Let's begin with a pop quiz. Suppose first that you wanted a directional 3-element quad array to cover as much of 40 meters as possible. Suppose further that space for the array is not problem. Finally, suppose that you had a choice among the following three designs: the "Classic #14," "the Single W-B #12," and the "Dual W-B #12." Which would you choose?
So far, the question is not fair. So let's provide some grounds for selection with a few performance graphs.
Fig. 1 shows the gain curves for the three choices. The classic #14 peaks at about 7.15 MHz, but falls off rapidly on either side of the design frequency, especially the low frequency side. Still, this is a normal curve for a quad beam in almost every performance category. The single W-B #12 has its gain peak at about 7.05 MHz, although the design frequency is higher. It is not clear from the graph whether the dual W-B #12 has a gain peak at 7.0 MHz or somewhat lower in frequency. From the graph, the antenna with the most consistent gain from one end of the band to the other is clear.
The front-to-back ratio curves in Fig. 2 are equally clear. The peak front-to-back ratio in all cases occurs between 7.1 and 7.15 MHz. However, the classic #14 does not reach 20 dB (with the possibile exception of a few kHz at its peak). The single W-B #12 does considerably better, but still manages >20 dB front-to-back ratio for only about 85 kHz. The dual W-B #12 has the widest >20 dB front-to-back ratio bandwidth and never drops below 14 dB across the 40-meter band.
The classic #14 array is--near the design frequency--a 50-Ohm antenna, and the SWR curve in Fig. 3 is referenced to that value. Unfortunately, the <2:1 SWR region is only about 130 kHz wide. The single W-B #12 version of the antenna covers about 200 kHz with under 2:1 SWR--this time referenced to the array's near-75-Ohm feedpoint impedance. Only the dual W-B #12 model manages under 2:1 SWR (referenced to 75 Ohms) across the entire band.
For someone interested in the entire 40-meter band, there is a clear winner in this selection process: the dual W-B #12 model. But, before we look at what this model is, let's review the lesser arrays in the group.
The Classic #14 3-Element Quad Design
For at least a quarter century, we have been given a set of formulas for constructing 3-element quads:
Reflector loop circumference in feet = 1030/frequency in MHz Driver loop circumference in feet = 1005/frequency in MHz Director loop circumference in feet = 975/frequency in MHz
Many hams have believed that an independently fed quad loop answers to the driver formula, but it does not--not even close. Likewise, other hams have believed that we can make a 2-element quad using just the driver and reflector formulas. Any such array is less than optimal. Few folks have noticed that the spacing is left vacant, subject to our own construction limitations.
In fact, the formulas apply to fairly short 3-element quads using quite thin wire. The formulas are not perfect and require some optimization to bring the gain, front-to-back ratio, and SWR "best" numbers into reasonably close alignment. The following design in #14 AWG copper wire provides good figures at the design frequency (close to 7.15 MHz):
Reflector loop length: 1719.4" 143.29' Driver loop length: 1683.8" 140.31' Director loop length: 1634.9" 136.24' Reflector-Driver space: 219.5" 18.30' Driver-Director space: 284.4" 23.70' Total boom length 503.9" 42.00'
Although this array is capable of about 8.6 dBi free-space gain at the design frequency, it has a very narrow operating bandwidth in every performance category. The gain drops to about 7.5 dB (1.1 dB off peak) at the low end of the band. The front-to-back ratio is below 10 dB for much of the band. The 2:1 SWR bandwidth covers less than half of the 40- meter band.
The selected azimuth patterns that scan 40-meters in 100 kHz intervals tell much of the classic #14's story in graphical detail in Fig. 4. Beyond the center 100 kHz of the band, the pattern of the array is more bi-directional than directional.
The use of the classical formulas on 40 meters provides somewhat of an overstatement of the inadequacies of these old numbers. A beam of this design might make a useful array for either the CW or the SSB end of 40 meters, but certainly not both. (This conclusion, of course, references the US 40-meter band. The array might be adequate to European interests in the band.)
For those who model and might wish to adjust the design to one or the other end of the 40-meter band, the following model description may be useful:
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3-element 40-meter classic quad Frequency = 7 MHz.
Wire Loss: Copper -- Resistivity = 1.74E-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
1 W4E2 -17.911, 0.000,-17.911 W2E1 17.911, 0.000,-17.911 # 14 11
2 W1E2 17.911, 0.000,-17.911 W3E1 17.911, 0.000, 17.911 # 14 11
3 W2E2 17.911, 0.000, 17.911 W4E1 -17.911, 0.000, 17.911 # 14 11
4 W3E2 -17.911, 0.000, 17.911 W1E1 -17.911, 0.000,-17.911 # 14 11
5 W8E2 -17.539, 18.296,-17.539 W6E1 17.539, 18.296,-17.539 # 14 11
6 W5E2 17.539, 18.296,-17.539 W7E1 17.539, 18.296, 17.539 # 14 11
7 W6E2 17.539, 18.296, 17.539 W8E1 -17.539, 18.296, 17.539 # 14 11
8 W7E2 -17.539, 18.296, 17.539 W5E1 -17.539, 18.296,-17.539 # 14 11
9 W12E2 -17.030, 41.998,-17.030 W10E1 17.030, 41.998,-17.030 # 14 11
10 W9E2 17.030, 41.998,-17.030 W11E1 17.030, 41.998, 17.030 # 14 11
11 W10E2 17.030, 41.998, 17.030 W12E1 -17.030, 41.998, 17.030 # 14 11
12 W11E2 -17.030, 41.998, 17.030 W9E1 -17.030, 41.998,-17.030 # 14 11
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 6 5 / 50.00 ( 5 / 50.00) 0.707 0.000 V
Ground type is Free Space
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The Single-Wire Wide-Band #12 3-Element Quad Design
How might we improve the classic design? First, we should go to a larger diameter wire. However, #12 AWG copper wire is about the largest value that most hams will use. That fact will initially limit the improvements we can make.
Fig. 5 illustrates a second design move we can make: enlarge the spacing to something nearer to optimal. The figure shows the profiles of the classic and the improved designs, revealing that it will take another 20+ feet of boom to get significant improvements in operating bandwidth on 40 meters.
I used the wide-band version of the automated design program that I presented in an earlier article to obtain the widest-band 40-meter beam I could develop with #12 wire. The dimensions that resulted are these:
Reflector loop length: 1736.8" 144.73' Driver loop length: 1669.2" 139.10' Director loop length: 1560.3" 130.02' Reflector-Driver space: 246.8" 20.56' Driver-Director space: 522.6" 43.55' Total boom length 769.4" 64.11'
Wide-band design requires a driver-to-director spacing that is greater than the entire boom length of the classic design. Wide-band operation of a 3-element quad beam simply needs considerably greater boom-length than we have thought about using in the past.
Even with the longer boom length, the wire diameter we have chosen continues to limit performance. #12 wire is a very thin conductor at 40 meters--about 5E-5 wavelengths. Consequently, optimizing loop dimensions and element spacing will not provide full 40-meter coverage.
Gain is not the problem, since it holds to a free-space value of about 8.4 dBi or better across the band. The front-to-back ratio, although significantly improved compared to the classic #14 model, remains less than stellar. It actually falls below 10 dB at the low end of the band and exceeds 20 dB for less than 100 kHz. The 75-Ohm 2:1 SWR passband is only about 180 kHz wide--about 50 kHz wider than for the classic #14 design. Although the single-wire #12 wide-band design provides considerable improvements in gain and front-to-back ratio relative to the classic #14 model, it falls short of covering the band by a wide margin. Just getting full SWR coverage would require a wire about 3-4" in diameter.
Fig. 6 shows our situation graphically through spot azimuth patterns across the band. The single-wire array will simply not do the job we specified at the beginning of this exercise.
Those who wish to try some adjustments to the array under discussion may benefit from the following model description:
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3-element 40-meter single-wire wide-band quad Frequency = 7 MHz.
Wire Loss: Copper -- Resistivity = 1.74E-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
1 W4E2 -18.091, 0.000,-18.091 W2E1 18.091, 0.000,-18.091 # 12 11
2 W1E2 18.091, 0.000,-18.091 W3E1 18.091, 0.000, 18.091 # 12 11
3 W2E2 18.091, 0.000, 18.091 W4E1 -18.091, 0.000, 18.091 # 12 11
4 W3E2 -18.091, 0.000, 18.091 W1E1 -18.091, 0.000,-18.091 # 12 11
5 W8E2 -17.388, 20.563,-17.388 W6E1 17.388, 20.563,-17.388 # 12 11
6 W5E2 17.388, 20.563,-17.388 W7E1 17.388, 20.563, 17.388 # 12 11
7 W6E2 17.388, 20.563, 17.388 W8E1 -17.388, 20.563, 17.388 # 12 11
8 W7E2 -17.388, 20.563, 17.388 W5E1 -17.388, 20.563,-17.388 # 12 11
9 W12E2 -16.253, 64.113,-16.253 W10E1 16.253, 64.113,-16.253 # 12 11
10 W9E2 16.253, 64.113,-16.253 W11E1 16.253, 64.113, 16.253 # 12 11
11 W10E2 16.253, 64.113, 16.253 W12E1 -16.253, 64.113, 16.253 # 12 11
12 W11E2 -16.253, 64.113, 16.253 W9E1 -16.253, 64.113,-16.253 # 12 11
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 6 5 / 50.00 ( 5 / 50.00) 0.707 0.000 V
Ground type is Free Space
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The Dual-Wire Wide-Band #12 3-Element Quad Design
A 40-meter quad beam by any accounting is a sizable structure. The spreaders should easily be able to support 2 #12 AWG wires. Therefore, we may simulate a fat wire by using double-wire elements in a planar arrangement. Fig. 7 shows the general outline for such a beam. Note the connections between each element loop at every corner.
It proved possible to cover all of the first MHz of 10 meters with a very good front-to- back ratio using a single 0.5" diameter wire or 2 #14 wires spaced 5" apart. A 40-meter quad with comparable coverage would need wires spaced more than 20 inches apart. As a more modest design project, I aimed simply to achieve an SWR of under 2:1 across the band. This goal required the use of 10" #12 wire spacing.
The optimized dimensions for the dual-wire model yields an array that is close to 4' shorter than the single-wire version. The following dimensions list the circumferences of both the inner and outer loops for each element:
Reflector loop length: Outer 1823.3" 151.94'
Inner 1743.3" 145.27'
Driver loop length: Outer 1725.9" 143.83'
Inner 1645.9" 137.16'
Director loop length: Outer 1569.4" 130.79'
Inner 1489.4" 124.12'
Reflector-Driver space: 287.7" 23.97'
Driver-Director space: 435.6" 36.30'
Total boom length 723.3" 60.27'
For our trouble, we obtain a smooth gain curve across the band with under 0.3 dB variation. In addition, the front-to-back ratio is above 14 dB across the band and above 20 dB for over half the band. Finally, the 75-Ohm SWR is less than 2:1 across the entire band. Although still less than perfect, the 10" spacing of the dual-wire elements provides very significant improvements in performance over either of the other models.
Fig. 8 provides a graphic sense of the improvements. All of the pattern elements are more tightly grouped than in the comparable azimuth pattern sweeps for the other designs. For those who wish to examine the model structure, the following listing may be useful.
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3-element 40-meter dual-wire wide-band quad Frequency = 7 MHz.
Wire Loss: Copper -- Resistivity = 1.74E-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
1 W4E2 -17.978, 0.000,-17.978 W2E1 17.978, 0.000,-17.978 # 12 29
2 W10E1 17.978, 0.000,-17.978 W3E1 17.978, 0.000, 17.978 # 12 29
3 W9E1 17.978, 0.000, 17.978 W4E1 -17.978, 0.000, 17.978 # 12 29
4 W12E1 -17.978, 0.000, 17.978 W11E1 -17.978, 0.000,-17.978 # 12 29
5 W8E2 -17.145, 0.000,-17.145 W6E1 17.145, 0.000,-17.145 # 12 23
6 W10E2 17.145, 0.000,-17.145 W7E1 17.145, 0.000, 17.145 # 12 23
7 W9E2 17.145, 0.000, 17.145 W8E1 -17.145, 0.000, 17.145 # 12 23
8 W12E2 -17.145, 0.000, 17.145 W11E2 -17.145, 0.000,-17.145 # 12 23
9 W2E2 17.978, 0.000, 17.978 W6E2 17.145, 0.000, 17.145 # 12 1
10 W1E2 17.978, 0.000,-17.978 W5E2 17.145, 0.000,-17.145 # 12 1
11 W1E1 -17.978, 0.000,-17.978 W5E1 -17.145, 0.000,-17.145 # 12 1
12 W3E2 -17.978, 0.000, 17.978 W7E2 -17.145, 0.000, 17.145 # 12 1
13 W16E2 -18.992,-23.973,-18.992 W14E1 18.992,-23.973,-18.992 # 12 29
14 W22E1 18.992,-23.973,-18.992 W15E1 18.992,-23.973, 18.992 # 12 29
15 W21E1 18.992,-23.973, 18.992 W16E1 -18.992,-23.973, 18.992 # 12 29
16 W24E1 -18.992,-23.973, 18.992 W23E1 -18.992,-23.973,-18.992 # 12 29
17 W20E2 -18.159,-23.973,-18.159 W18E1 18.159,-23.973,-18.159 # 12 23
18 W22E2 18.159,-23.973,-18.159 W19E1 18.159,-23.973, 18.159 # 12 23
19 W21E2 18.159,-23.973, 18.159 W20E1 -18.159,-23.973, 18.159 # 12 23
20 W24E2 -18.159,-23.973, 18.159 W23E2 -18.159,-23.973,-18.159 # 12 23
21 W14E2 18.992,-23.973, 18.992 W18E2 18.159,-23.973, 18.159 # 12 1
22 W13E2 18.992,-23.973,-18.992 W17E2 18.159,-23.973,-18.159 # 12 1
23 W13E1 -18.992,-23.973,-18.992 W17E1 -18.159,-23.973,-18.159 # 12 1
24 W15E2 -18.992,-23.973, 18.992 W19E2 -18.159,-23.973, 18.159 # 12 1
25 W28E2 -16.348, 36.302,-16.348 W26E1 16.348, 36.302,-16.348 # 12 29
26 W34E1 16.348, 36.302,-16.348 W27E1 16.348, 36.302, 16.348 # 12 29
27 W33E1 16.348, 36.302, 16.348 W28E1 -16.348, 36.302, 16.348 # 12 29
28 W36E1 -16.348, 36.302, 16.348 W35E1 -16.348, 36.302,-16.348 # 12 29
29 W32E2 -15.515, 36.302,-15.515 W30E1 15.515, 36.302,-15.515 # 12 23
30 W34E2 15.515, 36.302,-15.515 W31E1 15.515, 36.302, 15.515 # 12 23
31 W33E2 15.515, 36.302, 15.515 W32E1 -15.515, 36.302, 15.515 # 12 23
32 W36E2 -15.515, 36.302, 15.515 W35E2 -15.515, 36.302,-15.515 # 12 23
33 W26E2 16.348, 36.302, 16.348 W30E2 15.515, 36.302, 15.515 # 12 1
34 W25E2 16.348, 36.302,-16.348 W29E2 15.515, 36.302,-15.515 # 12 1
35 W25E1 -16.348, 36.302,-16.348 W29E1 -15.515, 36.302,-15.515 # 12 1
36 W27E2 -16.348, 36.302, 16.348 W31E2 -15.515, 36.302, 15.515 # 12 1
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 15 1 / 50.00 ( 1 / 50.00) 0.707 0.000 V
2 12 5 / 50.00 ( 5 / 50.00) 0.707 0.000 V
Ground type is Free Space
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Note in the model the use of two sources which are essentially in parallel. You may use the standard parallel impedance equations to calculate the composite feedpoint impedance. In practice, of course, a builder would bring the two loop wires together at the feedpoint for a single feedline connection.
The dual-wire planar loop design is not the answer to all limitations of 3-element quad bandwidth, but it goes a long way toward overcoming them. For such a large initial array, the two-wire loop is fairly straightforward, if not simple, to implement. The cost will be something over 400' in extra wire.
A Note on Designing 3-Element Quads
I habitually use a mixture of two NEC programs for quad design--NECWin Plus and EZNEC. Although many of the graphics that appear here are from models cross-checked on EZNEC/4, the basic design work was done with NECWin Plus using the model-by-equation facility.
Fig. 9 provides a simple illustration--chosen because a quad design with a single-wire structure makes a more compact graphic. (The same illustration using the dual wire model would have required 36 lines in the "wires page" section.) By setting the "half-side" dimensions of the quad in terms of a fraction of a wavelength, the task of hand-optimizing a design is considerably eased. In this case, the director spacing is actually the spacing from the reflector to the director, and finding the distance from the driver to the director is a simple case of subtraction. Alternatively, one might set the driver at zero and use a negative value for the reflector spacing and a positive value for the director. Finding the total boom length then becomes a simple case of addition.
The earlier note on the rough equivalency of a 3-4" wire to the 10" double #12 wire arrangement can be verified by using the 3-element wide-band automated design program. A 3" wire is the minimum diameter single copper wire that will yield a 75-Ohm <2:1 SWR curve for a 40-meter array. The model below is one example of such a design. Note that when run on NEC-4, the properties will show a slight displacement (un 50 kHz) in frequency. The curve was developed in NEC-2.
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3-Element Wide-Band 40-M design: 3" elements Frequency = 7.15 MHz.
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 -226.06, 0.000,-226.06 W2E1 226.061, 0.000,-226.06 3.00E+00 11
2 W1E2 226.061, 0.000,-226.06 W3E1 226.061, 0.000,226.061 3.00E+00 11
3 W2E2 226.061, 0.000,226.061 W4E1 -226.06, 0.000,226.061 3.00E+00 11
4 W3E2 -226.06, 0.000,226.061 W1E1 -226.06, 0.000,-226.06 3.00E+00 11
5 W8E2 -211.88,273.902,-211.88 W6E1 211.876,273.902,-211.88 3.00E+00 11
6 W5E2 211.876,273.902,-211.88 W7E1 211.876,273.902,211.876 3.00E+00 11
7 W6E2 211.876,273.902,211.876 W8E1 -211.88,273.902,211.876 3.00E+00 11
8 W7E2 -211.88,273.902,211.876 W5E1 -211.88,273.902,-211.88 3.00E+00 11
9 W12E2 -194.11,727.268,-194.11 W10E1 194.109,727.268,-194.11 3.00E+00 11
10 W9E2 194.109,727.268,-194.11 W11E1 194.109,727.268,194.109 3.00E+00 11
11 W10E2 194.109,727.268,194.109 W12E1 -194.11,727.268,194.109 3.00E+00 11
12 W11E2 -194.11,727.268,194.109 W9E1 -194.11,727.268,-194.11 3.00E+00 11
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 6 5 / 50.00 ( 5 / 50.00) 0.707 0.000 V
Ground type is Free Space
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
To obtain a >20 dB front-to-back curve for the entirety of the US 40-meter band requires a much greater single-wire diameter: about 20". The following model provides such a curve on NEC-2, with the usual slight frequency displacement in NEC-4.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-Element Wide-Band 40-M design: 3" elements Frequency = 7.15 MHz.
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 -238.14, 0.000,-238.14 W2E1 238.145, 0.000,-238.14 2.00E+01 11
2 W1E2 238.145, 0.000,-238.14 W3E1 238.145, 0.000,238.145 2.00E+01 11
3 W2E2 238.145, 0.000,238.145 W4E1 -238.14, 0.000,238.145 2.00E+01 11
4 W3E2 -238.14, 0.000,238.145 W1E1 -238.14, 0.000,-238.14 2.00E+01 11
5 W8E2 -215.68,280.836,-215.68 W6E1 215.680,280.836,-215.68 2.00E+01 11
6 W5E2 215.680,280.836,-215.68 W7E1 215.680,280.836,215.680 2.00E+01 11
7 W6E2 215.680,280.836,215.680 W8E1 -215.68,280.836,215.680 2.00E+01 11
8 W7E2 -215.68,280.836,215.680 W5E1 -215.68,280.836,-215.68 2.00E+01 11
9 W12E2 -189.54,696.975,-189.54 W10E1 189.536,696.975,-189.54 2.00E+01 11
10 W9E2 189.536,696.975,-189.54 W11E1 189.536,696.975,189.536 2.00E+01 11
11 W10E2 189.536,696.975,189.536 W12E1 -189.54,696.975,189.536 2.00E+01 11
12 W11E2 -189.54,696.975,189.536 W9E1 -189.54,696.975,-189.54 2.00E+01 11
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 6 5 / 50.00 ( 5 / 50.00) 0.707 0.000 V
Ground type is Free Space
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Developing a multi-wire equivalent for a 20" diameter wire is likely not feasible with only two wires. Even if the SWR and front-to-back curves can be replicated, the full gain (9.2 dB at design center frequency) will not be available without several wires per loop--perhaps 4 wires on 10" centers (as a speculative guess). The 20" wire in the model presses the limits of wire diameter (0.01 wl) for which the design program has been calibrated.
I have been asked why I use an independent value for the wavelength (D3) in most of my equations. When letting software perform a string of calculations, I tend to prefer the most precise value for physical and mathematical constants that I can find. This includes such values as PI, the speed of electromagnetic radiation in free space, and the ratio of natural to common logarithms. I then save rounding for the final step of calculations performed by software programs. Others may wish to use only the least number of significant digits in the weakest input value in all numeric entries.
Whatever procedure one finds most comfortable, the process of developing a wide-band 40-meter 3-element quad takes more than a few formulas whose limitations have been lost in the mists of summary, custom, and usage. Even the best of the designs here can be improved by judicious further modeling using either wider spacing of dual wires or larger multi-wire loops. There are many modeling challenges ahead before the quad beam has exhausted its potential.
Updated 04-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for March, 2001. 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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