Transmission Line (strip line)

Question

1) As written in the task the L and H should be greater than 20h and impedance should be 50 ohms. Please help to adjust these parameters so that after changing the L and H I still get 50 ohms.

2) In the codes, in the last, I am not able to understand the Tolerance testing Part.

Codes:

%Clearing variables in memory and Matlab command screen
close all;
clear all;
clc;

%Problem data
L = 10; 
H = 4.5;
h = 0.5;
w = 0.6;
epsilon_0 = 8.854*10^-12;
epsilon_r = 3.05*epsilon_0;

%Dimensions of the simulation grid in x (xdim) and y (ydim) directions
xdim=50;
ydim=50;
dx = L/xdim;
dy = H/ydim;
N_strip1x = floor((L-h)/2/dx); % number of node along x axis of the left strip
N_strip2x = floor(N_strip1x + h/dx); % number of node along x axis of the left strip
N_strip1y = floor((H-w)/2/dy);
N_strip2y = floor(N_strip1y + w/dy);
r = cos(pi/(xdim/L))+cos(pi/(H/ydim));
alpha = 1;
%Initializing initial Potential matrix & boundary conditions for V_init
V=zeros(xdim,ydim);
V(N_strip1x,N_strip1y:N_strip2y) = 1;
V(N_strip2x,N_strip1y:N_strip2y) = 1;

%Initializing maximum number of iterations
max_iterations = 500;
Z0 = zeros(1,max_iterations);
figure,
for i = 1:max_iterations
    clc
    display(['iteration n° ',num2str(i),'/',num2str(max_iterations)])
    V_old = V;
    for x = 2:xdim-1
        for y = 2:ydim-1
            % evaluate on the same line of the strips
             if x == N_strip1x && y > N_strip2y && y  N_strip2y && y  N_strip1x
                V(x,y)=epsilon_r*V_old(x,y)+alpha*(((epsilon_r*V_old(x-1,y)+epsilon_r*V_old(x+1,y)+epsilon_r*V_old(x,y-1)+epsilon_r*V_old(x,y+1))/4)-epsilon_r*V_old(x,y));
                V(x,y) = (1/epsilon_r) * V(x,y);             
            end
            %evaluate outside the strips
            if x > N_strip2x || x  N_strip2y && y  N_strip2y && y  N_strip1x
                    V(x,y)=epsilon_r*V_old(x,y)+omega(o)*(((epsilon_r*V_old(x-1,y)+epsilon_r*V_old(x+1,y)+epsilon_r*V_old(x,y-1)+epsilon_r*V_old(x,y+1))/4)-epsilon_r*V_old(x,y));
                    V(x,y) = (1/epsilon_r) * V(x,y);             
                end
                %evaluate outside the strips
                if x > N_strip2x || x  0
            break
        end
    end
    n_iterations(1,o) = i;
end
figure,
plot(omega,n_iterations);
xlim([0.9 1.02]);
xlabel('Omega')
ylabel('Number of iteration')
title('Plot of number of iteration versus omega')

Answer 1

As written in the task the L and H should be greater than 20h and impedance should be 50 ohms. Please help to adjust these parameters so that after changing the L and H I still get 50 ohms.

The point of this requirement is that if \$L\$ and \$H\$ are large compared to \$W\$ and \$h\$, then they will not affect the characteristic impedance much. Adjusting \$L\$ or \$H\$ should not change \$Z_0\$ noticeably.

In general, increasing \$W\$ should reduce \$Z_0\$ and increasing \$h\$ should increase \$Z_0\$. That should give you enough to nail down a combination of \$W\$ and \$h\$ that reaches \$Z_0=50\ \Omega \pm 5\ \Omega\$ within 3 or 4 tries.

In the codes, in the last, I am not able to understand the Tolerance testing Part.

I can't read your codes, but this likely means simulating small changes in \$W\$ and \$h\$ to see how big a change they cause in \$Z_0\$.