How to 3D plot Complex Fraction: Voltage Reflection Coefficient With Increasing Reactance

Question

I am super struggling with this problem. I need to show in 3D how the magnitude of the Voltage Reflection Coefficient changes for a fixed Z_0 BUT with a changing Z_L, i.e. a changing load impedance.

It is not working at all and have no idea how to proceed. It seems MATLAB will not allow sum or difference operations for 3d plots.

clear,clc,cla,clf;

figure;

resistance = 0:10:400;
reactance = -400:10:400;

R = 50;     % Fixed resistance of Transmission Line
X = 0;      % Fixed reactance of Transmission Line

R_matrix = zeros(length(resistance),length(resistance));
R_matrix(:) = R;

X_matrix = zeros(length(reactance),length(reactance));
X_matrix(:) = X;


[RESISTANCE,REACTANCE] = meshgrid(resistance,reactance);


VRC = ((resistance - R_matrix).^2  + (reactance - X_matrix).^2) ./ ((resistance + R_matrix).^2 + (reactance - X_matrix).^2);

surf(RESISTANCE,REACTANCE,VRC);

xlabel('Resistance (\Omega)',"FontSize",14);
ylabel('Reactance X','FontSize',14);
zlabel('Voltage Reflection Coefficient','FontSize',14);

user_3943170 · Answer

The resistance and reactance cannot have different lengths. Use linspace(0,400) and linspace(-400,400) to make sure both have 100 values, for example.

clear, clc, close

resistance = linspace(0,400);
reactance = linspace(-400,400);

R = 50;     % Fixed resistance of Transmission Line
X = 0;      % Fixed reactance of Transmission Line

R_matrix(1:length(resistance),1:length(resistance)) = R;
X_matrix(1:length(reactance),1:length(reactance)) = X;

VRC = ((resistance - R_matrix).^2 + (reactance - X_matrix).^2) ./ ...
      ((resistance + R_matrix).^2 + (reactance + X_matrix).^2);

[RESISTANCE,REACTANCE] = meshgrid(resistance,reactance);
surf(RESISTANCE,REACTANCE,VRC);

xlabel('Resistance (\Omega)',"FontSize",14);
ylabel('Reactance X','FontSize',14);
zlabel('Voltage Reflection Coefficient','FontSize',14);

Edit: The reflection coefficient can only approach zero if ZL=Z0 because Γ=(ZL−Z0)/(ZL+Z0). If you change resistance = 0:100 you will get Γ=0 at exactly resistance=50, because at resistance=50 the reactance is zero.

Just change this line:

resistance = linspace(0,100);

to get the following figure:

user_3943170 · Answer

This is a new answer to address the enquiries raised by the OP in comments:

resistance = linspace(0,99);
reactance = linspace(-100,100);
R = 50;     % Fixed resistance of Transmission Line
X = 0;      % Fixed reactance of Transmission Line

% 2D plot:
VRC = ((resistance - R).^2 + (reactance - X).^2) ./ ...
      ((resistance + R).^2 + (reactance + X).^2);
plot(resistance,VRC,reactance,VRC)
xlabel('Resistance (\Omega), Reactance X',"FontSize",12);
ylabel('Voltage Reflection Coefficient','FontSize',12);

% 3D plot:
[RESISTANCE,REACTANCE] = meshgrid(resistance,reactance);
VRC = ((RESISTANCE - R).^2 + (REACTANCE - X).^2) ./ ...
      ((RESISTANCE + R).^2 + (REACTANCE + X).^2);
figure
surf(RESISTANCE,REACTANCE,VRC);
xlabel('Resistance (\Omega)',"FontSize",12);
ylabel('Reactance X','FontSize',12);
zlabel('Voltage Reflection Coefficient','FontSize',12);

How to 3D plot Complex Fraction: Voltage Reflection Coefficient With Increasing Reactance

2 Answers