Help in Sloving S-Matrix

Question

CHARUMATHI P R 2024-3-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2095681-help-in-sloving-s-matrix

回答： Aditya 2024-3-26

采纳的回答： Aditya

I have uploaded the matlab file. Please help me in solving the matrix

clc

clear all

close all

clearvars

%%% S Parameters Calculation

%% Input Parameters

L_R = 2.5e-9; % Inductance (H/m)

L_L = 2.5e-9; % Inductance (H/m)

C_R = 1e-12; % Capacitance (F/m)

C_L = 1e-12; % Capacitance (F/m)

R = 10e-4; % Resistance (Ohm/m)

G = 10e-4; % Resistance (Ohm/m)

Z_C = 50 % Transmission line Inductance (ohm)

f = 0.1e9:0.1e9:10e9; % Frequency in Hertz

w = 2*pi.*f; % Angular Frequency (rad/s)

Z = R + 1i*((w.*L_R)-(1./(w.*C_L))) % Impendance

Y = G + 1i*((w.*C_R)-(1./(w.*L_L))) % Ampendance

A = 1 + ((Z.*Y)./2);

B = Z.*(1+(Z.*Y)./2);

C = Y;

D = 1 + ((Z.*Y)./4);

M = [A B; C D];

Here, I need help to calculate the following matrices

Where, N = 10, 20, 30

Later, I need to calculate the S - Matrix

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Answer 1

Aditya 2024-3-26

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Hi CHARUMATHI P R,

I understand that you need to calculate the ABCD parameters for different values of N (10, 20, 30) and then use these parameters to compute the S-Parameters. Here's how you can approach both parts:

First, let's calculate the ABCD parameters for (N = 10, 20, 30). This involves creating the ABCD matrix and then raising it to the power of N. The ABCD parameters are dependent on frequency, so this operation needs to be performed for each frequency point:

% Rest of the code
% Calculate matrices for N = 10, 20, 30
N_values = [10, 20, 30];
for N_idx = 1:length(N_values)
    N = N_values(N_idx);
    M = [A; B; C; D];
    M = reshape(M, [2,2,length(f)]); % Reshape so that we can perform element-wise matrix power
    for f_idx = 1:length(f)
        M_N(:,:,f_idx) = M(:,:,f_idx)^N; % Matrix power
    end
    % M_N now contains Matrix M raised to power N
end

Next, we use the ABCD parameters obtained for each N to calculate the S-Parameters. This involves extracting the A_N, B_N, C_N, and D_N parameters from the matrix and then using them in the S-Parameter equations:

S_matrices = cell(length(N_values), 1);
% Using the same for loop as above
for N_idx = 1:length(N_values)
    N = N_values(N_idx);
    % Assuming M_N is calculated as shown above 
    A_N = squeeze(M_N(1,1,:));
    B_N = squeeze(M_N(1,2,:));
    C_N = squeeze(M_N(2,1,:));
    D_N = squeeze(M_N(2,2,:));
    
    % Calculate S-parameters based on the equations provided
    S11 = (A_N + B_N/Z_C - C_N*Z_C - D_N) ./ (A_N + B_N/Z_C + C_N*Z_C + D_N);
    S21 = 2 ./ (A_N + B_N/Z_C + C_N*Z_C + D_N);
    % Similarly, Calculate the rest ...
    
    S_matrices{N_idx} = [S11; S21; S12; S22];
end