The document appears to be a lab manual for an antenna and wave propagation course. It contains instructions for various MATLAB programs and simulations involving antenna radiation patterns, including dipole antennas, monopole antennas, loop antennas, and various array configurations like linear arrays, circular arrays, and rectangular apertures. It provides theoretical background, sample MATLAB code, and example outputs for each practical simulation. The document is meant to help students complete their lab work and simulations for the course.

1. 1
LAB MANUAL
OF
ANTENNA AND WAVE
PROPAGATION
Using MATLAB
DEPARTMENT OF EC
GOVERNMENT ENGINEERING COLLEGE
DAHOD -389151
Prepared By :
Prof. Alpesh H. Dafda
Asst. Prof. (E.C.)

2. 2
CERTIFICATE
This is to certify that
__________________________________ Enrollement
number ____________________ has successfully
completed his/her term work and practical work in the
subject Antenna and Wave Propagation(161003) for
the term ending in __________________ at
Government Engineering College, Dahod, for partial
fulfillment of B.E. degree to be awarded by Gujarat
Technological University. This work has been carried
out under my supervision and is to my satisfaction.
Date:
Place:
Subject Teacher Head of Department

3. 3
INDEX
NO SUBJECT DATE PAGE SIGN REMARKS
1 To write a program to plot the
radiation pattern of Dipole
Antenna.
2 To write a program to plot radiation
pattern of Monopole antenna.
3 To write a program to plot radiation
pattern of Loop antenna.
4 To write a Program to plot radiation
pattern of Linear array antenna.
5 To write a Program to plot radiation
pattern of Circular array antenna.
6 To write program to plot radiation
pattern of rectangular aperture
antenna.
7 To write a program to plot radiation
pattern of travelling wave antenna.
8 To write a program to plot radiation
pattern of linear array of isotropic
antennas.
9 To perform the numerical
evaluation of directivity for a half
wave dipole.
10 To write a program to determine
the directivity [D(θ,Φ)], the beam
solid angle ΩA and the maximum
directivity [Do] of an antenna
defined by F(θ,Φ) = sin2
θcos2
θ.
11 To write a program to Design
Microstrip Antenna.

4. 4
12 To write a program to plot 3-D
pattern of Rectangular Apertures as
a function of the independent
variables vx, vy, for aperture
dimensions a = 8λ and b = 4λ.
13 To write a program to plot 3-D
pattern of Circular Aperture as a
function of the independent
variables vx = (a/λ)sinθcosφ and vy
= (a/λ)sinθsinφ, for an aperture
radius of a = 3λ.
14 To write a program to plot the
radiation pattern of a horn
antenna.
15 To write a program to plot the
radiation pattern of a Optimized
six-element Yagi-Uda antenna.
16 To write a program to plot the
radiation pattern for Binomial
antenna array.
17 To write a program to plot radiation
pattern for Broadside antenna
array.
18 To write a program to plot radiation
pattern for Endfire antenna array.
19 To write a program to plot 3D
radiation pattern for Binomial
antenna array.
20 To write a program to plot 3D
radiation pattern for Broadside
antenna array.
21 To write a program to plot 3D
radiation pattern for Endfire
antenna array.
22 To write a program to plot 3-D
Radiation Pattern of Dipole
Antenna.

5. 5
Practical -1
AIM : To write a program to plot the radiation pattern of Dipole Antenna.
THEORY :

6. 6
MATLAB PROGRAM :
%This program print pattern (AF) for Short and any Dipole
%Antenna by giving the length of your Dipole and the
%wavelength you work with
clc;
lamda=input('enter the value of wave length= ');
l=input('enter your dipole length l in terms of lamda(for ex:
0.5 for 0.5lamda)= ');
ratio=l/lamda;
B=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
if ratio<= 0.1 %check if Short Dipole
E=sin(theta);
En=abs(E);
polar(theta,En) %This plot polar pattern in plane
which dipole appear as line
else %check if not short dipole
f1=cos(B*l/2.*cos(theta));
f2=cos(B*l/2);
f3=sin(theta);
E=(f1-f2)./f3;
En=abs(E);
polar(theta,En) %This plot polar pattern in plane
which dipole appear as line
end
OUTPUT :
enter the value of wave length= 1
enter your dipole length l in terms of lamda(for ex: 0.5 for
0.5lamda)= 0.5

7. 7
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

8. 8
Practical - 2
AIM : To write a program to plot radiation pattern of Monopole antenna.
THEORY :

9. 9
MATLAB PROGRAM :
%%This program print pattern for Short and any monopole
%Antenna by giving the length of your Dipole
%and the wavelength you work with
lamda=input('enter the value of wave length= ');
l=input('enter your monopole length l= ');
ratio=l/lamda;
B=(2*pi/lamda);
theta= -pi/2:pi/100:pi/2;
if ratio<= 0.1 %check if Short monopole
E=sin(theta);
En=abs(E);
polar(theta,En) %This plot polar pattern in plane
which monopole appear as line
else %check if not short monopole
f1=cos(B*l/2.*cos(theta));
f2=cos(B*l/2);
f3=sin(theta);
E=(f1-f2)./f3;
En=abs(E);
polar(theta,En) %This plot polar pattern in plane
which monopole appear as line
end
OUTPUT :
enter the value of wave length= 1
enter your monopole length l= 0.5

10. 10
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

11. 11
Practical -3
AIM : To write a program to plot radiation pattern of Loop antenna.
THEORY :

12. 12
MATLAB PROGRAM :
%This program print pattern for Loop Antenna by giving the
%radius of your Loop and the wavelength you work with
clc;
lamda=input('enter the value of wave length= ');
a=input('enter your loop radius a= ');
B=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
E=besselj(1,B*a.*sin(theta));
polar(theta,E)
OUTPUT :
enter the value of wave length= 1
enter your loop radius a= 0.5
0.2
0.4
0.6
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

13. 13
Practical - 4
AIM : To write a Program to plot radiation pattern of Linear array
antenna.
THEORY :

14. 14
MATLAB PROGRAM :
%This program print pattern for linear Array (uniform) Antenna
%by giving N,alfa,d and the wavelength you work with
%if you want full pattern multiply this pattern by any Antenna
%pattern
clc;
lamda=input('enter the value of wave length= ');
N=input('enter the no. of elements(3,4,5...)= ');
alfa=input('enter your progressive phase(alpha=0,45...)= ');
d=input('enter the seperation distance between elements(in
terms of lamda for ex: 0.3 for 0.3lamda)= ');
B=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
w=alfa+B*d.*cos(theta);
AF=sinc(N*(w./2))./sinc(w./2);
polar(theta,AF)
OUTPUT :
enter the value of wave length= 1
enter the no. of elements(3,4,5...)= 6
enter your progressive phase(alpha=0,45...)= 0
enter the seperation distance between elements(in terms of
lamda for ex: 0.3 for 0.3lamda)= 0.3

15. 15
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

16. 16
Practical - 5
AIM : To write a Program to plot radiation pattern of Circular array
antenna.
THEORY :

17. 17
MATLAB PROGRAM :
% This program print pattern for circular Array (uniform)
%Antenna by giving N,a and the wavelength you work with
%if you want full pattern multiply this pattern by any Antenna
%pattern
clc;
lamda=input('enter the value of wave length= ');
N=input('enter the no. of elements(3,4,5...)= ');
a=input('enter your circular radius( in terms of lamda for ex
0.2 for 0.2lamda)= ');
theta0=input('enter angle theta at which main lobe occurs(ex:
45)= ');
phi0=input('enter angle phi at which main lobe occurs(ex: 90)=
');
B=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
phi=pi/100:pi/100:2*pi;
f1=sin(theta0)*cos(phi0);
f2=sin(theta0)*sin(phi0);
f3=sin(theta).*cos(phi);
f4=sin(theta).*sin(phi);
x=f3-f1;
y=f4-f2;
ro=a.*sqrt(x.^2+y.^2);
AFn=besselj(0,B.*ro);
polar(theta,AFn)
OUTPUT :
enter the value of wave length= 1
enter the no. of elements(3,4,5...)= 2
enter your circular radius( in terms of lamda for ex 0.2 for
0.2lamda)= 0.2
enter angle theta at which main lobe occurs(ex: 45)= 45
enter angle phi at which main lobe occurs(ex: 90)= 90

18. 18
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

19. 19
Practical - 6
AIM : To write program to plot radiation pattern of rectangular aperture
antenna.
THEORY :

20. 20
MATLAB PROGRAM :
% This program prints electric field pattern for rectangular
%Aperture Antenna by giving the a,b
%and the wavelength you work with
kind=input('Enter your antenna type Rectangular (1) or
circular (2)= ');
lamda=input('enter the value of wave length= ');
theta= pi/100:pi/100:2*pi;
B=(2*pi/lamda);
u0=0; %@phi=90
u=B.*(sin(theta));
v0=0; %@phi=0
v=B.*(sin(theta));
if kind==1
feeding=input('enter your feeding type "uniform(1),blocked
in one dim. Aperture(2),TE10(3)": ');
if feeding==1 %uniform
a=input('enter ur larg rectanglar length a= ');
b=input('enter ur small rectanglar length b= ');
E1=sinc((b.*v)./2); %E-plane phi=90
E2=sinc((a.*u)./2); %H-plane phi=0
subplot(3,3,1)
polar(theta,E1),title('E-plane')
subplot(3,3,2)
polar(theta,E1),title('H-plane')
elseif feeding==2
%blocked
delta=input('enter value of blocking= ');
E1=(b.*sinc((b.*v)./2)) -
(delta.*sinc((delta.*v)./2)); %E-plane
E2=sinc((a.*u)./2);
%H-plane phi=0
subplot(3,3,3)
polar(theta,E1),title('E-plane')
subplot(3,3,4)
polar(theta,E1),title('H-plane')
elseif feeding==3 %TE10
E1=sinc((b.*v)./2); %E-plane phi=90
f1=(a/2).*(u-(pi/a));
f2=(a/2).*(u+(pi/a));
E2=sinc(f1)+sinc(f2); %H-plan phi=0
subplot(3,3,5)
polar(theta,E1),title('E-plane')
subplot(3,3,6)
polar(theta,E1),title('H-plane')
end
elseif kind==2
a=input('Enter radius of Circular Aperture= ');

21. 21
f1=B*a;
f=f1.*(sin(theta));
E=(besselj(1,f))./f; %E-plane or H-plane
subplot(3,3,7)
polar(theta,E)
end
OUTPUT :
Enter your antenna type Rectangular (1) or circular (2)= 1
enter the value of wave length= 1
enter your feeding type "uniform(1),blocked in one dim.
Aperture(2),TE10(3)": 1
enter ur larg rectanglar length a= 0.3
enter ur small rectanglar length b= 0.2
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
E-plane
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
H-plane
CONCLUSIONS :

22. 22
Practical - 7
AIM : To write a program to plot radiation pattern of travelling wave
antenna.
THEORY :

23. 23
MATLAB PROGRAM :
%This program print pattern for TWA(Travelling Wave Antenna)
%by giving the length of your Line
%and the wavelength you work with
clc;
lamda=input('enter the value of wave length= ');
l=input('enter your Line length l= ');
B=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
f1=sin(theta);
f2=1-cos(theta);
f3=sin(B*l/2.*(f2));
E=(f1./f2).*f3;
En=abs(E);
polar(theta,En);
OUTPUT:
enter the value of wave length= 1
enter your Line length l= 1
0.5
1
1.5
2
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

24. 24
Practical - 8
AIM : To write a program to plot radiation pattern of linear array of
isotropic antennas.
THEORY :

25. 25
MATLAB PROGRAM :
% clc;
lamda=input('enter the value of wave length(in
meter)= ');
N=input('enter the no. of elements= ');
alpha=input('enter your progressive phase= ');
d=input('enter the separation distance between
elements(in meter)= ');
beta=(2*pi/lamda);
theta= pi/100:pi/100:2*pi;
psi=alpha+beta*d.*cos(theta);
e=sin(N*(psi./2))./sin(psi./2);
polar(theta,e/N);
Case 1: When α=0, d=λ/4
N=2 N=4
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0

26. 26
N=8 N=16
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
Observation: As the number of isotropic antennas increase, the
directivity increases.
Case 2: When N=2, α=0°
d=λ/4 d=λ/2
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0

27. 27
d=3/4λ d=λ
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
d=5/2λ d=3/2λ
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
Observation: As the distance between antennas increases, the radiation
pattern is not only broadsided but also radiates in other directions.

28. 28
Case 3: When N=2, d=λ/2
α=0° α=45°
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
α=90° α=135°
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
Observation: As the phase difference between the excitation increases,
the main lobe directivity is decreasing whereas the side lobe is increasing.
CONCLUSIONS :

29. 29
Practical - 9
AIM : To perform the numerical evaluation of directivity for a half wave
dipole .
THEORY :

30. 30
MATLAB PROGRAM :
% sum=0.0;
N=input(’Enter the number of segments in the theta
directionn’);
for i=1:N
thetai=(pi/N)*(i-0.5);
sum=sum+(cos((pi/2)*cos(thetai)))^2/sin(thetai);
end
D=(2*N)/(pi*sum)
OUTPUT :
Enter number of segments in the theta direction
5
D =
1.6428
Enter number of segments in the theta direction
10
D =
1.6410
Enter number of segments in the theta direction
15
D =
1.6409
Enter number of segments in the theta direction
20
D =
1.6409
CONCLUSIONS:

31. 31
Practical - 10
AIM : To write a program to determine the directivity [D(θ,Φ)], the
beam solid angle ΩA and the maximum directivity [Do] of an
antenna defined by F(θ,Φ) = sin2
θcos2
θ.
THEORY :

32. 32

33. 33
MATLAB PROGRAM :
% for i=1:100
theta(i)=pi*(i-1)/99;
d(i)=7.5*((cos(theta(i)))^2)*((sin(theta(i)))^2);
end
polar(theta,d)
OUTPUT :
0.5
1
1.5
2
30
210
60
240
90
270
120
300
150
330
180 0
CONCLUSIONS :

34. 34
Practical - 11
AIM : To write a program to Design Microstrip Antenna.
THEORY :

35. 35
MATLAB PROGRAM :
% clc
clear all
format long
% er=2.2;
% f=10e9;
% h=0.1588*10;
er=input('Enter the di-electric constant:');
h=input('Enter the substrate thickness (in mil)');
f=input('Enter the frequency (GHz):');
% er=3.5;
f=f*1e9;
h=h*0.0254; % in mm
wid=(3e8/(sqrt((er+1)/2)*2*f))*1000; %in mm
e_eff=((er+1)/2)+ (((er-1)/2)* (1+((12*h)/wid))^-0.5);
l_eff=(3e8/(2*f*sqrt(e_eff)))*1000;
del_l=(((e_eff+0.3)*((wid/h)+0.264))/((e_eff-
0.258)*((wid/h)+0.8)))*(0.412*h); %in mm
L=l_eff-(2*del_l);
la=(3e8/f)*1000;
k=(2*pi)/la;
x=k*(wid);
i1=-2+cos(x)+(x*sinint(x))+(sin(x)/x);
g1=i1/(120*pi*pi);
%Conductance % jb=besselj(0,(k.*L.*sin(th)));
a=@(th)(((sin((x./2).*cos(th))./cos(th)).^2).*(besselj(0,(k.*L
.*sin(th)))).*(sin(th)).^3); a1=quad(a,0,pi);
g12=a1/(120*pi*pi); %in siemens
r_in=1/(2*(g1+g12)); %in ohms
inset=(L/pi)*(acos(sqrt(50/r_in))); %in mm
disp(['The width is:',num2str(wid),' mm'])
disp(['The length is:',num2str(L),' mm'])
disp(['The inset feed point is:',num2str(inset),' mm'])
OUTPUT :
Enter the di-electric constant:12
Enter the substrate thickness (in mil)15
Enter the frequency (GHz):7
The width is:8.405 mm
The length is:6.1601 mm
The inset feed point is:2.5294 mm
CONCLUSIONS :

36. 36
Practical - 12
AIM : To write a program to plot 3-D pattern of Rectangular Apertures
as a function of the independent variables vx, vy, for aperture
dimensions a = 8λ and b = 4λ.
THEORY :

37. 37
MATLAB PROGRAM :
% a = 8; b = 4;
[theta,phi] = meshgrid(0:1:90, 0:9:360);
theta = theta*pi/180; phi = phi*pi/180;
vx = a*sin(theta).*cos(phi);
vy = b*sin(theta).*sin(phi);
E = abs((1 + cos(theta))/2 .* sinc(vx) .* sinc(vy));
surfl(vx,vy,E);
shading interp; colormap(gray(16));
OUTPUT :
-10
-5
0
5
10
-4
-2
0
2
4
0
0.2
0.4
0.6
0.8
1
CONCLUSIONS :

38. 38
Practical - 13
AIM : To write a program to plot 3-D pattern of Circular Aperture as a
function of the independent variables vx = (a/λ)sinθcosφ and vy
= (a/λ)sinθsinφ, for an aperture radius of a = 3λ.
THEORY :

39. 39
MATLAB PROGRAM :
% a = 3;
[theta,phi] = meshgrid(0:1:90, 0:9:360);
theta = theta*pi/180; phi = phi*pi/180;
vx = a*sin(theta).*cos(phi);
vy = a*sin(theta).*sin(phi);
u = a*sin(theta);
E = ones(size(u));
i = find(u);
E(i) = abs(2*besselj(1,2*pi*u(i))./(2*pi*u(i)));
surfl(vx,vy,E);
shading interp; colormap(gray(16));
OUTPUT :
-4
-2
0
2
4
-4
-2
0
2
4
0
0.2
0.4
0.6
0.8
1
CONCLUSIONS :

40. 40
Practical - 14
AIM : To write a program to plot the radiation pattern of a horn
antenna.
THEORY :

41. 41
MATLAB PROGRAM :
% function []=horn;
disp('E-Plane and H-Plane Horn Specifications');
%R1=[]; R2=[];
%R1 = input('rho1(in wavelengths) = ');
%R2 = input('rho2(in wavelengths) = ');
R1=6; R2=6;a=0.5; b=0.25; a1=5.5; b1=2.75;
%a=[]; b=[];
%a = input('a(in wavelengths) = ');
%b = input('b(in wavelengths) = ');
%a1=[]; b1=[];
%a1 = input('a1(in wavelengths) = ');
%b1 = input('b1(in wavelengths) = ');
u = (1/sqrt(2))*((sqrt(R2)/a1)+(a1/sqrt(R2)));
v = (1/sqrt(2))*((sqrt(R2)/a1)-(a1/sqrt(R2)));
u = Fresnel(u);
v = Fresnel(v);
w = Fresnel(b1/sqrt(2*R1));
DH = 4*pi*b*R2/a1*((real(u)-real(v))^2 + (imag(u)-imag(v))^2);
DE = 64*a*R1/(pi*b1)*((real(w))^2 + (imag(w))^2);
DP = pi/(32*a*b)*DE*DH;
k = 2*pi;
Emax = 0;
Hmax = 0;
% E and H plane Outputs
% E-Plane Amplitude
for(theta = 0:0.5:360);
I = theta*2 + 1;
theta = theta*pi/180;
phi = pi/2;
ky = k*sin(theta);
kxp = pi/a1;
kxdp = -pi/a1;
t1 = sqrt(1/(pi*k*R1))*(-k*b1/2-ky*R1);
t2 = sqrt(1/(pi*k*R1))*(k*b1/2-ky*R1);
t1p = sqrt(1/(pi*k*R2))*(-k*a1/2-pi/a1*R2);
t2p = sqrt(1/(pi*k*R2))*(k*a1/2-pi/a1*R2);
t1dp = -t2p;
t2dp = -t1p;
I1 =.5*sqrt(pi*R2/k)*(exp(j*R2/(2*k)*kxp^2)*(Fresnel(t2p)-
Fresnel(t1p)) + exp(j*R2/(2*k)*kxdp^2)*(Fresnel(t2dp) -
Fresnel(t1dp)));
I2 = sqrt(pi*R1/k) * exp(j*R1/(2*k)*ky^2) * (Fresnel(t2) -
Fresnel(t1));
y(I) = (1 + cos(theta))*I1*I2;
y(I) = abs(y(I));
end
for(I = 1:721)
if(y(I) > Emax)
Emax = y(I);

42. 42
end
end
for(I = 1:721)
if(y(I) <= 0)
Edb = -100;
else
Edb = 20*log10(abs(y(I))/Emax);
end
theta = (I-1)/2;
x(I)=theta;
q1(I)=Edb;
end
% H-Plane Amplitude
for(theta = 0:0.5:360);
I = theta*2 + 1;
theta = theta*pi/180;
phi = 0;
kxp = k*sin(theta) + pi/a1;
kxdp = k*sin(theta) - pi/a1;
t1 = sqrt(1/(pi*k*R1))*(-k*b1/2);
t2 = sqrt(1/(pi*k*R1))*(k*b1/2);
t1p = sqrt(1/(pi*k*R2))*(-k*a1/2-kxp*R2);
t2p = sqrt(1/(pi*k*R2))*(k*a1/2-kxp*R2);
t1dp = sqrt(1/(pi*k*R2))*(-k*a1/2-kxdp*R2);
t2dp = sqrt(1/(pi*k*R2))*(k*a1/2-kxdp*R2);
I1 = .5*sqrt(pi*R2/k)*(exp(j*R2/(2*k)*kxp^2)*(Fresnel(t2p)-
Fresnel(t1p)) + exp(j*R2/(2*k)*kxdp^2)*(Fresnel(t2dp) -
Fresnel(t1dp)));
I2 = sqrt(pi*R1/k) * exp(j*R1/(2*k)*ky^2) * (Fresnel(t2) -
Fresnel(t1));
y(I) = (1 + cos(theta))*I1*I2;
y(I) = abs(y(I));
end
for(I = 1:721)
if(y(I) > Hmax)
Hmax = y(I);
end
end
for(I = 1:721)
if(y(I) <= 0)
Hdb = -100;
else
Hdb = 20*log10(abs(y(I))/Hmax);
end
theta = (I-1)/2;
x(I)=theta;
q2(I)=Hdb;
end
% Figure 1
ha=plot(x,q1); set(ha,'linestyle','-','linewidth',2);
hold on; hb=plot(x,q2,'r--'); set(hb,'linewidth',2);

43. 43
xlabel('Theta (degrees)');
ylabel('Field Pattern (dB)');
title('Horn Analysis');
legend('E-Plane','H-Plane');
grid on;
axis([0 360 -60 0]);
% Figure 2
figure(2)
ht1=polar(x*pi/180,q1,'b-');
hold on;
ht2=polar(x*pi/180,q2,'r--');
set([ht1 ht2],'linewidth',2);
legend([ht1 ht2],{'E-plane','H-plane'});
title('Field patterns');
% Directivity Output
directivity = 10*log10(DP)
% Fresnel Subfunction
function[y] = Fresnel(x);
A(1) = 1.595769140;
A(2) = -0.000001702;
A(3) = -6.808508854;
A(4) = -0.000576361;
A(5) = 6.920691902;
A(6) = -0.016898657;
A(7) = -3.050485660;
A(8) = -0.075752419;
A(9) = 0.850663781;
A(10) = -0.025639041;
A(11) = -0.150230960;
A(12) = 0.034404779;
B(1) = -0.000000033;
B(2) = 4.255387524;
B(3) = -0.000092810;
B(4) = -7.780020400;
B(5) = -0.009520895;
B(6) = 5.075161298;
B(7) = -0.138341947;
B(8) = -1.363729124;
B(9) = -0.403349276;
B(10) = 0.702222016;
B(11) = -0.216195929;
B(12) = 0.019547031;
CC(1) = 0;
CC(2) = -0.024933975;
CC(3) = 0.000003936;
CC(4) = 0.005770956;
CC(5) = 0.000689892;
CC(6) = -0.009497136;
CC(7) = 0.011948809;
CC(8) = -0.006748873;
CC(9) = 0.000246420;

44. 44
CC(10) = 0.002102967;
CC(11) = -0.001217930;
CC(12) = 0.000233939;
D(1) = 0.199471140;
D(2) = 0.000000023;
D(3) = -0.009351341;
D(4) = 0.000023006;
D(5) = 0.004851466;
D(6) = 0.001903218;
D(7) = -0.017122914;
D(8) = 0.029064067;
D(9) = -0.027928955;
D(10) = 0.016497308;
D(11) = -0.005598515;
D(12) = 0.000838386;
if(x==0)
y=0;
return
elseif(x<0)
x=abs(x);
x=(pi/2)*x^2;
F=0;
if(x<4)
for(k=1:12)
F=F+(A(k)+j*B(k))*(x/4)^(k-1);
end
y = F*sqrt(x/4)*exp(-j*x);
y = -y;
return
else
for(k=1:12)
F=F+(CC(k)+j*D(k))*(4/x)^(k-1);
end
y = F*sqrt(4/x)*exp(-j*x)+(1-j)/2;
y =-y;
return
end
else
x=(pi/2)*x^2;
F=0;
if(x<4)
for(k=1:12)
F=F+(A(k)+j*B(k))*(x/4)^(k-1);
end
y = F*sqrt(x/4)*exp(-j*x);
return
else
for(k=1:12)
F=F+(CC(k)+j*D(k))*(4/x)^(k-1);
end
y = F*sqrt(4/x)*exp(-j*x)+(1-j)/2;

45. 45
return
end
end
OUTPUT :
E-Plane and H-Plane Horn Specifications
directivity =
18.827820259174445
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
Theta (degrees)
FieldPattern(dB)
Horn Analysis
E-Plane
H-Plane

46. 46
20
40
60
80
100
30
210
60
240
90
270
120
300
150
330
180 0
Field patterns
E-plane
H-plane
CONCLUSIONS :

47. 47
Practical - 15
AIM : To write a program to plot the radiation pattern of a Optimized
six-element Yagi-Uda antenna.
THEORY :

48. 48
Chen and Cheng, applied King’s three-term current approximation and
devised procedures for optimizing the choices of the antenna lengths and
separations of Yagi-Uda arrays. The gains before and after optimization of
a six-element Yagi-Uda array were calculated with the functions yagi and
gain2s. The antenna radii were a = 0.003369λ. For the unoptimized case,
the antenna lengths and x-locations were in units of λ: L = [L1, L2, L3,
L4, L5, L6]= [0.510, 0.490, 0.430, 0.430, 0.430, 0.430] d = [x1, x2, x3,
x4, x5, x6]= [−0.25, 0, 0.310, 0.620, 0.930, 1.240]. The directors were
identical and equally spaced at spacing of 0.31λ. The computed directivity
and front/back ratio were 11 dB and 9.84 dB, respectively. The optimized
case has slightly different lengths and x-locations: L = [L1, L2, L3, L4, L5,
L6]= [0.476, 0.452, 0.436, 0.430, 0.434, 0.430] d = [x1, x2, x3, x4, x5,
x6]= [−0.25, 0, 0.289, 0.695, 1.018, 1.440]. The optimized directivity
was 12.54 dB and the forward/backward ratio 17.6 dB.
MATLAB PROGRAM :
% clear all;
clc;
L = [0.476, 0.452, 0.436, 0.430, 0.434, 0.430];
a = 0.003369 * [1,1,1,1,1,1];
d = [-0.25, 0, 0.289, 0.695, 1.018, 1.440];
[I,D,Rfb] = yagi(L,a,d);
[ge,gh,th] = gain2(L,d,I,360);
figure; dbz2(th,gh,30,40);
figure; dbp2(th,ge,30,40);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% yagi.m - simplified Yagi-Uda array design
%
% Usage: [I,D,Rfb] = yagi(L,a,d)
%
% L = dipole lengths (in wavelengths) = [L1,L2,..,LK]
% a = dipole diameters = [a1,a2,...,aK]
% d = dipole locations along x-axis = [d1,d2,...,dK]
%
% I = input currents on dipoles = [I1,I2,...,IK]
% D = directivity in absolute units
% Rfb = forward-backward ratio in absolute units
%
% notes: dipole 1 is the reflector,
% dipole 2 is the driving element,
% dipoles 3:K are the directors (K>=3)
%
% current on p-th dipole is assumed to be sinusoidal:
I(p)*sin(2*pi(L(p)/2 - z)),
% this assumption is approximately correct if all the
lengths are near lambda/2,
% none of the lengths should be a multiple of lambda.
%

49. 49
% imput impedance of driven element is 1/I(2)
%
% the currents I can be passed to ARRAY2D to compute the
array gain
function [I,D,Rfb] = yagi(L,a,d)
if nargin==0, help yagi; return; end
K = length(L); % must have three or
more antennas, K>=3
Z = impedmat(L,a,d); % mutual impedance
matrix for the yagi array
V = [0; 1; zeros(K-2,1)]; % driving voltage
V(2) = 1
I = Z V; % solve Z*I = V
Nint = 16; % number of Gauss-
Legendre quadrature points
[wth,th] = quadr(0,pi,Nint); % quadrature weights
and angle points
[wph,ph] = quadr(0,2*pi,Nint);
A = zeros(Nint,Nint); % matrix of values
of array factor
Af = 0;
Ab = 0;
h = L/2;
for p=1:K,
A = A + I(p) * F(h(p),d(p),th,ph);
Af = Af + I(p) * F(h(p),d(p),pi/2,0); % forward
endfire
Ab = Ab + I(p) * F(h(p),d(p),pi/2,pi); % backward
endfire
end
Rfb = abs(Af/Ab)^2; % forward-backward
ratio
A = A / Af;
g = abs(A.*A); % normalized gain
for m=1:Nint,

50. 50
g(:,m) = g(:,m).*sin(th); % sin(th) comes from
dOmega = sin(th)*dth*dph
end
DOm = wth' * g * wph; % integrate over
th,ph to get beam solid angle
D = 4*pi / DOm; % directivity
% --------------------------------------------------------------
-------------------
function A = F(h,d,th,ph) % array factor of
dipole at distance x=d
k = 2*pi;
th = th(:); % theta is a column
ph = ph(:)'; % phi is a row
G = zeros(length(th),1); % G(th) is column of
dipole pattern values
i = find(th~=0 & th~=pi);
G(i) = (cos(k*h*cos(th(i))) - cos(k*h)) ./ (sin(k*h) *
sin(th(i)));
A = exp(j*k*d*sin(th)*cos(ph)); % displacement phase
factors
for m=1:length(ph),
A(:,m) = A(:,m) .* G;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% gain2.m - normalized gain of arbitrary 2D array of linear
sinusoidal antennas
%
% Usage: [ge,gh,th] = gain2(L,d,I,N,ph0)
% [ge,gh,th] = gain2(L,d,I,N) (equivalent to ph0=0)
%
% L = antenna lengths in wavelengths, L = [L1,L2,...,LK]
% d = [x,y] or [x] locations of the K antennas, d must be Kx2
or Kx1 or 1xK
% I = input currents at antenna terminals, I = [I1,I2,...,IK]
= Kx1 or 1xK
% N = number of azimuthal and polar angles over [0,2*pi]
% ph0 = azimuthal direction for E-plane pattern (in degrees)
%

51. 51
% ge,gh = E-plane/H-plane gains at (N+1) polar or azimuthal
angles over [0,2*pi]
% th = (N+1) equally-spaced polar or azimuthal angles over
[0,2*pi] in radians
%
% notes: I = [I1,I2,...,IK] are the input currents on the K
antennas,
% the current distributions on the antennas are assumed
to sinusoidal,
% for example, on the p-th antenna, Ip(z) = Ip *
sin(k*(Lp/2-abs(z))).
%
% d is the matrix of the [x,y] locations of the antennas
and is Kx2, that is,
% d = [x1,y1; x2,y2; ...; xK,yK]. If the antennas are
along the x-axis then
% d is the vector of x-coordinates only and can be
entered either as a column
% or row vector, d=[x1,x2,...,xK].
%
% E-plane gain is evaluated at phi = ph0 for 0 <= theta
<= 2*pi. The range
% [0,pi] corresponds to the forward ph0-direction and the
range [pi,2*pi] to the
% backward (ph0+pi)-direction. The E-plane gain must be
plotted with DBP2 or ABP2.
%
% H-plane gain is evaluated at theta = pi/2 for 0 <= phi
<= 2*pi and must be
% plotted with DBZ2 or ABZ2.
%
% The input currents I can be obtained from the input
driving voltages
% V = [V1,V2,...,VK]' by I = ZV, where Z is the mutual
impedance matrix
% obtained from IMPEDMAT, Z = impedmat(L,a,d), (a=antenna
diameters).
%
% for an isotropic array, use L=[0,0,...,0]
function [ge,gh,th] = gain2(L,d,I,N,ph0)
if nargin==0, help gain2; return; end
if nargin==4, ph0=0; end
I = I(:); % U(th,phi)
expects I,L to be columns
L = L(:);
K = length(L);

52. 52
if max(size(d))~=K,
error('d must have size Kx2 or Kx1 or 1xK');
end
if min(size(d))==1,
d = [d(:),zeros(K,1)]; % make d
into [x,y] pairs
end
ph0 = ph0*pi/180;
th = 0 : 2*pi/N : 2*pi;
for i=1:N+1,
ge(i) = U(L,d,I,th(i),ph0);
gh(i) = U(L,d,I,pi/2,th(i)); % here th is
the azimuthal angle
end
ge = ge/max(ge);
gh = gh/max(gh);
% --------------------------------------------------------------
--------------
function G = U(L,d,I,th,phi) % radiation
intensity U(th,phi)
k = 2*pi;
kx = k*sin(th)*cos(phi);
ky = k*sin(th)*sin(phi);
kz = k*cos(th);
x = d(:,1);
y = d(:,2);
A = (I./sin(pi*L)) .* (exp(j*kx*x).*exp(j*ky*y)); % K-
dimensional array factor
if sin(th)==0, % gains of
antenna elements
F = zeros(length(L),1); % F is K-
dimensional column
else
F = (cos(k*L*cos(th)/2) - cos(k*L/2)) / sin(th);
end
if max(L)==0, % isotropic
array case
F = ones(K,1);

53. 53
end
G = abs(F'*A)^2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% dbz2.m - azimuthal gain plot in dB - 2pi angle range
%
% Usage: h = dbz2(phi, g, rays, Rm, width)
%
% Examples: dbz2(phi, g); default (30-degree
lines and 40-dB scale)
% dbz2(phi, g, 45); use 45-degree grid
lines
% dbz2(phi, g, 30, 60); 30-degree rays and
60-dB scale
% dbz2(phi, g, 30, 60, 1.5); use thicker line for
gain
% h = dbz2(phi, g, 30, 60, 1.5); use h to add legends
(see dbadd)
%
% plots 10*log10(g(phi)), it assumes max-g is unity
% phi = azimuthal angles over [0,2pi]
%
% rays = 30 degrees by default, and can be omitted
% rays = 45 draws rays at 45-degree angles
%
% Rm = minimum dB level
% Rm = 40 by default
% Rm/4, 2Rm/4, 3Rm/4 grid circles displayed
%
% width = linewidth of gain curve
% width = 1.0 points by default
% width = 1.5 for thicker line
%
% useful when the gain is not an even function of phi,
% as for an array along the y-axis
%
% see also DBZ, ABZ, ABZ2, ABP, DBP, ARRAY
function h = dbz2(phi, g, rays, Rm, width)
if nargin==0, help dbz2; return; end
if nargin<3, rays = 30; end
if nargin<4, Rm = 40; end
if nargin<5, width = 1; end
sty = ':'; % grid
line style

54. 54
gdb = g .* (g > eps) + eps * (g <= eps); % make g=0
into g=eps, avoids -Inf's
gdb = 10 * log10(gdb);
gdb = gdb .* (gdb > -Rm) + (-Rm) * (gdb <= -Rm); % lowest
is Rm dB
gdb = (gdb + Rm)/Rm; % scale to
unity max.
x = gdb .* cos(phi);
y = gdb .* sin(phi);
N0 = 400;
phi0 = (0:N0) * 2*pi / N0;
x0 = sin(phi0); % gain
circles
y0 = cos(phi0);
h = plot(x, y, 'LineWidth', width);
hold on;
plot(x0, y0, 0.75*x0, 0.75*y0, sty, 0.50*x0, 0.50*y0, sty,
0.25*x0, 0.25*y0, sty);
axis square;
R = 1.1;
axis([-R, R, -R, R]);
axis off;
Nf = 15; % fontsize of labels
line([0,0],[-1,1]);
line([-1,1],[0,0]);
text(0, 1.02, ' 90^o', 'fontsize', Nf, 'horiz', 'center',
'vert', 'bottom');
text(0, -0.99, '-90^o', 'fontsize', Nf, 'horiz', 'center',
'vert', 'top');
text(1, 0.01, ' 0^o', 'fontsize', Nf, 'horiz', 'left', 'vert',
'middle');
text(-1.02, 0.01, '180^o', 'fontsize', Nf, 'horiz', 'right',
'vert', 'middle');
text(1.07*cos(pi/12), 1.07*sin(pi/12), 'phi', 'fontsize',
Nf+2, 'horiz', 'left');
if rays == 45,
x1 = 1/sqrt(2); y1 = 1/sqrt(2);
line([-x1,x1], [-y1,y1], 'linestyle', sty);
line([-x1,x1], [y1,-y1], 'linestyle', sty);

55. 55
text(1.04*x1, y1, '45^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'bottom');
text(0.97*x1, -0.97*y1, '-45^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'top');
text(-0.97*x1, 1.02*y1, '135^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-1.01*x1, -1.01*y1, '-135^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
else
x1 = cos(pi/3); y1 = sin(pi/3);
x2 = cos(pi/6); y2 = sin(pi/6);
line([-x1,x1], [-y1,y1], 'linestyle', sty);
line([-x2,x2], [-y2,y2], 'linestyle', sty);
line([-x2,x2], [y2,-y2], 'linestyle', sty);
line([-x1,x1], [y1,-y1], 'linestyle', sty);
text(1.02*x1,1.02*y1, '60^o', 'fontsize', Nf,
'horiz', 'left', 'vert', 'bottom');
text(0.95*x1,-0.97*y1, '-60^o', 'fontsize', Nf,
'horiz', 'left', 'vert', 'top');
text(1.04*x2,0.97*y2, '30^o', 'fontsize', Nf, 'horiz', 'left',
'vert', 'bottom');
text(0.98*x2,-0.93*y2, '-30^o', 'fontsize', Nf,
'horiz', 'left', 'vert', 'top');
text(-0.91*x1,1.02*y1, '120^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-0.97*x1,-1.01*y1, '-120^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
text(-1.02*x2,0.97*y2, '150^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-1.01*x2,-1.01*y2, '-150^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
end
s1 = sprintf('-%d', 0.25*Rm);
s2 = sprintf('-%d', 0.50*Rm);
s3 = sprintf('-%d', 0.75*Rm);
text(0.765, 0.125, s1, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.515, 0.125, s2, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.265, 0.125, s3, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.55, -0.005, 'dB', 'fontsize', Nf, 'horiz', 'left',
'vert', 'top');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

56. 56
% dbp2.m - polar gain plot in dB - 2*pi angle range
%
% Usage: h = dbp2(th, g, rays, Rm, width)
% h = dbp2(th, g) (equivalent to rays=30,
Rm=40, width=1)
% h = dbp2(th, g, rays) (equivalent to Rm=40,
width=1)
% h = dbp2(th, g, rays, Rm) (equivalent to width=1)
%
% th = polar angles over [0,pi]
% g = gain at th (g is in absolute units)
% rays = ray grid at 30 degree (default) or at 45 degree angles
% Rm = minimum dB level (Rm = 40 dB by default)
% width = linewidth of gain curve (width=1 by default)
%
% h = handle to use for adding more gains and legends (see
DBADD)
%
% examples: dbp2(th, g); default (30-degree lines
and 40-dB scale)
% dbp2(th, g, 45); use 45-degree grid lines
% dbp2(th, g, 30, 60); 30-degree rays and 60-dB
scale
% dbp2(th, g, 30, 60, 1.5); use thicker line for
gain
%
% notes: makes polar plot of gdb=10*log10(g) versus th,
%
%
% max-g is assumed to be unity (e.g., as in the output of
ARRAY),
% grid circles at Rm/4, 2Rm/4, 3Rm/4 are added and
labeled,
% for EPS output, use width=1.50 for thicker gain line
(thinnest width=0.75)
%
function h = dbp(th, g, rays, Rm, width)
if nargin==0, help dbp; return; end
if nargin<3, rays = 30; end
if nargin<4, Rm = 40; end
if nargin<5, width = 1; end
sty = ':'; % grid line
style
gdb = g .* (g > eps) + eps * (g <= eps); % make g=0
into g=eps, avoids -Inf's
gdb = 10 * log10(gdb);

57. 57
gdb = gdb .* (gdb > -Rm) + (-Rm) * (gdb <= -Rm); % lowest is
-Rm dB
gdb = (gdb + Rm)/Rm; % scale to
unity max.
x = gdb .* sin(th); % x-axis
plotted vertically
y = gdb .* cos(th);
N0 = 400;
phi0 = (0:N0) * 2*pi / N0;
x0 = sin(phi0); % gain
circles
y0 = cos(phi0);
h = plot(x, y, 'LineWidth', width);
hold on;
plot(x0, y0, 0.75*x0, 0.75*y0, sty, 0.50*x0, 0.50*y0, sty,
0.25*x0, 0.25*y0, sty);
axis square;
R = 1.1;
axis([-R, R, -R, R]);
axis off;
Nf = 15; % fontsize of labels
line([0,0],[-1,1]);
line([-1,1],[0,0]);
text(0, 1.02, ' 0^o', 'fontsize', Nf, 'horiz', 'center',
'vert', 'bottom');
text(0, -0.99, ' 180^o', 'fontsize', Nf, 'horiz', 'center',
'vert', 'top');
text(1, 0.01, ' 90^o', 'fontsize', Nf, 'horiz', 'left', 'vert',
'middle');
text(-1.02, 0.01, '90^o', 'fontsize', Nf, 'horiz', 'right',
'vert', 'middle');
text(1.07*cos(5*pi/12), 1.07*sin(5*pi/12), 'theta',
'fontsize', Nf+2, 'horiz', 'left');
text(-1.07*cos(5*pi/12), 1.07*sin(5*pi/12), 'theta',
'fontsize', Nf+2, 'horiz', 'right');
if rays == 45,
x1 = 1/sqrt(2); y1 = 1/sqrt(2);
line([-x1,x1], [-y1,y1], 'linestyle', sty);
line([-x1,x1], [y1,-y1], 'linestyle', sty);

58. 58
text(1.04*x1, y1, '45^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'bottom');
text(0.98*x1, -0.98*y1, '135^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'top');
text(-0.97*x1, 1.02*y1, '45^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-1.01*x1, -1.01*y1, '135^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
else
x1 = cos(pi/3); y1 = sin(pi/3);
x2 = cos(pi/6); y2 = sin(pi/6);
line([-x1,x1], [-y1,y1], 'linestyle', sty);
line([-x2,x2], [-y2,y2], 'linestyle', sty);
line([-x2,x2], [y2,-y2], 'linestyle', sty);
line([-x1,x1], [y1,-y1], 'linestyle', sty);
text(1.02*x1,1.02*y1, '30^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'bottom');
text(0.96*x1,-0.98*y1, '150^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'top');
text(1.04*x2,0.97*y2, '60^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'bottom');
text(x2,-0.95*y2, '120^o', 'fontsize', Nf, 'horiz',
'left', 'vert', 'top');
text(-0.91*x1,1.02*y1, '30^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-0.97*x1,-1.01*y1, '150^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
text(-1.02*x2,0.97*y2, '60^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'bottom');
text(-1.01*x2,-1.01*y2, '120^o', 'fontsize', Nf, 'horiz',
'right', 'vert', 'top');
end
s1 = sprintf('-%d', 0.25*Rm);
s2 = sprintf('-%d', 0.50*Rm);
s3 = sprintf('-%d', 0.75*Rm);
text(0.765, 0.125, s1, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.515, 0.125, s2, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.265, 0.125, s3, 'fontsize', Nf, 'horiz', 'left', 'vert',
'top');
text(0.55, -0.005, 'dB', 'fontsize', Nf, 'horiz', 'left',
'vert', 'top');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

59. 59
OUTPUT :
90o
-90o
0o
180o

60o
-60o
30o
-30o
120o
-120o
150o
-150o
-10-20-30
dB
0o
180o
90o
90o
 30o
150o
60o
120o
30o
150o
60o
120o
-10-20-30
dB
CONCLUSIONS :

60. 60
Practical - 16
AIM : To write a program to plot the radiation pattern for Binomial
antenna array.
THEORY :

61. 61
MATLAB PROGRAM :
% tic;
clear;
clc;
%%Intialisation
% AF = zeros(1,360);
% AE = zeros(1,360);
%%ACCEPTING INPUTS..
N= 7;%input('nEnter the number of Elements::->');
d= 0.5;%input('nEnter the distance between the elements::-
>');
k= 360;
beta= 0;
theta=1:360;
%%CALCULATING ARRAY FACTOR AND ARRAY ELEMENT...
psi= (k.*d.*cosd(theta)) + beta;
AF= (1+exp(1j.*(deg2rad(psi)))).^(N-1);
AE= (cosd(90.*cosd(theta)))./sind(theta);
AF=abs(AF);
%%PLOTTING...
theta= linspace(0,2*pi,360);
subplot(221);
polar(theta,AE)
subplot(222);
polar(theta,AF)
subplot(2,2,[3,4]);
polar(theta,AE.*AF)
legend('Binomial array','Location','SouthEastOutside')
toc;

62. 62
OUTPUT :
Elapsed time is 0.572803 seconds.
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
50
100
30
210
60
240
90
270
120
300
150
330
180 0
50
100
30
210
60
240
90
270
120
300
150
330
180 0
Binomial array
CONCLUSIONS :

63. 63
Practical - 17
AIM : To write a program to plot radiation pattern for Broadside antenna
array.
THEORY :

64. 64
MATLAB PROGRAM :
%%MATLAB PROGRAM FOR BROADSIDE ARRAY....
clear;
clc;
tic;
%%Initialising
AF = zeros(1,360);
AE = zeros(1,360);
theta=1:360;
%%ACCEPTING INPUTS..
N= input('nEnter the number of Elements::->');
d= input('nEnter the distance between the elements::->');
k= 360;
c= (k.*d)./2;
%%CALCULATING ARRAY FACTOR AND ARRAY ELEMENT...
num= ((1./N).*sind(N.*c.*cosd(theta)));
den= sind(c.*cosd(theta));
AF = num./den;
AE = (cosd(90.*cosd(theta)))./sind(theta);
AF=abs(AF);
%%PLOTTING...
theta= linspace(0,2*pi,360);
subplot(221);
polar(theta,AE)
subplot(222);
polar(theta,AF)
subplot(2,2,[3,4]);
polar(theta,AE.*AF)
legend('Broadside array','Location','SouthEastOutside')
toc;

65. 65
OUTPUT :
Enter the number of Elements::->5
Enter the distance between the elements::->0.5
Elapsed time is 11.856490 seconds.
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
Broadside array
CONCLUSIONS :

66. 66
Practical - 18
AIM : To write a program to plot radiation pattern for Endfire antenna
array.
THEORY :

67. 67
MATLAB PROGRAM :
% clear;
clc;
tic;
%%Initialisation
%AF = zeros(1,360);
%AE = zeros(1,360);
theta=1:360;
%%ACCEPTING INPUTS..
N= input('nEnter the number of Elements::->');
d= input('nEnter the distance between the elements::->');
k= 360;
c= (k.*d)./2;
%%CALCULATING ARRAY FACTOR AND ARRAY ELEMENT...
num= ((1./N).*sind(N.*c.*(cosd(theta)+1)));
den= sind(c.*(cosd(theta)+1));
AF= num./den;
AE= (cosd(90.*cosd(theta-90)))./sind(theta-90);
AF=abs(AF);
%%PLOTTING...
theta= linspace(0,2*pi,360);
subplot(221);
polar(theta,AE)
subplot(222);
polar(theta,AF)
subplot(2,2,[3,4]);
polar(theta,AE.*AF)
legend('Endfire array','Location','SouthEastOutside')
toc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

68. 68
OUTPUT :
Enter the number of Elements::->5
Enter the distance between the elements::->0.5
Elapsed time is 6.356738 seconds.
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
Endfire array
CONCLUSIONS :

69. 69
Practical - 19
AIM : To write a program to plot 3D radiation pattern for Binomial
antenna array.
THEORY :

70. 70
MATLAB PROGRAM :
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% MATLAB code for Binomial Array in 3D
%% Pre-initialisation
clear;
clc;
close all;
%% Accepting inputs
N = input('nEnter the number of Elements::(eg., 5,6,7,etc)-
>');
d = input('nEnter the distance between the
elements::(eg.,0.4,0.5,etc)->');
tic;
k = 2*pi;
beta = 0;
[theta phi]=meshgrid(linspace(0,2*pi,180));
%% Calculating Array element(AE) and Array Factor(AF)
psi = (k.*d.*cos(theta)) + beta;
AF = (1+exp(1j.*(psi))).^(N-1);
AF = AF - min(min(AF));
AE = sqrt(1- ((sin(theta).^2).*(cos(phi).^2)));
%% Calculating Array Pattern(AP)
% Array Pattern is calculated as follows,
%
% Array Pattern = ArrayFactor * ArrayElement
AP = AF .* AE;
toc;
%% Plotting results
[x1,y1,z1] = sph2cart(phi,theta,abs(AE));
surf(x1,y1,z1,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);

71. 71
legend('Array Element','Location','SouthEastOutside')
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
axis image
figure
[x2,y2,z2] = sph2cart(phi,theta,abs(AF));
surf(x2,y2,z2,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
legend('Array Factor','Location','SouthEastOutside')
axis image
figure
[x3,y3,z3] = sph2cart(phi,theta,abs(AP));
surf(x3,y3,z3,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
legend('Array Pattern','Location','SouthEastOutside')
axis image
OUTPUT :
Enter the number of Elements::(eg., 5,6,7,etc)->6
Enter the distance between the elements::(eg.,0.4,0.5,etc)-
>0.5
Elapsed time is 0.056854 seconds.

72. 72
CONCLUSIONS :

73. 73
Practical - 20
AIM : To write a program to plot 3D radiation pattern for Broadside
antenna array.
THEORY :

74. 74
MATLAB PROGRAM :
%%% MATLAB code for Broadside Array in 3D
%% Pre-initialisation
clear;
clc;
close all;
%% Accepting inputs
N = input('nEnter the number of Elements::(eg., 5,6,7,etc)-
>');
d = input('nEnter the distance between the
elements::(eg.,0.4,0.5,etc)->');
tic;
[theta phi] = meshgrid(linspace(0,2*pi,180));
k = 2*pi;
c = (k.*d)./2;
%% Calculating Array element(AE) and Array Factor(AF)
num = ((1./N).*sin(N.*c.*cos(theta)));
den = sin(c.*cos(theta));
AF = num./den;
AF = AF - min(min(AF));
AE = sqrt(1- ((sin(theta).^2).*(cos(phi).^2)));
%% Calculating Array Pattern(AP)
% Array Pattern is calculated as follows,
%
% Array Pattern = ArrayFactor * ArrayElement
AP = AF .* AE;
toc;
%% Plotting results
[x1,y1,z1] = sph2cart(phi,theta,AE);
surf(x1,y1,z1,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Element','Location','SouthEastOutside')
axis image

75. 75
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
figure
[x2,y2,z2] = sph2cart(phi,theta,AF);
surf(x2,y2,z2,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Factor','Location','SouthEastOutside')
axis image
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
figure
[x3,y3,z3] = sph2cart(phi,theta,AP);
surf(x3,y3,z3,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Pattern of Broadside
array','Location','SouthEastOutside')
axis image
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%

76. 76
OUTPUT :
Enter the number of Elements::(eg., 5,6,7,etc)->6
Enter the distance between the elements::(eg.,0.4,0.5,etc)-
>0.5
Elapsed time is 0.173608 seconds.
CONCLUSIONS :

77. 77
Practical - 21
AIM : To write a program to plot 3D radiation pattern for Endfire
antenna array
THEORY :

78. 78
MATLAB PROGRAM :
%%% MATLAB code for Endfire Array in 3D
%% Pre-initialisation
clear;
clc;
close all;
%% Accepting inputs
N = input('nEnter the number of Elements::(eg., 5,6,7,etc)-
>');
d = input('nEnter the distance between the
elements::(eg.,0.4,0.5,etc)->');
tic;
[theta phi] = meshgrid(linspace(0,2*pi,360));
k = 2*pi;
c = (k.*d)./2;
%% Calculating Array element(AE) and Array Factor(AF)
num = ((1./N).*sin(N.*c.*(cos(theta)+1)));
den = sin(c.*(cos(theta)+1));
AF = num./den;
AF = AF - min(min(AF));
AE = sqrt(1- ((sin(theta).^2).*(cos(phi).^2)));
%% Calculating Array Pattern(AP)
% Array Pattern is calculated as follows,
%
% Array Pattern = ArrayFactor * ArrayElement
AP = AF .* AE;
toc;
%% Plotting results
[x1,y1,z1] = sph2cart(phi,theta,AE);
surf(x1,y1,z1,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Element','Location','SouthEastOutside')

79. 79
axis image
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
figure
[x2,y2,z2] = sph2cart(phi,theta,AF);
surf(x2,y2,z2,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Factor','Location','SouthEastOutside')
axis image
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
figure
[x3,y3,z3] = sph2cart(phi,theta,AP);
surf(x3,y3,z3,'FaceLighting','phong',...
'LineStyle','none',...
'FaceColor',[1 0 0]);
legend('Array Pattern of Endfire
Array','Location','SouthEastOutside')
axis image
light('Style','local',...
'Position',[-10.162701816704 -0.924193626363743
14.9951905283833]);
OUTPUT :
Enter the number of Elements::(eg., 5,6,7,etc)->6
Enter the distance between the elements::(eg.,0.4,0.5,etc)-
>0.5
Elapsed time is 0.136698 seconds.

80. 80
CONCLUSIONS :

81. 81
Practical - 22
AIM : To write a program to plot 3-D Radiation Pattern of Dipole
Antenna.
THEORY :

82. 82
MATLAB PROGRAM :
% Name: RadPattern3D
% Description: 3-D Radiation Pattern of Dipole Antenna
% Reference Constantine A.Balanis, Antenna Theory
% Analysis And Design , 3rd Edition, page 173, eq. 4-64
%*************************************************************
*************
%Usage:
%This program plots 3-D radiation Pattern of a Dipole Antenna
%All the parameters are entered in the M-File
clear all
%Defining variables in spherical coordinates
theta=[0:0.12:2*pi];%theta vector
phi=[0:0.12:2*pi];%phi vector
l_lamda1=1/100;% length of antenna in terms of wavelengths
I0=1;% max current in antenna structure
n=120*pi;%eta
% evaluating radiation intensity(U)
U1=( n*( I0^2 )*( ( cos(l_lamda1*cos(theta-(pi/2))/2) -
cos(l_lamda1/2) )./ sin(theta-(pi/2)) ).^2 )/(8*(pi)^2);
%converting to dB scale
U1_1=10*log10(U1);
%normalizing in order to make U vector positive
min1=min(U1_1);
U=U1_1-min1;
% expanding theta to span entire space
U(1,1)=0;
for n=1:length(phi)
theta(n,:)=theta(1,:);
end
% expanding phi to span entire space
phi=phi';
for m=1:length(phi)
phi(:,m)=phi(:,1);
end
% expanding U to span entire space
for k=1:length(U)
U(k,:)=U(1,:);
end

83. 83
% converting to spherical coordinates
[x,y,z]=sph2cart(phi,theta,U);
%plotting routine
surf(x,y,z)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
OUTPUT :
-40
-20
0
20
40
-40
-20
0
20
40
-30
-20
-10
0
10
20
30
CONCLUSIONS :