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MoM_plate_mutual.asv
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MoM_plate_mutual.asv
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clear; close all
lambda = 1;
load em_constants.mat
mu0 = mu_0;
ep0 = epsilon_0;
omega = 2*pi*c/lambda;
K = 2*pi/lambda;
w = lambda/2;
L1 = .9*w;
L2 = .9*w;
len = 1;
M = 600; % Sections on the strip
deltax1 = L1 / M;
deltax2 = L2 / M;
gamma = exp(vpa(eulergamma));
e = exp(1);
euler = vpa(eulergamma);
% x = linspace(0 + deltax , L - deltax, M);
x1 = linspace(-0.5*L1 , .5*L1 , M);
x2 = linspace(-.5*L2, .5*L2, M);
% y-spacing
y1 = .2*lambda/2;
Z = zeros(1,2*M);
for j = 1 : 1 % Only one iteration is needed as impedance matrix can be constructed through its Toeplitz property
for k = 1 : M
fun = @(xp1) besselh(0,2,K*abs(x1(j) - xp1));% Make a symbolic Function of x_prime
% This calculation is based on the reference cited in the code
% introduction.
% Mathematical Modeling of Eq. 4.63
xp_upper = x1(k) + deltax1; % Upper limit of integration
xp_lower = x1(k); % Lower limit of integration
%% Numerical Integration Using Gauss_Quadratures
% if abs( j - k) >= 1
int_part = integral(fun,xp_lower,xp_upper,'RelTol',1e-12,'AbsTol',1e-12);
%
Z(j,k) = int_part; % Pocklington Integral for j not equal to k
% elseif j == k
% Z(j,k) = deltax*(1 - 1i*2/pi*log(gamma*K*deltax/(4*e)));
% end
end
for k = 1 : M
fun = @(xp) besselh(0,2,K*sqrt((x1(j) - xp).^2 + y1^2));% Make a symbolic Function of x_prime
% Mathematical Modeling of Eq. 4.63
xp_upper = x2(k) + deltax2; % Upper limit of integration
xp_lower = x2(k); % Lower limit of integration
%% Numerical Integration Using Gauss_Quadratures
% if abs( j - k) >= 1
int_part = integral(fun,xp_lower,xp_upper,'RelTol',1e-15,'AbsTol',1e-15);
%
Z(j,M + k) = int_part; % Pocklington Integral for j not equal to k
if j == k
Z(j,M + k) = (deltax2)*(1 - 1i*2/pi*log(gamma*K*sqrt(deltax2^2+y1^2)/(4*e)));
end
end
end
Z_self = Z(1:M);
Z_mutual = Z(M+1 : 2*M);
Z = toeplitz(real(Z(:))) + 1i*toeplitz(imag(Z(:))); % Make a Toeplitz matrix out of a row vector
Z_self = toeplitz(real(Z_self(:))) + 1i*toeplitz(imag(Z_self(:))); % Make a Toeplitz matrix out of a row vector
Z_mutual = toeplitz(real(Z_mutual(1,:))) + 1i*toeplitz(imag(Z_mutual(1,:))); % Make a Toeplitz matrix out of a row vector
% Z = toeplitz(Z);
%
phi = 1*pi/2;
X = [x1,x1];
% V = 4\(omega*mu0)*exp(1i*K*x'*cos(phi));
V = exp(1i*K*X'*cos(phi));
V_self = exp(1i*K*x1'*cos(phi));
V_mutual = exp(1i*K*(x1+y1)'*cos(phi));
I = Z\V;
I_self = Z_self\ V_self;
I_mutual = Z_mutual\ V_mutual;
% Current Plot
figure(1)
% x = linspace(-.7*lambda/2, .7*lambda/2, M) ;
H = plot(x2, real(I_mutual),x2, imag(I_mutual));
ax = gca;
H(1).Color = 'black';
H(1).LineWidth = 1.4;
H(2).Color = 'black';
H(2).LineWidth = 1.4;
H(2).LineStyle = '--';
% title(['Current on the wire of half-length $ h = .35\lambda$ at f = ',int2str(f/1e6), ' MHz'],'Interpreter','latex')
set(gcf,'Color','white'); % Set background color to white
set(gca,'FontName','times new roman','FontSize',11) % Set axes fonts to Times New Roman
% ax.XTick = [-.3498 -0.2625 -0.1750 -0.0875 0 0.0875 0.1750 0.2625 0.3498];
% ax.XTickLabel = { '-h','-.75h','-.5h','-.25h' , '0' ,'.25h', '5h', '.75h', 'h'};
% ax.YTick = [-2e-3 -1e-3 0 1e-3 2e-3];
% ax.YTickLabel = { '-.002','-.001','0' , '.001', '.002'};
% axis([ -.3498 .3498 -2.5e-3 2.5e-3]);
hold on
title(['Mutual Current Distribution on a PEC plate of length ',int2str(len), '$\lambda$ at $\phi_i = \pi/4$'],'Interpreter','latex')
xlabel('$\frac{x}{\lambda}$','interpreter','latex')
ylabel('$J_z \mathrm{A}$','interpreter','latex')
legend('Real Part', 'Imaginary Part');
grid on
% Current Plot
figure(2)
% x = linspace(-.7*lambda/2, .7*lambda/2, M) ;
H = plot(x2, abs(I_mutual));
ax = gca;
H(1).Color = 'black';
H(1).LineWidth = 1.4;
% title(['Current on the wire of half-length $ h = .35\lambda$ at f = ',int2str(f/1e6), ' MHz'],'Interpreter','latex')
set(gcf,'Color','white'); % Set background color to white
set(gca,'FontName','times new roman','FontSize',11) % Set axes fonts to Times New Roman
% ax.XTick = [-.3498 -0.2625 -0.1750 -0.0875 0 0.0875 0.1750 0.2625 0.3498];
% ax.XTickLabel = { '-h','-.75h','-.5h','-.25h' , '0' ,'.25h', '5h', '.75h', 'h'};
% ax.YTick = [-2e-3 -1e-3 0 1e-3 2e-3];
% ax.YTickLabel = { '-.002','-.001','0' , '.001', '.002'};
% axis([ -.3498 .3498 -2.5e-3 2.5e-3]);
hold on
title(['Mutual Current Distribution on a PEC plate of length ',int2str(len), '$\lambda$ at $\phi_i = \pi/4$'],'Interpreter','latex')
xlabel('$\frac{x}{\lambda}$','interpreter','latex')
ylabel('$J_z \mathrm{A}$','interpreter','latex')
grid on
% Current Plot
figure(3)
% x = linspace(-.7*lambda/2, .7*lambda/2, M) ;
H = plot(x1, real(I_self),x1, imag(I_self));
ax = gca;
H(1).Color = 'black';
H(1).LineWidth = 1.4;
H(2).Color = 'black';
H(2).LineWidth = 1.4;
H(2).LineStyle = '--';
% title(['Current on the wire of half-length $ h = .35\lambda$ at f = ',int2str(f/1e6), ' MHz'],'Interpreter','latex')
set(gcf,'Color','white'); % Set background color to white
set(gca,'FontName','times new roman','FontSize',11) % Set axes fonts to Times New Roman
% ax.XTick = [-.3498 -0.2625 -0.1750 -0.0875 0 0.0875 0.1750 0.2625 0.3498];
% ax.XTickLabel = { '-h','-.75h','-.5h','-.25h' , '0' ,'.25h', '5h', '.75h', 'h'};
% ax.YTick = [-2e-3 -1e-3 0 1e-3 2e-3];
% ax.YTickLabel = { '-.002','-.001','0' , '.001', '.002'};
% axis([ -.3498 .3498 -2.5e-3 2.5e-3]);
hold on
title(['Self Current Distribution on a PEC plate of length ',int2str(len), '$\lambda$ at $\phi_i = \pi/4$'],'Interpreter','latex')
xlabel('$\frac{x}{\lambda}$','interpreter','latex')
ylabel('$J_z \mathrm{A}$','interpreter','latex')
legend('Real Part', 'Imaginary Part');
grid on
% Current Plot
figure(4)
% x = linspace(-.7*lambda/2, .7*lambda/2, M) ;
H = plot(x1, abs(I_self));
ax = gca;
H(1).Color = 'black';
H(1).LineWidth = 1.4;
% title(['Current on the wire of half-length $ h = .35\lambda$ at f = ',int2str(f/1e6), ' MHz'],'Interpreter','latex')
set(gcf,'Color','white'); % Set background color to white
set(gca,'FontName','times new roman','FontSize',11) % Set axes fonts to Times New Roman
% ax.XTick = [-.3498 -0.2625 -0.1750 -0.0875 0 0.0875 0.1750 0.2625 0.3498];
% ax.XTickLabel = { '-h','-.75h','-.5h','-.25h' , '0' ,'.25h', '5h', '.75h', 'h'};
% ax.YTick = [-2e-3 -1e-3 0 1e-3 2e-3];
% ax.YTickLabel = { '-.002','-.001','0' , '.001', '.002'};
% axis([ -.3498 .3498 -2.5e-3 2.5e-3]);
hold on
title(['Self Current Distribution on a PEC plate of length ',int2str(len), '$\lambda$ at $\phi_i = \pi/4$'],'Interpreter','latex')
xlabel('$\frac{x}{\lambda}$','interpreter','latex')
ylabel('$J_z \mathrm{A}$','interpreter','latex')
grid on