From: little@nuts2u.enet.dec.com (nuts2u::little)
Subject: Re: spacing dimensions for quad antennas
Organization: Digital Equipment Corporation
Date: Mon, 23 Nov 1992 05:13:01 GMT
X-Posted-Via: NEWS-NOTES gateway (a hack!)

Here are some NEC-2 decks and Postscript pattern plots for antennas that
come close to your criteria.  The impedances are all a little low, but
would certainly provide a fine match to 50 ohm cable.  If you need designs
that are closer to 50 ohms, just let me know.  Also remember that these are
theoretical designs from NEC-2 and I've never built one of these designs,
so your mileage may vary.

73,
Todd
N9MWB

PS  From the results, I must have over emphasized the F/B ratio and under
    emphasized the impedances, sigh.

4 element quad with: F/B = 42 dB  Gain = 10.2 dBi  Impedance = 40 Ohms
===============================Begin Here=======================================
CM  4 element QUAD on a 4.000000m boom for 52.000000 Mhz 
CM  Generated on Sun Nov 22 21:21:35 1992
CE
GW 1 3 0.086481 0.000000 -0.778326 0.086481 0.778326 -0.778326 0.001885
GW 1 6 0.086481 0.778326 -0.778326 0.086481 0.778326 0.778326 0.001885
GW 1 3 0.086481 0.778326 0.778326 0.086481 0.000000 0.778326 0.001885
GW 2 3 1.045064 0.000000 -0.730699 1.045064 0.730699 -0.730699 0.001885
GW 2 6 1.045064 0.730699 -0.730699 1.045064 0.730699 0.730699 0.001885
GW 2 3 1.045064 0.730699 0.730699 1.045064 0.000000 0.730699 0.001885
GW 3 3 2.652253 0.000000 -0.720672 2.652253 0.720672 -0.720672 0.001885
GW 3 6 2.652253 0.720672 -0.720672 2.652253 0.720672 0.720672 0.001885
GW 3 3 2.652253 0.720672 0.720672 2.652253 0.000000 0.720672 0.001885
GW 4 3 4.000000 0.000000 -0.687161 4.000000 0.687161 -0.687161 0.001885
GW 4 6 4.000000 0.687161 -0.687161 4.000000 0.687161 0.687161 0.001885
GW 4 3 4.000000 0.687161 0.687161 4.000000 0.000000 0.687161 0.001885
GX  100  010
GE
FR  0    0    0    0    52.000000
EX  0    2    1    0    5.   0.
EX  0  102    1    0   -5.   0.
PT -1
PL  3   2    0    3
RP  0   1  181 1100   90.     0.      0.     1.0
EN
=================================End Here=======================================
===============================Begin Here=======================================
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% polar coordinate grid
% arguments are radius of chart, number of 5 dB rings required, and
% max phi (360 for full circle chart, 180 for half chart, etc.)  max phi
% is rounded up to a multiple of 5.
% saves scaling parameters for subsequent plot: ring, r
% r rings maxphi --
/pch {
  5 div ceiling 5 mul /maxphi exch def
  /rings exch def /r exch def 
  r rings div /ring5 exch def ring5 5 div /ring exch def
  180 ring5 div ceiling ring5 mul /r1 exch def
  40 ring5 div ceiling ring5 mul /r2 exch def
  15 ring div ceiling ring mul /r10 exch def
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  0 90 maxphi { r exch pm 0 0 lineto stroke } for
} def

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stroke
showpage
=================================End Here=======================================

5 element quad with: F/B = 50 dB  Gain = 10.4 dBi  Impedance = 38 Ohms
===============================Begin Here=======================================
CM  5 element QUAD on a 4.000000m boom for 52.000000 Mhz 
CM  Generated on Sun Nov 22 21:29:34 1992
CE
GW 1 3 0.000000 0.000000 -0.778326 0.000000 0.778326 -0.778326 0.001885
GW 1 6 0.000000 0.778326 -0.778326 0.000000 0.778326 0.778326 0.001885
GW 1 3 0.000000 0.778326 0.778326 0.000000 0.000000 0.778326 0.001885
GW 2 3 1.000000 0.000000 -0.734994 1.000000 0.734994 -0.734994 0.001885
GW 2 6 1.000000 0.734994 -0.734994 1.000000 0.734994 0.734994 0.001885
GW 2 3 1.000000 0.734994 0.734994 1.000000 0.000000 0.734994 0.001885
GW 3 3 2.288269 0.000000 -0.720672 2.288269 0.720672 -0.720672 0.001885
GW 3 6 2.288269 0.720672 -0.720672 2.288269 0.720672 0.720672 0.001885
GW 3 3 2.288269 0.720672 0.720672 2.288269 0.000000 0.720672 0.001885
GW 4 3 2.855866 0.000000 -0.696650 2.855866 0.696650 -0.696650 0.001885
GW 4 6 2.855866 0.696650 -0.696650 2.855866 0.696650 0.696650 0.001885
GW 4 3 2.855866 0.696650 0.696650 2.855866 0.000000 0.696650 0.001885
GW 5 3 3.913519 0.000000 -0.672627 3.913519 0.672627 -0.672627 0.001885
GW 5 6 3.913519 0.672627 -0.672627 3.913519 0.672627 0.672627 0.001885
GW 5 3 3.913519 0.672627 0.672627 3.913519 0.000000 0.672627 0.001885
GX  100  010
GE
FR  0    0    0    0    52.000000
EX  0    2    1    0    5.   0.
EX  0  102    1    0   -5.   0.
PT -1
PL  3   2    0    3
RP  0   1  181 1100   90.     0.      0.     1.0
EN
=================================End Here=======================================
===============================Begin Here=======================================
%!PS-Adobe-2.1
%%Creator: PolarPlot X1.0
%%+Copyright (c) 1990 DIGITAL EQUIPMENT CORPORATION.  
%%+All Rights Reserved.
%%DocumentFonts: (atend)
%%EndComments
%%BeginProcSet PolarPlot X1.0

% polar to cartesian
% r phi -- x y
/pc { 2 copy cos mul 3 1 roll sin mul } def

% polar moveto
% r phi --
/pm { pc moveto } def

% polar lineto
% r phi --
/pl { pc lineto } def

% polar coordinate grid
% arguments are radius of chart, number of 5 dB rings required, and
% max phi (360 for full circle chart, 180 for half chart, etc.)  max phi
% is rounded up to a multiple of 5.
% saves scaling parameters for subsequent plot: ring, r
% r rings maxphi --
/pch {
  5 div ceiling 5 mul /maxphi exch def
  /rings exch def /r exch def 
  r rings div /ring5 exch def ring5 5 div /ring exch def
  180 ring5 div ceiling ring5 mul /r1 exch def
  40 ring5 div ceiling ring5 mul /r2 exch def
  15 ring div ceiling ring mul /r10 exch def
  0 setlinewidth newpath
  ring ring r { 0 0 3 -1 roll 0 maxphi arc stroke } for
  r r1 gt { 1 2 maxphi { dup r exch pm r1 exch pl stroke } for } if
  r r2 gt { 2 2 maxphi { dup r exch pm r2 exch pl stroke } for } if
  0.5 setlinewidth
  ring5 ring5 r { 0 0 3 -1 roll 0 maxphi arc stroke } for
  r r10 gt { 10 10 maxphi { dup r exch pm r10 exch pl stroke } for } if
  0 90 maxphi { r exch pm 0 0 lineto stroke } for
} def

% normalized dB value to cartesian
% db phi -- x y
/dc { exch ring mul r add dup 0 lt { pop 0 } if exch pc } def

% move to point given normalized dB value
% db phi --
/dm { dc moveto } def

% draw line to point given normalized dB value
% db phi --
/dl { dc lineto } def

%%EndProcSet
%%EndProlog
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stroke
showpage
=================================End Here=======================================

6 element quad with: F/B = 50 dB  Gain = 10.7 dBi  Impedance = 39 Ohms
===============================Begin Here=======================================
CM  6 element QUAD on a 4.000000m boom for 52.000000 Mhz 
CM  Generated on Sun Nov 22 21:40:49 1992
CE
GW 1 3 0.000000 0.000000 -0.778326 0.000000 0.778326 -0.778326 0.001885
GW 1 6 0.000000 0.778326 -0.778326 0.000000 0.778326 0.778326 0.001885
GW 1 3 0.000000 0.778326 0.778326 0.000000 0.000000 0.778326 0.001885
GW 2 3 0.944134 0.000000 -0.740183 0.944134 0.740183 -0.740183 0.001885
GW 2 6 0.944134 0.740183 -0.740183 0.944134 0.740183 0.740183 0.001885
GW 2 3 0.944134 0.740183 0.740183 0.944134 0.000000 0.740183 0.001885
GW 3 3 1.931509 0.000000 -0.720672 1.931509 0.720672 -0.720672 0.001885
GW 3 6 1.931509 0.720672 -0.720672 1.931509 0.720672 0.720672 0.001885
GW 3 3 1.931509 0.720672 0.720672 1.931509 0.000000 0.720672 0.001885
GW 4 3 2.745923 0.000000 -0.727879 2.745923 0.727879 -0.727879 0.001885
GW 4 6 2.745923 0.727879 -0.727879 2.745923 0.727879 0.727879 0.001885
GW 4 3 2.745923 0.727879 0.727879 2.745923 0.000000 0.727879 0.001885
GW 5 3 2.998212 0.000000 -0.694728 2.998212 0.694728 -0.694728 0.001885
GW 5 6 2.998212 0.694728 -0.694728 2.998212 0.694728 0.694728 0.001885
GW 5 3 2.998212 0.694728 0.694728 2.998212 0.000000 0.694728 0.001885
GW 6 3 4.000000 0.000000 -0.666622 4.000000 0.666622 -0.666622 0.001885
GW 6 6 4.000000 0.666622 -0.666622 4.000000 0.666622 0.666622 0.001885
GW 6 3 4.000000 0.666622 0.666622 4.000000 0.000000 0.666622 0.001885
GX  100  010
GE
FR  0    0    0    0    52.000000
EX  0    2    1    0    5.   0.
EX  0  102    1    0   -5.   0.
PT -1
PL  3   2    0    3
RP  0   1  181 1100   90.     0.      0.     1.0
EN
=================================End Here=======================================
===============================Begin Here=======================================
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%%Creator: PolarPlot X1.0
%%+Copyright (c) 1990 DIGITAL EQUIPMENT CORPORATION.  
%%+All Rights Reserved.
%%DocumentFonts: (atend)
%%EndComments
%%BeginProcSet PolarPlot X1.0

% polar to cartesian
% r phi -- x y
/pc { 2 copy cos mul 3 1 roll sin mul } def

% polar moveto
% r phi --
/pm { pc moveto } def

% polar lineto
% r phi --
/pl { pc lineto } def

% polar coordinate grid
% arguments are radius of chart, number of 5 dB rings required, and
% max phi (360 for full circle chart, 180 for half chart, etc.)  max phi
% is rounded up to a multiple of 5.
% saves scaling parameters for subsequent plot: ring, r
% r rings maxphi --
/pch {
  5 div ceiling 5 mul /maxphi exch def
  /rings exch def /r exch def 
  r rings div /ring5 exch def ring5 5 div /ring exch def
  180 ring5 div ceiling ring5 mul /r1 exch def
  40 ring5 div ceiling ring5 mul /r2 exch def
  15 ring div ceiling ring mul /r10 exch def
  0 setlinewidth newpath
  ring ring r { 0 0 3 -1 roll 0 maxphi arc stroke } for
  r r1 gt { 1 2 maxphi { dup r exch pm r1 exch pl stroke } for } if
  r r2 gt { 2 2 maxphi { dup r exch pm r2 exch pl stroke } for } if
  0.5 setlinewidth
  ring5 ring5 r { 0 0 3 -1 roll 0 maxphi arc stroke } for
  r r10 gt { 10 10 maxphi { dup r exch pm r10 exch pl stroke } for } if
  0 90 maxphi { r exch pm 0 0 lineto stroke } for
} def

% normalized dB value to cartesian
% db phi -- x y
/dc { exch ring mul r add dup 0 lt { pop 0 } if exch pc } def

% move to point given normalized dB value
% db phi --
/dm { dc moveto } def

% draw line to point given normalized dB value
% db phi --
/dl { dc lineto } def

%%EndProcSet
%%EndProlog
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