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| % drawSpiral.m JW 21 March 2011
%
% Plots the conical logarithmic spiral antenna corresponding to the set of
% characteristic antenna parameters.
alpha = 50; % [degrees] Conductor wrap angle
delta = 76; % [degrees] Width of conductor around a circular plane parallel to the base
theta0 = 7.5; % [degrees] Half cone apex angle
minD = 12; % [mm] Minimum antenna diameter
maxD = 100; % [mm] Maximum antenna diameter
Hs = 332; % [mm] Vertical height of spiral
fGap = 1; % [mm] Gap at feedpoint of antenna
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Convert angles to radians
alpha = alpha*pi/180;
theta0 = theta0*pi/180;
Hc = Hs + Hs*minD/(maxD-minD); % Effective height of conical form
rho0 = sqrt((minD/2)^2 + (Hc-Hs)^2); % Initial radius
b = sin(theta0)/tan(alpha); % Spiral expansion factor
phiMax = tan(alpha)*log(maxD/minD)/sin(theta0); % Total rotation angle
figure;
hold on;
axis equal;
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% First spiral arm
for phi = 0:(phiMax*180/pi) % Upper side of spiral
rho = rho0*exp(b*pi*phi/180);
planeR = rho * sin(theta0);
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = cos(theta0)*(rho0-rho);
plot3(xPos, yPos, zPos);
end
for phi = 0:delta % Inside top edge of spiral
planeR = minD/2;
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = 0;
plot3(xPos, yPos, zPos);
end
for phi = delta:(delta+phiMax*180/pi) % Lower side of spiral
rho = rho0*exp(b*pi*(phi-delta)/180);
planeR = rho * sin(theta0);
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = cos(theta0)*(rho0-rho);
plot3(xPos, yPos, zPos);
end
for phi = (phiMax*180/pi):(delta+phiMax*180/pi) % Outside bottom edge of spiral
planeR = maxD/2;
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = -Hs;
plot3(xPos, yPos, zPos);
end
% Define tapered feed
feed1 = [minD/2 0 0; ...
fGap 0 0; ...
fGap*cos(delta*pi/180) fGap*sin(delta*pi/180) 0; ...
minD/2*cos(delta*pi/180) minD/2*sin(delta*pi/180) 0];
plot3(feed1(:,1), feed1(:,2), feed1(:,3));
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Second spiral arm
for phi = 180:(180+phiMax*180/pi) % Upper side of spiral
rho = rho0*exp(b*(pi*phi/180-pi));
planeR = rho * sin(theta0);
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = cos(theta0)*(rho0-rho);
plot3(xPos, yPos, zPos, 'r');
end
for phi = 180:(delta+180) % Inside top edge of spiral
planeR = minD/2;
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = 0;
plot3(xPos, yPos, zPos, 'r');
end
for phi = (180+delta):(delta+180+phiMax*180/pi) % Lower side of spiral
rho = rho0*exp(b*(pi*(phi-delta)/180-pi));
planeR = rho * sin(theta0);
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = cos(theta0)*(rho0-rho);
plot3(xPos, yPos, zPos, 'r');
end
for phi = (180+phiMax*180/pi):(delta+180+phiMax*180/pi) % Outside bottom edge of spiral
planeR = maxD/2;
xPos = planeR*cos(phi*pi/180);
yPos = planeR*sin(phi*pi/180);
zPos = -Hs;
plot3(xPos, yPos, zPos, 'r');
end
% Define tapered feed
plot3(-feed1(:,1), -feed1(:,2), -feed1(:,3), 'r'); |