ratio: at least 15 dB across each band--if possible
Only the upper end of 20 meters and the lowest end of 10 meters fail to reach the 15-dB front-to-back ratio. The 10-meter low-end failure stems from the fundamental narrow-band nature of wire quads. The SWR curve is wider than the front-to-back curve in virtually all cases, even when the front-to-back limit is lowered to 15 dB.
3. Source Impedance: less than 2:1 50-Ohm SWR for direct feed (individually) on each band with a standard 50-Ohm coaxial cable
The 4.5-element array, unlike the 3.5-element quad, achieves the SWR goal on all bands, with the restriction of 10 meters to the first 800 kHz of the band. The failure of the 3.5-element quad to achieve the SWR goal on 15 meters is correctable with slight shortening of the driven element. The SWR at the low end of the band (1.49:1) suggests that considerably more capacitive reactance can be tolerated at 21 MHz, with a consequent lowering of inductive reactance at the high end of the band. However, this approach does not work on 20 meters, since the low-end resistive component is well below 40 Ohms, indicating a limit to the capacitive reactance increase that might be tolerated. One or the other end of the band ends up with an SWR in excess of 2:1
4. Coverage: Full band coverage of all bands, with 800 kHz coverage of 10 meters
This criterion essentially is a replication of the SWR specification. The breadth of 10 meters has already been noted as the source of the cut-off at 28.8 MHz and the low front-to-back ratio and gain in the first 100 kHz of the band. However, 20 meters also calls for comment.
On a normal (20-10-meter) quad, 20-meters is unbounded on the outside. Moreover, the boom length for 4 elements is exceptionally short. 26' would be about the normal boom length for a 3-element monoband 20-meter quad, although the gain would be similar to the peak value for the large array on 20. To achieve full band coverage with the 4.5-element antenna, considerable changes to the director sizes were needed compared to the 3.5-element array director. As well, the forward director is larger than the inner director.
It is possible with larger directors to achieve higher gain over part of the 20-meter band. Free-space gain values up to 9.25 dBi were achieved in some versions, but the higher the gain, the narrower the available operating region, as defined by the 2:1 SWR figure. As well, the checkpoint numbers recorded to indicate array behavior tend to gloss over many facets of both gain and front-to-back ratio. For example, on 20 meters, maximum gain occurs just above the lower end of the band, with maximum front-to-back occurring at about 14.1 MHz. Hence, it pays to use checkpoint data with caution and to perform detailed frequency sweeps for each band to assess the performance more thoroughly.
To achieve an acceptable SWR value for the entire band, it was necessary to accept as well a lower gain value. The performance tapers off at the high end of the band, although operation on that portion of the band is possible. By accepting a bandwidth restriction on 20 meters, the smaller 3.5-element array was able to achieve somewhat higher gain at the low end of the band relative to its size. Therefore, the small average gain increase on 20 for the 4.5-element array results in part from differences in the design specifications for the two different antennas.
If one were to increase the boom length to 30 feet, changing the forward director spacing from 8' relative to the preceding elements to 12' from that element set, it is possible to elevate 20-meter performance by about 0.2 dB with a very slight decrease in the gain slope and to obtain a very slightly shallower front-to-back curve with small rises in the band edge performance. However, the cost in terms of a longer boom, with consequential loading considerations, may make this small gain somewhat gratuitous. In any event, the potential is there for anyone who wishes to re-tweak the array on all other bands.
Reality 1: Pattern Shapes
Some designers expect multi-band arrays to achieve patterns similar to those of monoband directional antennas. The forward lobe will be a single large oval, while the rearward radiation will consist of from 1 to 3 small lobes, each at least 20 dB under the forward gain. Unfortunately, multi-band arrays (with the possible exception of large LPDAs) tend to have patterns that are often far from well behaved. The interaction among the elements--even supposedly inactive elements--remains considerable, as would be evident from an exploration of the current tables produced by NEC. This problem or condition is not exclusively a quad problem, but also attends to large multi-band Yagis as well.
Not all bands suffer from ill-behaved patterns. As the 20-meter samples in Fig. 1 show, the patterns are quite ordinary. However, as the outside loop set, the 20 meter elements interact least with other elements in the array.
The sample 15-meter patterns in Fig. 2 show a truer picture of the effects of interactions between the active and inactive elements in the array--where "inactive" means elements for a band other than the one in use. One casualty of the interaction is the front-to-rear ratio, as rearward side lobes grow to considerable proportions. A number of design decisions were made in the process of modeling and optimizing this band. The gain was sacrificed to a small degree in order to obtain the best possible progression of rear lobe formation across the band.
The single 12-meter pattern in Fig. 3 frames another common element interaction problem--the formation of side lobes. The small side lobes appear from 15 meters on upward in frequency and are likely the result of harmonic operation of larger elements. Under these conditions, currents in the vertical side wires can yield radiation to the array sides in the form of minor side lobes.
Fig. 4 provides a progression of 10-meter patterns to display how radically a pattern may change across a wide band. The changes to the rear pattern are most evident. However, in the forward direction, note that the minor side lobes develop into considerable bulges with increases in frequency. Of all bands, 10 meter may be the most sensitive to excitation of inactive elements. The 12-meter elements are within the range of reflector size, and the 20 meter elements may operate in a harmonic mode, even though isolated from the 10-meter elements by intervening bands.
By no means does less-than-perfection in the array patterns count against the use of multi-band, multi-element quads. Rather, the patterns are a simple fact of life that one must take into account both in the design and utilization phases of the antenna.
Reality 2: Quad Construction
We have noted the relationship between the design-by-modeling process and the ultimate use of the quad array. Omitted to this point is the relationship between antenna design and modeling on the one hand and antenna construction on the other. Ordinarily, we have passed over this aspect of activity with simple cautions that the model applies accurately within the limitations of the construction process.
For the present array design, we should add something a little more concrete. Antenna models using bare wire do not take into account construction variables unless the modeler specifically simulates them. The present design is no exception. However, quad construction practices are highly variable, as illustrated simply in Fig. 5.
The sketch illustrates only 4 among a large number of conditions that may exist at the attachment point between the support arms and the wire elements. Two common methods of attachment are the use of hose clamps and the use of wire loops to fix the position of the element corner. It does not matter whether the element is connected electrically to the metal device that pins the element to the arm. The fixture acts as a simple closed loop connected or coupled to the element at the corner. A quad element has considerable current magnitude at its corners, and such a loop can alter the resonant frequency of the loop when compared to the system in the upper right of the figure, where attachment is made via a wholly non-conductive set of components.
Metal attachment fixtures can act as loads on the wire loop. For most cases, the loop size can be adjusted to accommodate the fixture. Perhaps the simplest way to do this with any accuracy is to model only the set of driven elements to obtain their independent resonant frequencies, but using the dimensions prescribed by the overall array model. Then construct the drive element set using the proposed construction technique. Measure the resonant frequency of each loop. For a given construction technique, any shift in frequency relative to the model should be consistent, although the amount may vary from one band to the next.
One may then create reactive loads at each corner of the modeled element until it has the same resonant frequency as the measured drivers. The same load values for each band can be inserted into each corner of each element in the full array. Then, the loop dimensions are adjusted in the model until design performance is restored. The resulting dimensions should prove to be an accurate guide to final construction. For an array of this size and potential performance, the extra modeling and test effort should not be considered excessive.
Some quads use aluminum arms with fiberglass or similar non-conductive sections for element attachment. The proximity of the aluminum sections of the arms to the elements suggests that the same test procedure is in order as used for the use of metal clamps to wholly insulated arms.
The quad array described here as a design project for NEC software also reveals another feature that impinges on construction. Many of the performance-improving increments of element adjustment involved changes of a tenth of an inch at a time, especially on the higher bands. Since the change was made to a variable representing 1/8 the loop circumference, some elements of the array may be sensitive to changes as small as an inch in overall wire length for a loop. The designer should flag extra-sensitive elements for special care during construction. Sensitivities of this order are natural to a 5-band array with 22 elements in an elongated cube that is only 18' per side by 26' in length.
Apart from this specific antenna, the general principle to be observed is that one cannot simply take modeled dimensions and create a physical antenna. One must first correlate the model to the physical conditions of the construction methods used. In some cases, the selection of materials will permit the modeled dimensions to be used as given. I have constructed both wire and tubular element antennas on 10 meters where the modeled dimensions and the physical antenna were under 1" apart.
However, wherever the physical antenna may have some potential for placing metal within the immediate field of the elements, either the modeler must simulate those objects in the model or one must develop a test regimen to establish a correlation between the design model and the physical prototype. We have illustrated only one of many possible correlation methods. The transition from model to physical antenna should be undertaken with as much care as is put into the modeling design process and into the construction process. Carelessness in any of the three phases of work can yield mediocre communications results.
The primary subject of these columns is antenna modeling. However, I hope that this foray into a specific design project not only provides some awareness of the modeling work involved, but as well helps one to integrate modeling into the overall process that runs from antenna idea to antenna reality.
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