rmsa.m

design of rectangular microstrip antenna using MATLAB

% The following program computes some important parameters of a rectangular
% microstrip  patch antenna
%Te inputs to the program are the thickness of the substrate h ,the
%desired resonant frequency fr , the width of the feed microstrip and
%the dielectric constant of the substrate Er.The layout is shown below.It uses inset feed

%               
%
%                              <----------      L     ------------->
%                                                          
%                             ___________________      
%              |             |                                           ____|      |      Feed  microstrip
%              |             |                                          |______|____________
%              |             |                                                                                                  |
%              W          |                                                          W0                                 |
%              |             |                                            __________________|        
%              |             |                                          |_____      
%              |             |___________________|

%                                                                         <------>
%                                                                              y0

clear all;
% warning off MATLAB:divideByZero;


fr1=input('Enter the resonant frequency in GHz : ');
Er=input('\n Enter the dielectric constant of the substrate : ');
h1=input('\n Enter the thickness of the substrate in mm : ')
Zc=input('\n Enter the characterstic impedance needed for the microstrip transmission line: ')


fr=fr1*1e9;
h=h1*1e-3;

% Velocity of light in vacuum
c0=299792458;

%Wavelength in free space Lambda
Lambda0=c0/fr;

% Free space wave impedance

Z0=120*pi;

%Determining the width of the microstrip transmission line needed


    A=(pi*sqrt(2*(Er+1)))*(Zc/Z0)+((Er-1)/(Er+1))*(0.23+0.11/Er);
    ratio1=4/(0.5*exp(A)-exp(-A));

    B=(pi/(2*sqrt(Er)))*(Z0/Zc);
    ratio2=((Er-1)/(pi*Er))*(log(B-1)+0.39-0.61/Er)+(2/pi)*(B-1-log(2*B-1));
    
    if ratio1 <= 2 
        ratio = ratio1;
    else ratio = ratio2;
    end
    
    W_tln=h*ratio;


% Width of the patch
W=(c0/(2*fr))*sqrt(2/(Er+1));

% The effective dielectric constant
Ereff=(Er+1)/2+((Er-1)/2)*(power((1+12*h/W),-0.5));

% Wavelength in effective medium
Lambda=Lambda0/sqrt(Ereff);

% Speed of light in effective medium 
c=c0/sqrt(Ereff);

%Length of microstrip TLN for a 360 degree phase shift
L_tln=Lambda


% The correction of length delL due to the fringing
delL=0.412*h*((Ereff+0.3)*(W/h+0.264))/((Ereff-0.258)*(W/h+0.8));

% Correct length needed
L=Lambda/2-2*delL;

%The feed  inset required


% Calculation of the conductance
 k0=2*pi/Lambda0;
 X=k0*W;

%Calculation of the integral of sin(x)/x
 syms t;
 f=sin(t)./t;
 SiX=quadl(inline('f'),eps,X);
 I1=-2+cos(X)+sin(X)./X+X*SiX;
 G1= I1/(120*(pi^2));
Rin0=1/(2*G1);

% Use cos^4 dependence

y0=(L/pi)*acos((power((Zc/Rin0),0.25)));

disp('All the values are in microns');

Ereff
Width_trans_line=W_tln/1e-6
W_Patch=W/1e-6
L_Patch=L/1e-6
inset=y0/1e-6