impedance matching single stub

I am trying to plot the reflection coefficient magnitude from 1 to 3 GHz for a single stub Short circuit to get the result below.

I worked on the code but I am not getting the same result.

clear all;

close all;

clc;

f = linspace(1e9, 3e9, 2000);

omega = 2 * pi * f; % Angular frequency

Z0 = 50;

R_load = 60;

C_load = 0.995e-12;

Gamma1 = zeros(size(f));

Gamma2 = zeros(size(f));

c = 3e8;

lambda = c ./ f

l_stub1 = 0.110*(c./2e9);

l_stub2 = 0.260*(c./2e9);

for i = 1:length(f)

lambda = c / f(i); % Wavelength

beta = 2 * pi / lambda; % Phase constant

% Load impedance (complex due to capacitor)

ZL = R_load - 1i./(omega(i) * C_load)*l_stub1;

ZL1 = R_load - 1i./(omega(i) * C_load)*l_stub2;

% Stub impedances (short-circuited stub)

Z_stub1 = -1i * Z0 * tan(beta * l_stub1); % Solution #1

Z_stub2 = -1i * Z0 * tan(beta * l_stub2); % Solution #2

% Total impedance at the point where the stub connects

Z_total1 = 1 ./ (1./ZL + 1./Z_stub1);

Z_total2 = 1 ./ (1./ZL + 1./Z_stub2);

% Reflection coefficients

Gamma1(i) = (Z_total1 - Z0) / (Z_total1 + Z0);

Gamma2(i) = (Z_total2 - Z0) / (Z_total2 + Z0);

end

absGamma1 = abs(Gamma1);

absGamma2 = abs(Gamma2);

figure;

plot(f / 1e9, absGamma1, 'b', f / 1e9, absGamma2, 'r--');

xlabel('Frequency (GHz)');

ylabel('|Γ|');

title('Magnitude of Reflection Coefficient |Γ| versus Frequency');

legend('Solution #1', 'Solution #2');

grid on;

Answer 1

[David Goodmanson]

Hi Moza,

You have most of it, but you need to add a step and change a sign error. The section terminated by R and C, I called that section A of length la, and the shorted section is section S of length ls.

At the point where the two lines connect, the impedance of section A is not ZL, which is at the right end of the line, but rather the impedance seen at left end of the line, which is

Za = Z0*(ZL + i*Z0*tan(beta*la))./(Z0 + i*ZL.*tan(beta*la));       (1)

and your shorted stub impedance has a sign error and should be

Zs = (i*Z0*tan(beta*ls));                                          (2)

I defined (same as what you have)

lambda0 = c/2e9;   so
case 1  la = .110*lambda0;  ls = .095*lambda0;  
case 2  la = .260*lambda0;  ls = .405*lambda0;

If you add the new Za and Zs in parallel and keep going you will reproduce the plots.

Incidentally, with vector f a for loop is unnecessary if enough .* and ./ are used, which it seems like you already have quite a few of but not all.