E-plane and H-plane patterns of a rectangular microstrip patch

I am trying to recreate a polar plot of gain in dB, but I am not sure how to create the graph. Any help is appreciated. This is what I have so far:

   if true
    % code
% the following values are given on page 836
dielectric_const = 2.2;   % unitless
h = 0.1588;               % in cm
f = 10e9;                 % in Hz
L = 0.906;                % in cm
L_e = 1.068;              % in cm
E0 = 1;                   % in V/cm, generic value of 1 given
V0 = h*E0;                % in V
theta = pi/2;             % in radians
k0 = (2*pi*f)/(3e8);      % wavenumber
W = 1.185;                % width in cm
phi = linspace(0, pi/2, 1e3);
theta = pi/2;
r = 1;
a = (k0*h)/2;
b = (k0*L_e)/2;
c = k0*W;
d = c/2;
e = cos(phi);
f = sin(phi);
multiplier = i*(c*V0*exp(-1*i*k0*r)/pi*r);
n_1 = sin(a*e);
n_2 = cos(b*f);
d_1 = a*e;
% E plane, eq. 14-45
E_phi = (multiplier.*n_1.*n_2)./d_1;
  end

Answer 1

[David Goodmanson]

Hi Maximiliano,

Before getting to the plot, there are a couple of things in the code that need to be changed. [1] In the multiplier, there should be some more parentheses included so that you are dividing by r instead of multiplying by it. [2] Since all units are in cm, you need a different value for c than 3e8. Anyway I will assume that you have a good function of E_phi vs. phi.

From the Eplane plot it looks like you want directivity and not gain, i.e. 0 dB as the maximum value. The following code is an example of such a plot, which has multiple curves but certainly works for just one. You can make the obvious change to have the angle go counterclockwise as in the Eplane plot.

I thought that the polaraxes command would work conveniently like the rlim command does, but not so. It looks like it can be made to work, but it’s a hassle. The ‘get’ command does a good job.

% reproduces a set of dipole antenna patterns
% from a book I don't know the name of

theta = (-1:.001:1)*pi;
lambda = 1;                           % arbitrary value, cancels out
d = lambda*[1/50 1/4 1/2 3/4 1]';     % full antenna length, both halves
k = 2*pi/lambda;
kd2 = k*d/2;
[THeta Kd2] = meshgrid(theta,kd2);
y = (cos(Kd2.*cos(THeta))-cos(Kd2))./sin(THeta);

% ---------  plot

y = 20*log10(abs(y));   % dB
ymax = max(y,[],2);
y = y-ymax;             % set max = 0dB to obtain directivity
y(y<-40) = -40;         % set a lower limit
fig(1)
polarplot(theta,y)
rlim([-40 0]);
% polaraxes command doesn't work with the following syntax
% polaraxes('thetazerolocation','top','thetadir','clockwise')
set(gca,'thetazerolocation','top','thetadir','clockwise');
legend('lambda/50','lambda/4','lambda/2','3 lambda/4','lambda')

[Maximiliano Rodallegas]

Thank you so much! This was very helpful!

[Neha Jetgonda]

@Maximiliano Rodallegas can i have the total code

Answer 2

[mohamed moumou]

Thank you very match sir for this script code Matlab. it helps me