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Five Band Multi Element Quad Modeling With EZNEC 4.0 and MATLAB Bob Hume KG6B 6-26-2004 In 1989 I put up a tri band quad for the 20, 15, and 10 Meter bands. I put up the same quad in 1983, and 1968. The dimensions came from a 1960s vintage CQ article. The boom length is 30 foot. It has four elements on the 20 and 15 Meter bands with ten foot spacing between all elements. It has a fifth element on the 10 Meter band with five foot spacing between the driven element, the reflector, and the first director. It uses separate 52 Ohm coax feed lines for each band that run to a mast mounted remote switch box. I have confirmed 347, 330, and 325 countries respectively on the 20, 15, and 10 Meter bands using this quad. My current objective is to put up a five band quad by adding 17 and 12 Meter band wires to the four elements used on the 20 and 15 Meter quad arms. I decided to explore the rescaling required to achieve gain, SWR, and FB across all five bands using EZNEC 4.0 to model the quads. First, I developed a multi band/multi element cubical quad modeling program using the MATLAB programming language that rapidly generates wire tables for export to EZNEC 4.0. This program accepts the wire diameter, driven element length, element boom locations, and percent element length scaling relative to the driven element for each band. There is a flag for choosing square or diamond quad elements. The program then creates a wire table using a matrix input for any band or band combinations desired. The first band declared in the matrix is the driven band such that the EZNEC 4.0 source wire #5 never needs to be changed. The non driven driven elements are shorted as modeled but the wire termination numbers are identified by the MATLAB program to support modeling of other termination impedance values. The following 13 diamond quad loop band combinations were modeled using the same per band design constants. The 20, 15, and 10 Meter quads are per the 1989 design dimensions. names=['20 MTR 4EL FIVE BAND QUAD'; % 1 array Figure ID numbers '20 MTR 4EL TRI BAND QUAD '; % 2 '20 MTR 4EL MONO BAND QUAD'; % 3 '17 MTR 4EL FIVE BAND QUAD'; % 4 '17 MTR 4EL MONO BAND QUAD'; % 5 '15 MTR 4EL FIVE BAND QUAD'; % 6 '15 MTR 4EL TRI BAND QUAD '; % 7 '15 MTR 4EL MONO BAND QUAD'; % 8 '12 MTR 4EL FIVE BAND QUAD'; % 9 '12 MTR 4EL MONO BAND QUAD'; % 10 '10 MTR 5EL FIVE BAND QUAD'; % 11 '10 MTR 5EL TRI BAND QUAD '; % 12 '10 MTR 5EL MONO BAND QUAD']; % 13 An example printout of the MATLAB program for the 20 Meter five band quad follows. >> quadmod89
MONO OR MULTI BAND CUBICAL QUAD DESIGN CONSTANTS @ DIAMOND ELEMENT SHAPES
FIRST BAND LISTED IS THE DRIVEN BAND. "DE" STANDS FOR DRIVEN ELEMENT DATA ELEMENT ORDER IS REF, DE, DIR1, DIR2, ...DIRn
20 MTR QUAD DESIGN CONSTANTS DE LENGTH CONSTANTS: k=997.6767 f=14.15 DE in FT=70.5072 ELEMENT LENGTHS AS A % FROM DE=2.976 0 -1.704 -1.725 ELEMENT BOOM LOCATIONS IN FT=0 10 20 30 SEGMENTS PER WIRE=9
17 MTR QUAD DESIGN CONSTANTS DE LENGTH CONSTANTS: k=987.6525 f=18.11 DE in FT=54.5363 ELEMENT LENGTHS AS A % FROM DE=3 0 -1.75 -1.75 ELEMENT BOOM LOCATIONS IN FT=0 10 20 30 SEGMENTS PER WIRE=7
15 MTR QUAD DESIGN CONSTANTS DE LENGTH CONSTANTS: k=996.9452 f=21.2 DE in FT=47.0257 ELEMENT LENGTHS AS A % FROM DE=3.071 0 -1.848 -1.77 ELEMENT BOOM LOCATIONS IN FT=0 10 20 30 SEGMENTS PER WIRE=7
12 MTR QUAD DESIGN CONSTANTS DE LENGTH CONSTANTS: k=993.935 f=24.93 DE in FT=39.869 ELEMENT LENGTHS AS A % FROM DE=3 0 -1.75 -1.75 ELEMENT BOOM LOCATIONS IN FT=0 10 20 30 SEGMENTS PER WIRE=7
10 MTR QUAD DESIGN CONSTANTS DE LENGTH CONSTANTS: k=997.528 f=28.45 DE in FT=35.0625 ELEMENT LENGTHS AS A % FROM DE=3.014 0 -2.066 -1.744 -1.723 ELEMENT BOOM LOCATIONS IN FT=0 5 10 20 30 SEGMENTS PER WIRE=7
SEGS DRIVEN ELEMENT WIRE #s MTR BAND PER TOTAL #WIRE 0% 100% BAND WIRES WIRE WIRES SEGS DEa# DEb# 20 16 9 16 144 5 8 17 16 7 32 256 21 24 15 16 7 48 368 37 40 12 16 7 64 480 53 56 10 20 7 84 620 69 72
For the diamond quad loop configuration EZNEC must use a split SI source at wire number 5 (0% end)
The above table also lists the driven element wire number(s) for the non driven bands in case impedance termination effects are to be modeled in EZNEC
EZNEC 4.0 can work with up to 1500 wire segments (SEGS) total EZNEC-M Pro version can work with up to 10,000 wire segments total EZNEC wire table output in Meter units with zero antenna height The EZNEC 4.0 antenna description table for the above wires with a change to feet units and a standard antenna height of 55 foot used for all 13 quad arrays follows. EZNEC+ ver. 4.0 20 MTR 4 EL FIVE BAND QUAD 89 6/26/2004 3:33:43 PM --------------- ANTENNA DESCRIPTION --------------- Frequency = 14.132 MHz Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1 --------------- WIRES --------------- No. End 1 Coord. (ft) End 2 Coord. (ft) Dia (in) Segs Insulation Conn. X Y Z Conn. X Y Z Diel C Thk(in) 1 W4E2 0, 0, 42.165 W2E1 0, 12.835, 55 .080827 9 1 0 2 W1E2 0, 12.835, 55 W3E1 0, 0, 67.835 .080827 9 1 0 3 W2E2 0, 0, 67.835 W4E1 0,-12.835, 55 .080827 9 1 0 4 W3E2 0,-12.835, 55 W1E1 0, 0, 42.165 .080827 9 1 0 5 W8E2 10, 0, 42.536 W6E1 10, 12.464, 55 .080827 9 1 0 6 W5E2 10, 12.464, 55 W7E1 10, 0, 67.464 .080827 9 1 0 7 W6E2 10, 0, 67.464 W8E1 10,-12.464, 55 .080827 9 1 0 8 W7E2 10,-12.464, 55 W5E1 10, 0, 42.536 .080827 9 1 0 9 W12E2 20, 0,42.7484 W10E1 20,12.2516, 55 .080827 9 1 0 10 W9E2 20,12.2516, 55 W11E1 20, 0,67.2516 .080827 9 1 0 11 W10E2 20, 0,67.2516 W12E1 20,-12.252, 55 .080827 9 1 0 12 W11E2 20,-12.252, 55 W9E1 20, 0,42.7484 .080827 9 1 0 13 W16E2 30, 0, 42.751 W14E1 30, 12.249, 55 .080827 9 1 0 14 W13E2 30, 12.249, 55 W15E1 30, 0, 67.249 .080827 9 1 0 15 W14E2 30, 0, 67.249 W16E1 30,-12.249, 55 .080827 9 1 0 16 W15E2 30,-12.249, 55 W13E1 30, 0, 42.751 .080827 9 1 0 17 W20E2 0, 0, 45.07 W18E1 0,9.92997, 55 .080827 7 1 0 18 W17E2 0,9.92997, 55 W19E1 0, 0, 64.93 .080827 7 1 0 19 W18E2 0, 0, 64.93 W20E1 0, -9.93, 55 .080827 7 1 0 20 W19E2 0, -9.93, 55 W17E1 0, 0, 45.07 .080827 7 1 0 21 W24E2 10, 0,45.3593 W22E1 10,9.64075, 55 .080827 7 1 0 22 W21E2 10,9.64075, 55 W23E1 10, 0,64.6407 .080827 7 1 0 23 W22E2 10, 0,64.6407 W24E1 10,-9.6407, 55 .080827 7 1 0 24 W23E2 10,-9.6407, 55 W21E1 10, 0,45.3593 .080827 7 1 0 25 W28E2 20, 0, 45.528 W26E1 20,9.47203, 55 .080827 7 1 0 26 W25E2 20,9.47203, 55 W27E1 20, 0, 64.472 .080827 7 1 0 27 W26E2 20, 0, 64.472 W28E1 20, -9.472, 55 .080827 7 1 0 28 W27E2 20, -9.472, 55 W25E1 20, 0, 45.528 .080827 7 1 0 29 W32E2 30, 0, 45.528 W30E1 30,9.47203, 55 .080827 7 1 0 30 W29E2 30,9.47203, 55 W31E1 30, 0, 64.472 .080827 7 1 0 31 W30E2 30, 0, 64.472 W32E1 30, -9.472, 55 .080827 7 1 0 32 W31E2 30, -9.472, 55 W29E1 30, 0, 45.528 .080827 7 1 0 33 W36E2 0, 0,46.4317 W34E1 0,8.56834, 55 .080827 7 1 0 34 W33E2 0,8.56834, 55 W35E1 0, 0,63.5683 .080827 7 1 0 35 W34E2 0, 0,63.5683 W36E1 0,-8.5683, 55 .080827 7 1 0 36 W35E2 0,-8.5683, 55 W33E1 0, 0,46.4317 .080827 7 1 0 37 W40E2 10, 0,46.6869 W38E1 10,8.31305, 55 .080827 7 1 0 38 W37E2 10,8.31305, 55 W39E1 10, 0, 63.313 .080827 7 1 0 39 W38E2 10, 0, 63.313 W40E1 10,-8.3131, 55 .080827 7 1 0 40 W39E2 10,-8.3131, 55 W37E1 10, 0,46.6869 .080827 7 1 0 41 W44E2 20, 0,46.8406 W42E1 20,8.15943, 55 .080827 7 1 0 42 W41E2 20,8.15943, 55 W43E1 20, 0,63.1594 .080827 7 1 0 43 W42E2 20, 0,63.1594 W44E1 20,-8.1594, 55 .080827 7 1 0 44 W43E2 20,-8.1594, 55 W41E1 20, 0,46.8406 .080827 7 1 0 45 W48E2 30, 0,46.8341 W46E1 30,8.16591, 55 .080827 7 1 0 46 W45E2 30,8.16591, 55 W47E1 30, 0,63.1659 .080827 7 1 0 47 W46E2 30, 0,63.1659 W48E1 30,-8.1659, 55 .080827 7 1 0 48 W47E2 30,-8.1659, 55 W45E1 30, 0,46.8341 .080827 7 1 0 49 W52E2 0, 0,47.7406 W50E1 0,7.25935, 55 .080827 7 1 0 50 W49E2 0,7.25935, 55 W51E1 0, 0,62.2593 .080827 7 1 0 51 W50E2 0, 0,62.2593 W52E1 0,-7.2594, 55 .080827 7 1 0 52 W51E2 0,-7.2594, 55 W49E1 0, 0,47.7406 .080827 7 1 0 53 W56E2 10, 0,47.9521 W54E1 10,7.04792, 55 .080827 7 1 0 54 W53E2 10,7.04792, 55 W55E1 10, 0,62.0479 .080827 7 1 0 55 W54E2 10, 0,62.0479 W56E1 10,-7.0479, 55 .080827 7 1 0 56 W55E2 10,-7.0479, 55 W53E1 10, 0,47.9521 .080827 7 1 0 57 W60E2 20, 0,48.0754 W58E1 20,6.92458, 55 .080827 7 1 0 58 W57E2 20,6.92458, 55 W59E1 20, 0,61.9246 .080827 7 1 0 59 W58E2 20, 0,61.9246 W60E1 20,-6.9246, 55 .080827 7 1 0 60 W59E2 20,-6.9246, 55 W57E1 20, 0,48.0754 .080827 7 1 0 61 W64E2 30, 0,48.0754 W62E1 30,6.92458, 55 .080827 7 1 0 62 W61E2 30,6.92458, 55 W63E1 30, 0,61.9246 .080827 7 1 0 63 W62E2 30, 0,61.9246 W64E1 30,-6.9246, 55 .080827 7 1 0 64 W63E2 30,-6.9246, 55 W61E1 30, 0,48.0754 .080827 7 1 0 65 W68E2 0, 0, 48.615 W66E1 0,6.38505, 55 .080827 7 1 0 66 W65E2 0,6.38505, 55 W67E1 0, 0, 61.385 .080827 7 1 0 67 W66E2 0, 0, 61.385 W68E1 0, -6.385, 55 .080827 7 1 0 68 W67E2 0, -6.385, 55 W65E1 0, 0, 48.615 .080827 7 1 0 69 W72E2 5, 0,48.8018 W70E1 5,6.19823, 55 .080827 7 1 0 70 W69E2 5,6.19823, 55 W71E1 5, 0,61.1982 .080827 7 1 0 71 W70E2 5, 0,61.1982 W72E1 5,-6.1982, 55 .080827 7 1 0 72 W71E2 5,-6.1982, 55 W69E1 5, 0,48.8018 .080827 7 1 0 73 W76E2 10, 0,48.9298 W74E1 10,6.07018, 55 .080827 7 1 0 74 W73E2 10,6.07018, 55 W75E1 10, 0,61.0702 .080827 7 1 0 75 W74E2 10, 0,61.0702 W76E1 10,-6.0702, 55 .080827 7 1 0 76 W75E2 10,-6.0702, 55 W73E1 10, 0,48.9298 .080827 7 1 0 77 W80E2 20, 0,48.9099 W78E1 20,6.09013, 55 .080827 7 1 0 78 W77E2 20,6.09013, 55 W79E1 20, 0,61.0901 .080827 7 1 0 79 W78E2 20, 0,61.0901 W80E1 20,-6.0901, 55 .080827 7 1 0 80 W79E2 20,-6.0901, 55 W77E1 20, 0,48.9099 .080827 7 1 0 81 W84E2 30, 0,48.9086 W82E1 30,6.09144, 55 .080827 7 1 0 82 W81E2 30,6.09144, 55 W83E1 30, 0,61.0914 .080827 7 1 0 83 W82E2 30, 0,61.0914 W84E1 30,-6.0914, 55 .080827 7 1 0 84 W83E2 30,-6.0914, 55 W81E1 30, 0,48.9086 .080827 7 1 0 Total Segments: 620 -------------- SOURCES -------------- No. Specified Pos. Actual Pos. Amplitude Phase Type Wire # % From E1 % From E1 Seg (V/A) (deg.) 1 5 0.00 5.56 1 1 0 SI No loads specified No transmission lines specified Ground type is Real, High-Accuracy --------------- MEDIA --------------- No. Cond. Diel. Const. Height R Coord. (S/m) (ft) (ft) 1 0.005 13 0 0 The above ground model was used on all 13 quad arrays evaluated. It only takes about one minute to define a quad array in MATLAB program quadmod89.m, run the program, load the resulting wire table file into EZNEC 4.0, change the units from meters to feet, and change the antenna height from zero to 55 foot to obtain an array model ready to run pattern or SWR plots. The alternative of loading the 84 wire segments by hand would take a lot longer and be prone to entry errors. Figures 1A to 13A show plots of the gain in dBi, front to back ratio (FB) in dB, front to back region ratio (FBR) in dB, and 10 times the SWR (required to get all data on one plot) for all 13 quad arrays. The SWR curves are for a 52 Ohm coax feed of each array. The FBR is based on the major back lobe in the -180+/-90 degree azimuth range from the array heading. I think the FBR is a better antenna design figure of merit than the FB. The dBi gains are based on the first vertical wave angle lobe maximum gain for each band with a 55 foot antenna height. Reference dipole dBi gains at the first vertical angle “theta” lobe maximum and the same 55 foot antenna height for the five bands are: BAND THETA (DEG) DIPOLE dBi GAIN 20 16.3 7.07 17 13.2 7.66 15 11.5 7.76 12 9.9 7.49 10 8.7 7.94 The array gains in dBd relative to a dipole can be calculated by subtracting the reference dipole dBi gain from the array dBi gain on each band. Figures 1B to 13B show plots of the driving point impedance real and imaginary parts as a function of frequency for each of the 13 quad arrays modeled. The plots allow one to assess array detuning effects when going from mono to tri band or tri band to five band designs. The plot scales on each band are the same such that a view graph of the five band plots could be laid over the tri band plots for direct visual comparisons. Figures 14A and 14B show the difference in the azimuth gain plots for the Figure 6 15 Meter five band quad array at the maximum FBR frequency versus the maximum FB frequency. Tuning and scaling of the quad for maximum FBR rather than FB over the prime DX window frequency range of interest looks like the best option to me.
Figure 14A Maximum FBR Frequency Plot For Fig 6 Quad Array
Figure 14B Maximum FB Frequency Plot For Fig 6 Quad Array
MATLAB PROGRAM quadmod89.m The purpose of this program is to create a multi band multi element quad design wire table for export to EZNEC 4.0. The program has comment statements that should make it easy to use. It can model any single or multi band quad of either the diamond or square configuration on the 20, 17, 15, 12, 10, and 6 Meter bands as coded. A listing of the program (or .m file MATLAB script) follows. % M-file quadmod89.m % MATLAB program designed to create an exportable wire table for the EZNEC or EZNEC-PRO % antenna modeling programs for any mono band or multi band % multi element Cubical Quad antenna in either the diamond or square loop % shape configuration. % % A note for radio amateurs not familiar with the MATLAB programming % language follows. MATLAB is a powerful high level scientific programming % language commonly used by college students and professional engineers. % The student version of MATLAB can be downloaded from the Mathworks web % site for $100. The professional version of MATLAB currently costs $1900. % Both PC and MAC versions are available. % % Written by Bob Hume KG6B on 6/26/2004 (310) 376-4192 (H) 814-7557 (W) % e-mail: rwhume@adelphia.net % Final EZNEC export file wire end locations and sizes are in meter units % with zero antenna height (i.e at center point of quad loops) % Export wire file includes the number of EZNEC segments used to model % each wire. % See detailed instructions on how export the quad wire table file generated % by this program to EZNEC at the end of this program listing. % %square=1; % Activate this line (remove leading %) for a square quad loop configuration. % EZNEC should use a source at the middle of wire #5 for the % driven band for the square loop configuration square=0; % Activate this line for a diamond quad loop configuration. % EZNEC should use a split SI source at the 0% end of wire #5 % for the driven band for the diamond loop configuration. % Select all bands common bare copper wire diameter in feet "dia" % on following line(s). % Note that EZNEC 3.0 can not properly model wire with a thick layer of % insulation. Enamel covered magnet wire can be properly modeled % since the insulation layer is very thin. %dia=.06408/12; % #14 wire diameter in feet dia=.08081/12; % #12 wire diameter in feet (new wire gauge selected for 2004 design) %dia=.09074/12; % #11 wire diameter in feet (actual 1989 wire gauge) % % Select Meter bands in quad on next line(s) that define matrix "bandset" %bandset=[20 17 15 12 10]'; % MTR bands in quad. Choose one or all of the 20, 17, % 15, 12, 10, or 6 MTR bands in any order except that the first band listed is % the driven band for which the antenna is evaluated. Consider the 1500 wire % segment limit of EZNEC 4.0 when choosing the number of bands and % elements in the quads. The driven band uses "segsA" segments per wire. The % non driven bands use "segsB" segments per wire. There are four wires per % quad loop. EZNEC may give a warning using 5 segments per wire but % this is OK since the currents in the non driven band element wires are % small. % segsA=9; % Segments per wire for driven band Quad wires (use odd integer) segsB=7; % Segments per wire for non driven band Quad wires (use odd integer) % % Remove leading % on one of the below lines to activate and select a quad antenna % design option %bandset=[20]'; % Mono band option 20 %bandset=[17]'; % Mono band option 17 %bandset=[15]'; % Mono band option 15 %bandset=[12]'; % Mono band option 12 %bandset=[10]'; % Mono band option 10 %bandset=[20 15 10]'; % Tri band option 20 driven %bandset=[15 10 20]'; % Tri band option 15 driven %bandset=[10 20 15]'; % Tri band option 10 driven bandset=[20 17 15 12 10]'; % Five band option 20 driven %bandset=[17 15 12 10 20]'; % Five band option 17 driven %bandset=[15 12 10 20 17]'; % Five band option 15 driven %bandset=[12 10 20 17 15]'; % Five band option 12 driven %bandset=[10 20 17 15 12]'; % Five band option 10 driven % % NRbands=length(bandset); wnr=zeros(NRbands,7); wnr(:,1)=bandset; nt=0; segtotal=0; % disp(' ') if square==1 disp('MONO OR MULTI BAND CUBICAL QUAD DESIGN CONSTANTS @ SQUARE ELEMENT SHAPES') else disp('MONO OR MULTI BAND CUBICAL QUAD DESIGN CONSTANTS @ DIAMOND ELEMENT SHAPES') end disp(' ') disp('FIRST BAND LISTED IS THE DRIVEN BAND. "DE" STANDS FOR DRIVEN ELEMENT') disp('DATA ELEMENT ORDER IS REF, DE, DIR1, DIR2, ...DIRn') for bandNR=1:NRbands % Band case loop MTRband=bandset(bandNR); % Selected MTR band in loop % % MODEL THE QUAD DESIGN CONSTANTS FOR EACH BAND ON THE FOLLOWING LINES. % THE PROGRAM QUAD MODEL ASSUMES THAT ONE REFLECTOR PER BAND IS USED. % ONLY QUAD METER BANDS USED IN THE MATRIX "bandset" NEED BE MODELED if MTRband==20 % 20 MTR Quad design constants follow k=997.6767; % Driven Element (DE) Length*Frequency Design Product in FT*MHZ units f=14.15; % DE Design Frequency in Mhz if bandNR==1 segs=segsA; % segs=EZNEC segments per wire. segs must be odd for square quad loops else segs=segsB; end elper=[2.976 0 -1.704 -1.725]'; % Percent change from driven element (DE) size for % each element. |
