Using MATLAB DEPARTMENT OF EC GOVERNMENT ENGINEERING COLLEGE DAHOD -389151
Prepared By : Prof. Alpesh H. Dafda Asst. Prof. (E.C.)
1
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
__________________
Government Engineering College, Dahod,
at
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. sa tisfaction.
Date: Place:
Subject Teacher
Head of Department
2
INDEX NO
SUBJECT
DATE PAGE
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 Ω A and the maximum directivity [Do] of an antenna defined by F (θ,Φ) (θ,Φ) = sin2θcos2θ.
11
To write a program Microstrip Antenna.
to
Design
3
SIGN
REMARKS
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 v y = (a/λ)sinθsinφ, for 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 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.
4
Practical -1
AIM : To write a program to plot the radiation pattern of Dipole Antenna. THEORY :
5
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
6
90
1
120
60 0.8 0.6
150
30 0.4 0.2
180
0
210
330
240
300 270
CONCLUSIONS
:
7
Practical - 2
AIM : To write a program to plot radiation pattern of Monopole antenna. THEORY :
8
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
9
90
1
120
60 0.8 0.6
150
30 0.4 0.2
180
0
210
330
240
300 270
CONCLUSIONS
:
10
Practical -3 AIM : To write a program to plot radiation pattern of Loop antenna. THEORY :
11
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
90
0.6
120
60 0.4
150
30 0.2
180
0
210
330
240
300 270
CONCLUSIONS
:
12
Practical - 4 AIM
:
To write a Program to plot radiation pattern of Linear array antenna.
THEORY :
13
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 enter enter enter lamda
:
the value of wave length= 1 the no. of elements(3,4,5...)= 6 your progressive phase(alpha=0,45...)= 0 the seperation distance between elements(in terms of for ex: 0.3 for 0.3lamda)= 0.3
14
90
1
120
60 0.8 0.6
150
30 0.4 0.2
180
0
210
330
240
300 270
CONCLUSIONS
:
15
Practical - 5 AIM
:
THEORY
To write a Program to plot radiation pattern of Circular array antenna. :
16
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
17
90
1
120
60 0.8 0.6
150
30 0.4 0.2
180
0
210
330
240
300 270
CONCLUSIONS :
18
Practical - 6 AIM : To write program to plot radiation pattern of rectangular aperture antenna. THEORY
:
19
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= ');
20
f1=B*a; f=f1.*(sin(theta)); E=(besselj(1,f))./f; subplot(3,3,7) polar(theta,E)
%E-plane or H-plane
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 E-plane 1 120 90 60 0.5 150 30 180
0
210 330 240270300
CONCLUSIONS
H-plane 1 120 90 60 0.5 150 30 180
0
210 330 240270300
:
21
Practical - 7 AIM
: To write a program to plot radiation pattern of travelling wave antenna.
THEORY
:
22
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
90
2
120
60 1.5 1
150
30
0.5
180
0
210
330
240
300 270
CONCLUSIONS
:
23
Practical - 8 AIM
:
THEORY
To write a program to plot radiation pattern of linear array of isotropic antennas. :
24
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
90
N=4
90
1
120
60
60
0.8
0.8
0.6
0.6
150
30
150
30
0.4
0.4
0.2
0.2
180
0
210
180
330
240
1
120
0
210
300
330
240
270
300 270
25
N=8
N=16 90
90
1
120
60
1
120
60
0.8
0.8
0.6
0.6
150
30
150
30
0.4
0.4
0.2
0.2
180
180
0
210
330
240
0
210
330
300
240
300
270
270
Observation: As the number of isotropic antennas increase, the directivity increases.
Case 2: When N=2, α=0° d=λ/4 90
d=λ/2 90
1
120
60 0.8
0.8
0.6
0.6 150
150
30 0.4
30
0.4 0.2
0.2 180
180
0
210
0
210
330
240
1
120
60
330
240
300
300 270
270
26
d=3/4λ
d=λ
90
90
1
120
60
1
120
60 0.8
0.8 0.6
0.6
150
30
150
30
0.4
0.4
0.2
0.2
180
180
0
210
330
240
0
210
330
240
300
300
270
270
d=5/2λ 90
d=3/2λ 90 1
120
60
60 0.8
0.8
0.6
0.6 150
150
30
0.4
30 0.4 0.2
0.2 180
180
0
210
0
210
330
240
1
120
330
240
300
300 270
270
Observation: As the distance between antennas increases, the radiation pattern is not only broadsided but also radiates in other directions.
27
Case 3: When N=2, d=λ/2 α=0°
α=45° 90
90
1
120
60 0.8
60 0.8
0.6 150
0.6
30
0.4
150
30 0.4
0.2
0.2
180
0
210
180
330
240
0
210
300
330
240
270
300 270
α=90° 90
α=135° 90
1
120
60
1
120
60
0.8
0.8
0.6
0.6
150
30
150
30
0.4
0.4
0.2
0.2
180
180
0
210
330
240
1
120
0
210
300
330
240
270
300 270
Observation: As the phase difference differenc e between the excitation excitati on increases, the main lobe directivity is decreasing whereas the side lobe is increasing. i ncreasing. CONCLUSIONS
:
28
Practical - 9 AIM :
THEORY
To perform the numerical evaluation of directivity for a half wave dipole . :
29
MATLAB PROGRAM : % sum=0.0; N=input(’Enter 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(t sum=sum+(cos((pi/2)*cos(thetai)))^2/sin hetai)))^2/sin(thetai); (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:
30
Practical - 10 AIM
:
THEORY
To write a program to determine the directivity [ D(θ,Φ)], the beam solid angle Ω A and the maximum directivity [ Do] of an antenna defined by F (θ,Φ) (θ,Φ) = sin = sin2θcos2θ. :
31
32
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
:
90
2
120
60 1.5 1
150
30
0.5
180
0
210
330
240
300 270
CONCLUSIONS
:
33
Practical - 11
AIM : THEORY
To write a program to Design Microstrip Antenna. :
34
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_eff0.258)*((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
:
35
Practical - 12
AIM : To write a program to plot 3-D pattern of Rectangular Apertures as a function of the independent variables v x, vy, for aperture dimensions a = 8λ and b = 4λ. THEORY
:
36
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
:
1 0.8 0.6 0.4 0.2 0 4 2
10 5
0
0
-2
-5 -4
CONCLUSIONS
-10
:
37
Practical - 13
AIM : To write a program to plot 3-D pattern of Circular Aperture as a function of the independent variables v x = (a/λ)sinθcosφ and v y = (a/λ)sinθsinφ, for an aperture radius of a = 3λ. THEORY
:
38
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
:
1 0.8 0.6 0.4 0.2 0 4 2
4 2
0
0
-2
-2 -4
CONCLUSIONS
-4
:
39
Practical - 14
AIM
:
THEORY
To write a program to plot the radiation pattern of a horn antenna. :
40
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);
41
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);
42
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;
43
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;
44
return end end
OUTPUT
:
E-Plane and H-Plane Horn Specifications directivity = 18.827820259174445 Horn Analysis 0 E-Plane H-Plane -10
) B d ( n r e t t a P d l e i F
-20
-30
-40
-50
-60
0
50
100
150 200 Theta (degrees)
45
250
300
350
Field patterns 90
100
120
60 80
E-plane H-plane
60 150
30
40 20
180
0
210
330
240
300 270
CONCLUSIONS
:
46
Practical - 15 AIM : To write a program to plot the radiation pattern of a Optimized six-element Yagi-Uda antenna. THEORY
:
47
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. %
48
% 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); more antennas, K>=3
% must have three or
Z = impedmat(L,a,d); matrix for the yagi array
% mutual impedance
V = [0; 1; zeros(K-2,1)]; V(2) = 1
% driving voltage
I = Z \ V;
% solve Z*I = V
Nint = 16; Legendre quadrature points
% number of Gauss-
[wth,th] = quadr(0,pi,Nint); and angle points [wph,ph] = quadr(0,2*pi,Nint);
% quadrature weights
A = zeros(Nint,Nint); of array factor Af = 0; Ab = 0;
% matrix of values
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); endfire Ab = Ab + I(p) * F(h(p),d(p),pi/2,pi); endfire end Rfb = abs(Af/Ab)^2; ratio
% %
forward backward
% forward-backward
A = A / Af; g = abs(A.*A);
% normalized gain
for m=1:Nint,
49
g(:,m) = g(:,m).*sin(th); dOmega = sin(th)*dth*dph end
% sin(th) comes from
DOm = wth' * g * wph; th,ph to get beam solid angle
% integrate over
D = 4*pi / DOm;
% directivity
% -------------------------------------------------------------------------------function A = F(h,d,th,ph) dipole at distance x=d
% array factor of
k = 2*pi; th = th(:); ph = ph(:)';
% theta is a column % phi is a row
G = zeros(length(th),1); dipole pattern values
% G(th) is column of
i = find(th~=0 & th~=pi); G(i) = (cos(k*h*cos(th(i))) sin(th(i))); A = exp(j*k*d*sin(th)*cos(ph)); factors
-
cos(k*h))
./
(sin(k*h)
*
% displacement phase
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) %
50
% 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(:); expects I,L to be columns L = L(:);
% U(th,phi)
K = length(L);
51
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)]; into [x,y] pairs end
% make d
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)); the azimuthal angle end
% here th is
ge = ge/max(ge); gh = gh/max(gh); % --------------------------------------------------------------------------function G = U(L,d,I,th,phi) intensity U(th,phi)
% radiation
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)) .* dimensional array factor
(exp(j*kx*x).*exp(j*ky*y));
if sin(th)==0, antenna elements F = zeros(length(L),1); dimensional column else F = (cos(k*L*cos(th)/2) - cos(k*L/2)) / sin(th); end if max(L)==0, array case F = ones(K,1);
%
K-
% gains of % F is K-
% isotropic
52
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 if if if
nargin==0, help dbz2; return; end nargin<3, rays = 30; end nargin<4, Rm = 40; end nargin<5, width = 1; end
sty = ':'; line style
% grid
53
gdb = g .* (g > eps) + eps * (g <= eps); into g=eps, avoids -Inf's gdb = 10 * log10(gdb); gdb = gdb .* (gdb > -Rm) + (-Rm) * (gdb <= -Rm); is Rm dB gdb = (gdb + Rm)/Rm; unity max.
% make g=0
% lowest % scale to
x = gdb .* cos(phi); y = gdb .* sin(phi); N0 = 400; phi0 = (0:N0) * 2*pi / N0; x0 = sin(phi0); circles y0 = cos(phi0);
% gain
h = plot(x, y, 'LineWidth', width); hold on; plot(x0, y0, 0.75*x0, 0.75*y0, sty, 0.25*x0, 0.25*y0, sty);
0.50*x0,
0.50*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', 'vert', 'bottom'); text(0, -0.99, '-90^o', 'vert', 'top');
'fontsize', Nf, 'fontsize',
Nf,
'horiz', 'center', 'horiz',
'center',
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), Nf+2, 'horiz', 'left');
'\phi',
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);
54
'fontsize',
text(1.04*x1, y1, '45^o', 'fontsize', 'left', 'vert', 'bottom'); text(0.97*x1, -0.97*y1, '-45^o', 'fontsize', 'left', 'vert', 'top'); text(-0.97*x1, 1.02*y1, '135^o', 'fontsize', 'right', 'vert', 'bottom'); text(-1.01*x1, -1.01*y1, '-135^o', 'fontsize', '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);
Nf, 'horiz', Nf,
'horiz',
Nf,
'horiz',
Nf,
'horiz',
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', 'right', 'vert', 'bottom'); text(-0.97*x1,-1.01*y1, '-120^o', 'right', 'vert', 'top'); text(-1.02*x2,0.97*y2, '150^o', 'right', 'vert', 'bottom'); text(-1.01*x2,-1.01*y2, '-150^o', 'right', 'vert', 'top'); end
'fontsize', 'fontsize', 'fontsize', 'fontsize',
Nf, Nf, Nf, Nf,
'horiz', 'horiz', 'horiz', 'horiz',
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, 'vert', 'top');
'dB',
'fontsize',
Nf,
'horiz',
'left',
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
55
% 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 if if if
nargin==0, help dbp; return; end nargin<3, rays = 30; end nargin<4, Rm = 40; end nargin<5, width = 1; end
sty = ':'; style
% grid line
gdb = g .* (g > eps) + eps * (g <= eps); into g=eps, avoids -Inf's gdb = 10 * log10(gdb);
56
% make g=0
gdb = gdb .* (gdb > -Rm) + (-Rm) * (gdb <= -Rm); -Rm dB gdb = (gdb + Rm)/Rm; unity max.
% lowest is % scale to
x = gdb .* sin(th); plotted vertically y = gdb .* cos(th);
% x-axis
N0 = 400; phi0 = (0:N0) * 2*pi / N0; x0 = sin(phi0); circles y0 = cos(phi0);
% gain
h = plot(x, y, 'LineWidth', width); hold on; plot(x0, y0, 0.75*x0, 0.75*y0, sty, 0.25*x0, 0.25*y0, sty);
0.50*x0,
0.50*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', 'vert', 'bottom'); text(0, -0.99, ' 180^o', 'vert', 'top');
'fontsize', 'fontsize',
Nf, Nf,
'horiz', 'horiz',
'center', 'center',
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), 'fontsize', Nf+2, 'horiz', 'left'); text(-1.07*cos(5*pi/12), 1.07*sin(5*pi/12), '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);
57
'\theta', '\theta',
text(1.04*x1, y1, '45^o', 'fontsize', 'left', 'vert', 'bottom'); text(0.98*x1, -0.98*y1, '135^o', 'fontsize', 'left', 'vert', 'top'); text(-0.97*x1, 1.02*y1, '45^o', 'fontsize', 'right', 'vert', 'bottom'); text(-1.01*x1, -1.01*y1, '135^o', 'fontsize', '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);
Nf, 'horiz', Nf,
'horiz',
Nf,
'horiz',
Nf,
'horiz',
text(1.02*x1,1.02*y1, '30^o', 'fontsize', Nf, 'left', 'vert', 'bottom'); text(0.96*x1,-0.98*y1, '150^o', 'fontsize', Nf, 'left', 'vert', 'top'); text(1.04*x2,0.97*y2, '60^o', 'fontsize', Nf, 'left', 'vert', 'bottom'); text(x2,-0.95*y2, '120^o', 'fontsize', Nf, 'left', 'vert', 'top');
'horiz',
text(-0.91*x1,1.02*y1, 'right', 'vert', 'bottom'); text(-0.97*x1,-1.01*y1, 'right', 'vert', 'top'); text(-1.02*x2,0.97*y2, 'right', 'vert', 'bottom'); text(-1.01*x2,-1.01*y2, 'right', 'vert', 'top'); end
'30^o', '150^o', '60^o', '120^o',
'fontsize', 'fontsize', 'fontsize', 'fontsize',
Nf, Nf, Nf, Nf,
'horiz', 'horiz', 'horiz',
'horiz', 'horiz', 'horiz', 'horiz',
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, 'vert', 'top');
'dB',
'fontsize',
Nf,
'horiz',
'left',
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
58
OUTPUT
: 120
150
o
90
o
60
o
o
30 30
o
0o
30o
60o
o
60o
180
-30 -20 -10 o 0 dB
o
-30 o
-150 o -120
o
CONCLUSIONS
-90
o
-30 -20 -10 90 o dB
90o
120o
120 o
-60 o
150o
:
59
180
o
150o
Practical - 16
AIM
:
THEORY
To write a program to plot the radiation pattern for Binomial antenna array. :
60
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= AF= AE=
(k.*d.*cosd(theta)) + beta; (1+exp(1j.*(deg2rad(psi)))).^(N-1); (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;
61
OUTPUT
:
Elapsed time is 0.572803 seconds.
120
90 1
60
0.5
150
120 30
180
180
330 240
270
120
330 240
270
90 100 60 50
180
30 0
210
330 240
270
300
Binomial array
:
62
30 0
210
300
150
CONCLUSIONS
50
150
0
210
90 100 60
300
Practical - 17
AIM : To write a program to plot radiation pattern for Broadside antenna array. THEORY
:
63
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= d= k= c=
input('\nEnter the number of Elements::->'); input('\nEnter the distance between the elements::->'); 360; (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;
64
OUTPUT
:
Enter the number of Elements::->5 Enter the distance between the elements::->0.5 Elapsed time is 11.856490 seconds.
90 1
120
60
120
0.5
150
30
180
180
330 240
270
120
270
60
180
30 0
210
330 240
CONCLUSIONS
330 240
0.5
150
270
300
Broadside array
:
65
30 0
210
300
90 1
60
0.5
150
0
210
90 1
300
Practical - 18 AIM : To write a program to plot radiation pattern for Endfire antenna array. THEORY
:
66
MATLAB PROGRAM : % clear;
clc; tic; %%Initialisation %AF = zeros(1,360); %AE = zeros(1,360); theta=1:360; %%ACCEPTING INPUTS.. N= d= k= c=
input('\nEnter the number of Elements::->'); input('\nEnter the distance between the elements::->'); 360; (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; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
67
OUTPUT
:
Enter the number of Elements::->5 Enter the distance between the elements::->0.5 Elapsed time is 6.356738 seconds.
90 1
120
60
120
0.5
150
30
180
180
330 240
270
180
30 0
210
330 240
CONCLUSIONS
270
60
0.5
150
330 240
90 1
270
300
Endfire array
:
68
30 0
210
300
120
60
0.5
150
0
210
90 1
300
Practical - 19 AIM
:
THEORY
To write a program to plot 3D radiation pattern for Binomial antenna array. :
69
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))
AF AF
(1+exp(1j.*(psi))).^(N-1); AF - min(min(AF));
= =
+ beta;
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]);
70
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.
71
CONCLUSIONS
:
72
Practical - 20 AIM
:
THEORY
To write a program to plot 3D radiation pattern for Broadside antenna array. :
73
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 den AF AF
= = = =
((1./N).*sin(N.*c.*cos(theta))); sin(c.*cos(theta)); num./den; 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 74
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]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
75
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
:
76
Practical - 21 AIM
:
THEORY
To write a program to plot 3D radiation pattern for Endfire antenna array :
77
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 AF
= num./den; = 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') 78
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.
79
CONCLUSIONS
:
80
Practical - 22 AIM
:
THEORY
To write a program to plot 3-D Radiation Pattern of Dipole Antenna. :
81
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 82
