Question

Plot using matlab and provide source code in text

3.15-3 A lossless coaxial cable having characteristic impedance 50 Ω is terminated by a load with impedance 25 +j25 Ω (a) What is the voltage reflection coefficient at the load? (b) Plot the input impedance for transmission line lengths from 0 to 0.45λ. Please plot as a single curve in the complex plane, with the horizontal axis as the real component and the vertical axis as the imaginary component. Indicate at each end of the curve the associated lengths. (c) For what lengths is the input impedance completely real-valued, and what is the impedance at these lengths?

Answer 1

%%% Matlab code

clc;
clear all;
close all;
zl=25+25i;
zo=25;
lemda=1;

%%% Reflection coefficient
T_l=(zl-zo)/(zl+zo);
a=real(T_l);
b=imag(T_l)*180/pi;
fprintf(' Refection coefficient = %f + %f i\n',a,b);

l=0:0.1:2;
z_i=zo*(zl+zo*tanh(2*pi*l))./(zo+zl*tanh(2*pi*l));
figure;
plot(imag(z_i),real(z_i),'-*');
xlabel('Real Zi');
ylabel('Imaginary Zi');
grid on
fprintf('Since Zl is complex hence Zin is also always complex\n ');

OUTPUT:

Refection coefficient = 0.200000 + 22.918312 i
Since Zl is complex hence Zin is also always complex

Answer 2

zl=25+1i*25; %load impedance

zo=50; %characteristic impedance

%%% Reflection coefficient

T_l=(zl-zo)/(zl+zo);

a=real(T_l);

b=imag(T_l);

fprintf(' Refection coefficient = %f + %f i\n',a,b);

l=0:0.1:0.45;

z_i=zo*(zl+1i*zo*tan(2*pi*l))./(zo+1i*zl*tan(2*pi*l));

figure;

plot(imag(z_i),real(z_i),'-*');

xlabel('Real Zi');

ylabel('Imaginary Zi');

grid on

fprintf('Since Zl is complex hence Zin is also always complex\n ');

Answer 3

%The plot was in reverse order in the above code.

zl=25+1i*25; %load impedance

zo=50; %characteristic impedance

%%% Reflection coefficient

T_l=(zl-zo)/(zl+zo);

a=real(T_l);

b=imag(T_l);

fprintf(' Refection coefficient = %f + %f i\n',a,b);

l=0:0.1:0.45;

z_i=zo*(zl+1i*zo*tan(2*pi*l))./(zo+1i*zl*tan(2*pi*l));

figure;

plot(real(z_i),imag(z_i),'-*');

xlabel('Real Zi');

ylabel('Imaginary Zi');

grid on

fprintf('Since Zl is complex hence Zin is also always complex\n ');

Output:

 Refection coefficient = -0.200000 + 0.400000 i

Since Zl is complex hence Zin is also always complex