lab manual of antenna and wave propagation

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

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

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.


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) = sin2θcos2θ.

11 To write a program to Design

Microstrip Antenna.

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.


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

Practical -1

AIM : To write a program to plot the radiation pattern of Dipole Antenna.

THEORY :

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);


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

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

CONCLUSIONS :

8

Practical - 2

AIM : To write a program to plot radiation pattern of Monopole antenna.

THEORY :

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


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);


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);


which monopole appear as line

end

OUTPUT :


enter your monopole length l= 0.5

10

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

CONCLUSIONS :

11

Practical -3

AIM : To write a program to plot radiation pattern of Loop antenna.

THEORY :

12

MATLAB PROGRAM :

%This program print pattern for Loop Antenna by giving the

%radius of your Loop and the wavelength you work with

clc;


a=input('enter your loop radius a= ');

B=(2*pi/lamda);


E=besselj(1,B*a.*sin(theta));

polar(theta,E)

OUTPUT :


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

Practical - 4

AIM : To write a Program to plot radiation pattern of Linear array

antenna.

THEORY :

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;


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);


w=alfa+B*d.*cos(theta);

AF=sinc(N*(w./2))./sinc(w./2);

polar(theta,AF)

OUTPUT :


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

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

CONCLUSIONS :

16

Practical - 5

AIM : To write a Program to plot radiation pattern of Circular array antenna.

THEORY :

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;


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);


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 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

0.2

0.4

0.6

0.8

1

30

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60

240

90

270

120

300

150

330

180 0

CONCLUSIONS :

19

Practical - 6

AIM : To write program to plot radiation pattern of rectangular aperture

antenna.

THEORY :

20

MATLAB PROGRAM : % This program prints electric field pattern for rectangular

%Aperture Antenna by giving the a,b


kind=input('Enter your antenna type Rectangular (1) or

circular (2)= ');



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)


subplot(3,3,4)


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)


subplot(3,3,6)


end

elseif kind==2

a=input('Enter radius of Circular Aperture= ');

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 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

Practical - 7

AIM : To write a program to plot radiation pattern of travelling wave antenna.

THEORY :

23

MATLAB PROGRAM : %This program print pattern for TWA(Travelling Wave Antenna)

%by giving the length of your Line


clc;


l=input('enter your Line length l= ');

B=(2*pi/lamda);


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

Practical - 8

AIM : To write a program to plot radiation pattern of linear array of

isotropic antennas.

THEORY :

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

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180 0

0.2

0.4

0.6

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180 0

26

N=8 N=16

0.2

0.4

0.6

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0.2

0.4

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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

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0.2

0.4

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180 0

27

d=3/4λ d=λ

0.2

0.4

0.6

0.8

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330

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0.2

0.4

0.6

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180 0

d=5/2λ d=3/2λ

0.2

0.4

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0.8

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0.2

0.4

0.6

0.8

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180 0

Observation: As the distance between antennas increases, the radiation pattern is not only broadsided but also radiates in other directions.

28

Case 3: When N=2, d=λ/2

α=0° α=45°

0.2

0.4

0.6

0.8

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0.2

0.4

0.6

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180 0

α=90° α=135°

0.2

0.4

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0.2

0.4

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0.8

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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

Practical - 9

AIM : To perform the numerical evaluation of directivity for a half wave dipole .

THEORY :

30

MATLAB PROGRAM : % sum=0.0;

N=input(’Enter the number of segments in the theta

direction\n’);

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


10

D =

1.6410


15

D =

1.6409


20

D =

1.6409

CONCLUSIONS:

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) = sin2θcos2θ.

THEORY :

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

Practical - 11

AIM : To write a program to Design Microstrip Antenna.

THEORY :

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

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

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

40

0.2

0.4

0.6

0.8

1

CONCLUSIONS :

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

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

40

0.2

0.4

0.6

0.8

1

CONCLUSIONS :

40

Practical - 14

AIM : To write a program to plot the radiation pattern of a horn antenna.

THEORY :

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

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

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

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

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)

Fie

ld P

att

ern

(dB

)

Horn Analysis

E-Plane

H-Plane

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

Practical - 15

AIM : To write a program to plot the radiation pattern of a Optimized

six-element Yagi-Uda antenna.

THEORY :

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

% 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

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

% 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 = Z\V, 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

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

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

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, ' 90ô', 'fontsize', Nf, 'horiz', 'center',

'vert', 'bottom');

text(0, -0.99, '-90ô', 'fontsize', Nf, 'horiz', 'center',

'vert', 'top');

text(1, 0.01, ' 0ô', 'fontsize', Nf, 'horiz', 'left', 'vert',

'middle');

text(-1.02, 0.01, '180ô', '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

text(1.04*x1, y1, '45ô', 'fontsize', Nf, 'horiz',

'left', 'vert', 'bottom');

text(0.97*x1, -0.97*y1, '-45ô', 'fontsize', Nf, 'horiz',

'left', 'vert', 'top');

text(-0.97*x1, 1.02*y1, '135ô', 'fontsize', Nf, 'horiz',

'right', 'vert', 'bottom');

text(-1.01*x1, -1.01*y1, '-135ô', 'fontsize', Nf, 'horiz',

'right', 'vert', 'top');

else

x1 = cos(pi/3); y1 = sin(pi/3);

x2 = cos(pi/6); y2 = sin(pi/6);





text(1.02*x1,1.02*y1, '60ô', 'fontsize', Nf,

'horiz', 'left', 'vert', 'bottom');

text(0.95*x1,-0.97*y1, '-60ô', 'fontsize', Nf,

'horiz', 'left', 'vert', 'top');

text(1.04*x2,0.97*y2, '30ô', 'fontsize', Nf, 'horiz', 'left',

'vert', 'bottom');

text(0.98*x2,-0.93*y2, '-30ô', 'fontsize', Nf,

'horiz', 'left', 'vert', 'top');

text(-0.91*x1,1.02*y1, '120ô', 'fontsize', Nf, 'horiz',


text(-0.97*x1,-1.01*y1, '-120ô', 'fontsize', Nf, 'horiz',




text(-1.01*x2,-1.01*y2, '-150ô', 'fontsize', Nf, 'horiz',


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');


'top');


'top');

text(0.55, -0.005, 'dB', 'fontsize', Nf, 'horiz', 'left',

'vert', 'top');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

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, ' 0ô', 'fontsize', Nf, 'horiz', 'center',

'vert', 'bottom');

text(0, -0.99, ' 180ô', 'fontsize', Nf, 'horiz', 'center',

'vert', 'top');

text(1, 0.01, ' 90ô', 'fontsize', Nf, 'horiz', 'left', 'vert',

'middle');

text(-1.02, 0.01, '90ô', '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);



58

text(1.04*x1, y1, '45ô', 'fontsize', Nf, 'horiz',


text(0.98*x1, -0.98*y1, '135ô', 'fontsize', Nf, 'horiz',


text(-0.97*x1, 1.02*y1, '45ô', 'fontsize', Nf, 'horiz',


text(-1.01*x1, -1.01*y1, '135ô', 'fontsize', Nf, 'horiz',


else

x1 = cos(pi/3); y1 = sin(pi/3);

x2 = cos(pi/6); y2 = sin(pi/6);





text(1.02*x1,1.02*y1, '30ô', 'fontsize', Nf, 'horiz',


text(0.96*x1,-0.98*y1, '150ô', 'fontsize', Nf, 'horiz',


text(1.04*x2,0.97*y2, '60ô', 'fontsize', Nf, 'horiz',


text(x2,-0.95*y2, '120ô', 'fontsize', Nf, 'horiz',




text(-0.97*x1,-1.01*y1, '150ô', 'fontsize', Nf, 'horiz',




text(-1.01*x2,-1.01*y2, '120ô', 'fontsize', Nf, 'horiz',


end

s1 = sprintf('-%d', 0.25*Rm);

s2 = sprintf('-%d', 0.50*Rm);

s3 = sprintf('-%d', 0.75*Rm);


'top');


'top');


'top');

text(0.55, -0.005, 'dB', 'fontsize', Nf, 'horiz', 'left',

'vert', 'top');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

59

OUTPUT :

90o

-90o

0o

180o

60o

-60o

30o

-30o

120o

-120o

150o

-150o

-10-20-30dB

0o

180o

90o

90o

30

o

150o

60o

120o

30o

150o

60o

120o

-10-20-30dB

CONCLUSIONS :

60

Practical - 16

AIM : To write a program to plot the radiation pattern for Binomial antenna array.

THEORY :

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

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

Practical - 17

AIM : To write a program to plot radiation pattern for Broadside antenna array.

THEORY :

64

MATLAB PROGRAM : %%MATLAB PROGRAM FOR BROADSIDE ARRAY....

clear;

clc;

tic;

%%Initialising

AF = zeros(1,360);

AE = zeros(1,360);

theta=1:360;


N= input('\nEnter the number of Elements::->');

d= input('\nEnter the distance between the elements::->');

k= 360;

c= (k.*d)./2;


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...


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

OUTPUT :

Enter the number of Elements::->5

Enter the distance between the elements::->0.5


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

Practical - 18

AIM : To write a program to plot radiation pattern for Endfire antenna array.

THEORY :

67

MATLAB PROGRAM : % clear;

clc;

tic;

%%Initialisation

%AF = zeros(1,360);

%AE = zeros(1,360);

theta=1:360;


N= input('\nEnter the number of Elements::->');

d= input('\nEnter the distance between the elements::->');

k= 360;

c= (k.*d)./2;


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...


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

OUTPUT :

Enter the number of Elements::->5

Enter the distance between the elements::->0.5


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

Practical - 19

AIM : To write a program to plot 3D radiation pattern for Binomial

antenna array.

THEORY :

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

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));





'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

legend('Array Factor','Location','SouthEastOutside')

axis image

figure

[x3,y3,z3] = sph2cart(phi,theta,abs(AP));





'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


72

CONCLUSIONS :

73

Practical - 20

AIM : To write a program to plot 3D radiation pattern for Broadside

antenna array.

THEORY :

74

MATLAB PROGRAM : %%% MATLAB code for Broadside Array in 3D


clear;

clc;

close all;

%% Accepting inputs


>');



tic;

[theta phi] = meshgrid(linspace(0,2*pi,180));

k = 2*pi;

c = (k.*d)./2;


num = ((1./N).*sin(N.*c.*cos(theta)));

den = sin(c.*cos(theta));

AF = num./den;





%


AP = AF .* AE;

toc;

%% Plotting results

[x1,y1,z1] = sph2cart(phi,theta,AE);





axis image

75


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

figure

[x2,y2,z2] = sph2cart(phi,theta,AF);





axis image


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

figure

[x3,y3,z3] = sph2cart(phi,theta,AP);




legend('Array Pattern of Broadside

array','Location','SouthEastOutside')

axis image


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%

76

OUTPUT :



>0.5


CONCLUSIONS :

77

Practical - 21

AIM : To write a program to plot 3D radiation pattern for Endfire

antenna array

THEORY :

78

MATLAB PROGRAM : %%% MATLAB code for Endfire Array in 3D


clear;

clc;

close all;

%% Accepting inputs


>');



tic;

[theta phi] = meshgrid(linspace(0,2*pi,360));

k = 2*pi;

c = (k.*d)./2;


num = ((1./N).*sin(N.*c.*(cos(theta)+1)));

den = sin(c.*(cos(theta)+1));

AF = num./den;





%


AP = AF .* AE;

toc;

%% Plotting results

[x1,y1,z1] = sph2cart(phi,theta,AE);





79

axis image


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

figure

[x2,y2,z2] = sph2cart(phi,theta,AF);





axis image


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

figure

[x3,y3,z3] = sph2cart(phi,theta,AP);




legend('Array Pattern of Endfire

Array','Location','SouthEastOutside')

axis image


'Position',[-10.162701816704 -0.924193626363743

14.9951905283833]);

OUTPUT :



>0.5


80

CONCLUSIONS :

81

Practical - 22

AIM : To write a program to plot 3-D Radiation Pattern of Dipole

Antenna.

THEORY :

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

% 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 :

lab manual of antenna and wave propagation

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