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K LUNIVERSITY MICROWAVE ANTENNA LABORATORY MANUAL COURSE CODE: 14EC541
Lab:1 Directivity of E-Plane and H-Plane sectorial Horn Aim: To find the directivity of E-plane and H-plane Horn antenna using given parameters Apparatus: MATLAB Theory: For a linearly-polarized antenna, this is the plane containing the electric field vector (sometimes called the E aperture) and the direction of maximum radiation. The electric field or "E" plane determines the polarization or orientation of the radio wave. For a vertically polarized antenna, the E-plane usually coincides with the vertical/elevation plane. For a horizontally polarized antenna, the E-Plane usually coincides with the horizontal/azimuth plane. E- plane and H-plane should be 90 degrees apart. In the case of the same linearly polarized antenna, this is the plane containing the magnetic field vector (sometimes called the H aperture) and the direction of maximum radiation. The magnetizing field or "H" plane lies at a right angle to the "E" plane. For a vertically polarized antenna, the H-plane usually coincides with the horizontal/azimuth plane. For a horizontally polarized antenna, the H-plane usually coincides with the vertical/elevation
plane. Procedure: 1. Open MATLAB Software. 2. Create new m-file. 3. Write the program for directivity and save with extension .m. 4. Check the errors and note output values.
Program Code: function []=horn; disp('Directivity of E-Plane sectorial Horn'); 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)); DE = 64*a*R1/(pi*b1)*((real(w))^2 + (imag(w))^2); DH = 4*pi*b*R2/a1*((real(u)-real(v))^2 + (imag(u)-imag(v))^2); DE = 10*log10(DE) %in db scale DH = 10*log10(DH) % in db scale 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; 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; return end end
Output:
Conclusion: Hence, Directivity of E-plane and H-plane horn antenna is calculated in MATLAB. Precautions: Use the system with care.
LAB -2 DIRECTIVITY OF PYRAMIDAL HORN ANTENNA AIM: To find the directivity of pyramidal Horn Antenna using MATLAB.
REQUIREMENTS: MATLAB software
THEORY: A horn antenna with the horn in the shape of a four-sided pyramid, with a rectangular cross section. They are a common type, used with rectangular waveguides, and radiate linearly polarized radio waves. For a given frequency and horn length, there is some flare angle that gives minimum reflection and maximum gain. The internal reflections in straight-sided horns come from the two locations along the wave path where the impedance changes abruptly; the mouth or aperture of the horn, and the throat where the sides begin to flare out. The amount of reflection at these two sites varies with the flare angle of the horn (the angle the sides make with the axis). In narrow horns with small flare angles most of the reflection occurs at the mouth of the horn. The gain of the antenna is low because the small mouth approximates an open-ended waveguide. As the angle is increased, the reflection at the mouth decreases rapidly and the antenna's gain increases. In contrast, in wide horns with flare angles approaching 90° most of the reflection is at the throat. The horn's gain is again low because the throat approximates an open-ended waveguide. As the angle is decreased, the amount of reflection at this site drops, and the horn's gain again increases.
PROGRAM: function []=horn; disp('Directivity of pyramidal Horn'); %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; 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; 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; return end end
PROCEDURE: 1.Open MATLAB software in your computer. 2.Open the new workspace and write the program to find directivity of Pyramidal Horn Antenna. 3.save the program & run it. 4.Check the errors and output is displayed.
PRECAUTIONS: 1.Handle the system with care. 2.Correct the errors if any any and note down the results without error.
RESULTS: Hence the directivity of Pyramidal Horn antenna is Directivity(dB) = 18.8278 dB.
LAB-3 RADIATION PATTERN OF E – PLANE SECTORIAL HORN ANTENNA AIM: To obtain the radiation pattern of an E – plane sectoral Horn Antenna by using MATLAB.
APPARATUS: MATLAB Software. THEORY:
A Horn Antenna is an antenna that consists of a flaring metal waveguide shaped like a Horn to direct radio wave in a beam. Horns are widely used as antennas at UHF and microwave frequencies above 300 MHZ. They are used as feeders for larger antenna structures such as parabolic antennas. There are many types of Horn antennas. Some of them are Pyramidal Horn, Sectorial Horn, Conical Horn, and Exponential Horn etc… Sectorial Horn antennas is again divided into two types E – Plane sectorial Horn antenna and H – Plane sectorial Horn antenna. E – Plane sectorial Horn antenna is flared in the direction of the electric field in the wave guide. This is having good directional radiation pattern. It produces high gain and directivity. E – Plane sectorial Horn antennas can be easily fabricated. The waves travel down a horn as spherical wave fronts, with their origin at the apex of the horn, a point called the phase center. The pattern of electric and magnetic fields at the aperture plane at the mouth of the horn, which determines the radiation pattern, is a scaled-up reproduction of the fields in the waveguide. Because the wave fronts are spherical, the phase increases smoothly from the edges of the aperture plane to the center, because of the difference in length of the center point and the edge points from the apex point. The difference in phase between the center point and the edges is called the phase error. This phase error, which increases with the flare angle, reduces the gain and increases the beam width, giving horns wider beam widths than similarsized plane-wave antennas such as parabolic dishes.
PROCEDURE:
Open MATLAB Software in System. Open new M- File. Write Program to find radiation pattern of E- plane sectoral horn. Save the program and run it. Output will come if there are no errors in the program.
PROGRAM: function []=horn; disp('E-Plane radiation pattern'); %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) = '); k = 2*pi; Emax = 0; %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); 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 % Figure 1 ha=plot(x,q1); set(ha,'linestyle'); hold on; xlabel('Theta (degrees)'); ylabel('Field Pattern (dB)'); title('E-plane'); legend('E-Plane'); grid on; axis([0 360 -60 0]); % Figure 2 figure(2) ht1=polar(x*pi/180,q1,'b-'); hold on; legend([ht1],{'E-plane'}); title('Field patterns'); 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; 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; return end end
PLOTTED WAVE FORMS:
RESULT: Radiation pattern of E – Plane sectorial Horn Antenna is obtained.
LAB-4 RADIATION PATTERN OF H – PLANE SECTORAL HORN ANTENNA AIM: To obtain radiation pattern of H – Plane sartorial Horn Antenna by using MATLAB. APPARATUS: MATLAB Software. THEORY : Horn antenna are popular in microwave band(above GHz). Horns provide high gain, low VSWR, relatively wide bandwidth and they are not difficult to make .it has three basic types *H-plane sectorial horn *E-plane sectorial horn *pyramidal horn H-plane sectorial horn antenna is flared in the direction of magnetic or H-field in the wave guide .The two fundamental dimensions for a construction of horn are width of horn & RH length of horn The directivity of H-plane sectorial horn antenna is DH= /a1λ {[C (u)-C (v)] 2+[S (u)-S (v)] 2}
PROCEDURE:
Open MATLAB software in System. Open new M – File. Write the program to find the radiation pattern of H – Plane sectoral Horn. Save the program and run it. Output will come if there are no errors in program.
PROGRAM: function []=horn; disp('H-plane radiation pattern '); %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) = '); k = 2*pi; Emax = 0; Hmax = 0; % H-Plane Amplitude for(theta = 0:0.5:360); I = theta*2 + 1; theta = theta*pi/180; phi = 0; ky = k*sin(theta); 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,q2); set(ha,'linestyle'); hold on; xlabel('Theta (degrees)'); ylabel('Field Pattern (dB)'); title('H-plane'); legend('H-Plane'); grid on; axis([0 360 -60 0]); % Figure 2 figure(2) ht2=polar(x*pi/180,q2,'r--'); set([ht2],'linewidth'); legend([ht2],{'H-plane'}); title('Field patterns'); % 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; 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; return end end PLOTTED WAVEFORMS:
RESULT: Hence the radiation pattern of H-plane sartorial horn antenna is plotted in MATLAB.
LAB-5 RADIATION PATTERN OF PYRAMIDAL HORN ANTENNA
AIM: To find the Radiation pattern of of pyramidal Horn Antenna using MATLAB.
REQUIREMENTS: MATLAB software
THEORY: The radiation pattern is a graphical representation of the strength of radiation of an antenna as a function of direction. The strength of radiation is usually measured in of field strength although sometimes radiation intensity (power radiated per unit solid angle) is also used. For the purpose of radiation pattern, one considers the given antenna to be located at the origin of a spherical polar coordinates systems (r,θ,φ) and the variation in the field strength at different points on an imaginary concentric spherical surface of radius r is noted. For sufficiently larger r, as explained later on, the field variation or the pattern is independent or r and also the fields are tangential to the hypothetical spherical surface. In general, separate patterns are plotted for θ and φ polarization. The wavefronts in the vicinity of an antenna have a small radius or curvature but after traveling some distance the radius of curvature increases to such an extent as to make the wave front practically a plane wave. A receiving antenna is considered to be in the far-field of the test antenna if the wavefront across it is practically plane. Most measurements are carried out in the far field region since; otherwise, when the receiving antenna is kept in the region of curved wavefornt, there will be a phase difference across the receiving aperture. It can be shown that the phase variation over the receiving aperture is less than one sixteenth of a wavelength if it is at a distance R from the transmitting antenna, where
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) = '); 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); 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); 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'); % 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; 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; return
end end PROCEDURE: 1.Open MATLAB software in your computer. 2.Open the new workspace and write the program to find directivity of Pyramidal Horn Antenna. 3.save the program & run it. 4.Check the errors and output is displayed.
OUTPUT WAVEFORMS:
PRECAUTIONS: 1.Handle the system with care. 2.Correct the errors if any any and note down the results without error. RESULT: Hence the Radiation pattern of Pyramidal Horn antenna is verified using MATLAB.
LAB-6 AIM: To find the radiation pattern of Rectangular Microstrip antenna Software: HFSS/ Matlab LAB-7 AIM: To find the radiation pattern of circular Microstrip antenn Software: HFSS/MATLAB
Lab:1 Directivity of E-Plane and H-Plane sectorial Horn Aim: To find the directivity of E-plane and H-plane Horn antenna using given parameters Apparatus: MATLAB Theory: For a linearly-polarized antenna, this is the plane containing the electric field vector (sometimes called the E aperture) and the direction of maximum radiation. The electric field or "E" plane determines the polarization or orientation of the radio wave. For a vertically polarized antenna, the E-plane usually coincides with the vertical/elevation plane. For a horizontally polarized antenna, the E-Plane usually coincides with the horizontal/azimuth plane. E- plane and H-plane should be 90 degrees apart. In the case of the same linearly polarized antenna, this is the plane containing the magnetic field vector (sometimes called the H aperture) and the direction of maximum radiation. The magnetizing field or "H" plane lies at a right angle to the "E" plane. For a vertically polarized antenna, the H-plane usually coincides with the horizontal/azimuth plane. For a horizontally polarized antenna, the H-plane usually coincides with the vertical/elevation
plane. Procedure: 1. Open MATLAB Software. 2. Create new m-file. 3. Write the program for directivity and save with extension .m. 4. Check the errors and note output values.
Program Code: function []=horn; disp('Directivity of E-Plane sectorial Horn'); 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)); DE = 64*a*R1/(pi*b1)*((real(w))^2 + (imag(w))^2); DH = 4*pi*b*R2/a1*((real(u)-real(v))^2 + (imag(u)-imag(v))^2); DE = 10*log10(DE) %in db scale DH = 10*log10(DH) % in db scale 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; 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; return end end
Output:
Conclusion: Hence, Directivity of E-plane and H-plane horn antenna is calculated in MATLAB. Precautions: Use the system with care.
LAB -2 DIRECTIVITY OF PYRAMIDAL HORN ANTENNA AIM: To find the directivity of pyramidal Horn Antenna using MATLAB.
REQUIREMENTS: MATLAB software
THEORY: A horn antenna with the horn in the shape of a four-sided pyramid, with a rectangular cross section. They are a common type, used with rectangular waveguides, and radiate linearly polarized radio waves. For a given frequency and horn length, there is some flare angle that gives minimum reflection and maximum gain. The internal reflections in straight-sided horns come from the two locations along the wave path where the impedance changes abruptly; the mouth or aperture of the horn, and the throat where the sides begin to flare out. The amount of reflection at these two sites varies with the flare angle of the horn (the angle the sides make with the axis). In narrow horns with small flare angles most of the reflection occurs at the mouth of the horn. The gain of the antenna is low because the small mouth approximates an open-ended waveguide. As the angle is increased, the reflection at the mouth decreases rapidly and the antenna's gain increases. In contrast, in wide horns with flare angles approaching 90° most of the reflection is at the throat. The horn's gain is again low because the throat approximates an open-ended waveguide. As the angle is decreased, the amount of reflection at this site drops, and the horn's gain again increases.
PROGRAM: function []=horn; disp('Directivity of pyramidal Horn'); %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; 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; 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; return end end
PROCEDURE: 1.Open MATLAB software in your computer. 2.Open the new workspace and write the program to find directivity of Pyramidal Horn Antenna. 3.save the program & run it. 4.Check the errors and output is displayed.
PRECAUTIONS: 1.Handle the system with care. 2.Correct the errors if any any and note down the results without error.
RESULTS: Hence the directivity of Pyramidal Horn antenna is Directivity(dB) = 18.8278 dB.
LAB-3 RADIATION PATTERN OF E – PLANE SECTORIAL HORN ANTENNA AIM: To obtain the radiation pattern of an E – plane sectoral Horn Antenna by using MATLAB.
APPARATUS: MATLAB Software. THEORY:
A Horn Antenna is an antenna that consists of a flaring metal waveguide shaped like a Horn to direct radio wave in a beam. Horns are widely used as antennas at UHF and microwave frequencies above 300 MHZ. They are used as feeders for larger antenna structures such as parabolic antennas. There are many types of Horn antennas. Some of them are Pyramidal Horn, Sectorial Horn, Conical Horn, and Exponential Horn etc… Sectorial Horn antennas is again divided into two types E – Plane sectorial Horn antenna and H – Plane sectorial Horn antenna. E – Plane sectorial Horn antenna is flared in the direction of the electric field in the wave guide. This is having good directional radiation pattern. It produces high gain and directivity. E – Plane sectorial Horn antennas can be easily fabricated. The waves travel down a horn as spherical wave fronts, with their origin at the apex of the horn, a point called the phase center. The pattern of electric and magnetic fields at the aperture plane at the mouth of the horn, which determines the radiation pattern, is a scaled-up reproduction of the fields in the waveguide. Because the wave fronts are spherical, the phase increases smoothly from the edges of the aperture plane to the center, because of the difference in length of the center point and the edge points from the apex point. The difference in phase between the center point and the edges is called the phase error. This phase error, which increases with the flare angle, reduces the gain and increases the beam width, giving horns wider beam widths than similarsized plane-wave antennas such as parabolic dishes.
PROCEDURE:
Open MATLAB Software in System. Open new M- File. Write Program to find radiation pattern of E- plane sectoral horn. Save the program and run it. Output will come if there are no errors in the program.
PROGRAM: function []=horn; disp('E-Plane radiation pattern'); %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) = '); k = 2*pi; Emax = 0; %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); 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 % Figure 1 ha=plot(x,q1); set(ha,'linestyle'); hold on; xlabel('Theta (degrees)'); ylabel('Field Pattern (dB)'); title('E-plane'); legend('E-Plane'); grid on; axis([0 360 -60 0]); % Figure 2 figure(2) ht1=polar(x*pi/180,q1,'b-'); hold on; legend([ht1],{'E-plane'}); title('Field patterns'); 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; 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; return end end
PLOTTED WAVE FORMS:
RESULT: Radiation pattern of E – Plane sectorial Horn Antenna is obtained.
LAB-4 RADIATION PATTERN OF H – PLANE SECTORAL HORN ANTENNA AIM: To obtain radiation pattern of H – Plane sartorial Horn Antenna by using MATLAB. APPARATUS: MATLAB Software. THEORY : Horn antenna are popular in microwave band(above GHz). Horns provide high gain, low VSWR, relatively wide bandwidth and they are not difficult to make .it has three basic types *H-plane sectorial horn *E-plane sectorial horn *pyramidal horn H-plane sectorial horn antenna is flared in the direction of magnetic or H-field in the wave guide .The two fundamental dimensions for a construction of horn are width of horn & RH length of horn The directivity of H-plane sectorial horn antenna is DH= /a1λ {[C (u)-C (v)] 2+[S (u)-S (v)] 2}
PROCEDURE:
Open MATLAB software in System. Open new M – File. Write the program to find the radiation pattern of H – Plane sectoral Horn. Save the program and run it. Output will come if there are no errors in program.
PROGRAM: function []=horn; disp('H-plane radiation pattern '); %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) = '); k = 2*pi; Emax = 0; Hmax = 0; % H-Plane Amplitude for(theta = 0:0.5:360); I = theta*2 + 1; theta = theta*pi/180; phi = 0; ky = k*sin(theta); 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,q2); set(ha,'linestyle'); hold on; xlabel('Theta (degrees)'); ylabel('Field Pattern (dB)'); title('H-plane'); legend('H-Plane'); grid on; axis([0 360 -60 0]); % Figure 2 figure(2) ht2=polar(x*pi/180,q2,'r--'); set([ht2],'linewidth'); legend([ht2],{'H-plane'}); title('Field patterns'); % 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; 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; return end end PLOTTED WAVEFORMS:
RESULT: Hence the radiation pattern of H-plane sartorial horn antenna is plotted in MATLAB.
LAB-5 RADIATION PATTERN OF PYRAMIDAL HORN ANTENNA
AIM: To find the Radiation pattern of of pyramidal Horn Antenna using MATLAB.
REQUIREMENTS: MATLAB software
THEORY: The radiation pattern is a graphical representation of the strength of radiation of an antenna as a function of direction. The strength of radiation is usually measured in of field strength although sometimes radiation intensity (power radiated per unit solid angle) is also used. For the purpose of radiation pattern, one considers the given antenna to be located at the origin of a spherical polar coordinates systems (r,θ,φ) and the variation in the field strength at different points on an imaginary concentric spherical surface of radius r is noted. For sufficiently larger r, as explained later on, the field variation or the pattern is independent or r and also the fields are tangential to the hypothetical spherical surface. In general, separate patterns are plotted for θ and φ polarization. The wavefronts in the vicinity of an antenna have a small radius or curvature but after traveling some distance the radius of curvature increases to such an extent as to make the wave front practically a plane wave. A receiving antenna is considered to be in the far-field of the test antenna if the wavefront across it is practically plane. Most measurements are carried out in the far field region since; otherwise, when the receiving antenna is kept in the region of curved wavefornt, there will be a phase difference across the receiving aperture. It can be shown that the phase variation over the receiving aperture is less than one sixteenth of a wavelength if it is at a distance R from the transmitting antenna, where
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) = '); 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); 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); 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'); % 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; 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; return
end end PROCEDURE: 1.Open MATLAB software in your computer. 2.Open the new workspace and write the program to find directivity of Pyramidal Horn Antenna. 3.save the program & run it. 4.Check the errors and output is displayed.
OUTPUT WAVEFORMS:
PRECAUTIONS: 1.Handle the system with care. 2.Correct the errors if any any and note down the results without error. RESULT: Hence the Radiation pattern of Pyramidal Horn antenna is verified using MATLAB.
LAB-6 AIM: To find the radiation pattern of Rectangular Microstrip antenna Software: HFSS/ Matlab LAB-7 AIM: To find the radiation pattern of circular Microstrip antenn Software: HFSS/MATLAB
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