% Impedance of coupled dipole antenna with respect to wavelength.The dipole antenna seperated by distance
% delta. The method used is Hallen's Integral. Here the second dipole is not fed by any
% voltage source
clear all;
lamda=1; %arbitary wavelength (in meter): this can be varied accourding to the problem
l=0.5*lamda; % length of dipole: this can be varied accourding to the problem
a=0.001*lamda; % radius of dipole: this can be varied accourding to the problem
N=50; % no.of segments i.e. the sampling points in antenna surface/for convergence: this can be varied accourding to the problem
dz=l/(2*(N-1/2));% incremental length of l/2 upper part of antenna
z=dz/2:dz:dz*(N); % stores the invremental length in upper part of antenna
k=2*pi/lamda; % wave number
etta=377; % free space impedance
V_impressed=-1; % impressed voltage on D1: this can be varied accourding to the problem
delta=0.1*lamda:0.1:5*lamda; % distance between the dipoles
for d=1:length(delta)
%%%%%% calculating the Green's Function on first dipole (with source)%%%%%
%%%%%%%%%%%%%%%%calculating Function's due to current in first and second dipole%%%%%%%%
for m=1:N %m is the obsevation point
for n=1:N-1% n is the source points
R1=sqrt(a^2+(z(m)-z(n))^2); % R+ in lecture notes for G11
R2=sqrt(a^2+(z(m)+z(n))^2); % R- in lecture notes for G11
R3=sqrt(delta(d)^2+(z(m)-z(n))^2); % R+ for G12
R4=sqrt(delta(d)^2+(z(m)+z(n))^2); % R- for G12
%%%%%%%%%%%%% evaluating greens function G11 %%%%%%%%%%%%%%%%
G1=exp(-j*k*R1)/(4*pi*R1); % G11(R+) in lecture notes
G2=exp(-j*k*R2)/(4*pi*R2); % G11(R-) in lecture notes
G_11(m,n)=(G1+G2)*dz; % G11(R) observation in D1 source:1
%%%%%%%%%%%%% evaluating greens function G12 %%%%%%%%%%%%%%
G3=exp(-j*k*R3)/(4*pi*R3); % G12(R+) in lecture notes
G4=exp(-j*k*R4)/(4*pi*R4); % G12 (R-)in lecture notes
G_12(m,n)=(G3+G4)*dz; % G12(R) observation in D1 source:2
end
v_1(m)=j/(2*etta)*(sin(k*z(m))); % Sine term due to impressed voltage in D1
end
%%%%%% calculating the Green's Function on second dipole (without source)%%%%%
%%%%%%%%%%%%%%%%calculating Function's due to current in first and second dipole%%%%%%%%
for m=1:N %m is the obsevation point
for n=1:N-1% n is the source points
R5=sqrt(a^2+(z(m)-z(n))^2); % R+ in lecture notes for G22
R6=sqrt(a^2+(z(m)+z(n))^2); % R- in lecture notes for G22
R7=sqrt(delta(d)^2+(z(m)-z(n))^2); % R+ for G21
R8=sqrt(delta(d)^2+(z(m)+z(n))^2); % R- for G21
%%%%%%%%%%%%% evaluating greens function G22 %%%%%%%%%%%%%%
G5=exp(-j*k*R5)/(4*pi*R5); % G22(R+) in lecture notes
G6=exp(-j*k*R6)/(4*pi*R6); % G22(R-) in lecture notes
G_22(m,n)=(G5+G6)*dz; % G22(R) observation in D2 source:2
%%%%%%%%%%%%% evaluating greens function G12 %%%%%%%%%%%%%%
G7=exp(-j*k*R7)/(4*pi*R7); % G21(R+) in lecture notes
G8=exp(-j*k*R8)/(4*pi*R8); % G21 (R-)in lecture notes
G_21(m,n)=(G7+G8)*dz; % G21(R) observation in D2 source:1
end
v_2(m)=0; % Sine term due to impressed voltage in D2 (no voltage applied in D2)
end
%%%%%%%%%%%% concatenating G11 and G12%%%%%%%%%%%
G_D1=horzcat(G_11,G_12);
s=size(G_D1);
N_t1=s(2);
G_D1(:,N_t1+1)=[-cos(k*z)]; % N element holds the cosine terms for D1
G_D1(:,N_t1+2)=[0]; % N+1 element holds the cosine terms for D2 which is zero for D1
%%%%%%%%%%%% concatenating G21 and G22%%%%%%%%%%%
G_D2=horzcat(G_21,G_22);
s_1=size(G_D2);
N_t2=s_1(2);
G_D2(:,N_t2+1)=[0]; % N element holds the cosine terms from D1 which is zero for D1
G_D2(:,N_t2+2)=[-cos(k*z)]; % N+1 element holds the cosine terms from D2
%%%%%%%%%%%%%concatenating Sine terms i.e. Vm%%%%%%%%%%%%%
Vm=horzcat(v_1,v_2);
%%% Defining the matrix required to evaluate the current%%%%%%%%
G_eval=vertcat(G_D1,G_D2);
%%%% evaluate current%%%
I=inv(G_eval)*Vm.'; % this will give a column vector of current
%%%%%%%%%%% for question number 4 (LAB part)%%%%%%%%%%%%%%%%%%%%
s_2= size(I);
N_t3=s_2(1); % this will give the number of elements in column
N1=(N_t3-2)/2;
I1=I(1); % first element gives the current in the centre of D1
I2=I(N1+1); % this gives the current in the centre of D2
Z_11(d)=V_impressed/I1;
Z_12(d)=V_impressed/I2;
end
plot(delta,real(Z_11));
hold on
plot(delta,imag(Z_11),'r')
legend('real-Z11','Imaginary-Z11')
title('阻抗的实部和虚部')
xlabel('delta');
ylabel('阻抗')
grid on
figure
plot (delta, real(Z_12),'b:<')
hold on
plot (delta,imag(Z_12),'r-->')
legend('real-Z12','Imaginary-Z12')
title('阻抗的实部和虚部')
xlabel('delta');
ylabel('阻抗')
grid on
