Hi Ammar,
The code looks interesting.
I understand that you are encountering errors while using MATLAB's 'integral' function for integration.
According to the documentation, the 'integral' function requires the input argument 'integrand' to be a function handle.
Based on the code and theory you have provided,
The Kernel and function integral can be defined as below.
% Kernel function
Kernel = F_1 * F_2 * (F_3 * F_4 + F_5);
% Convert Kernel to a function handle
Kernel_handle = matlabFunction(Kernel, 'Vars', [z, z_prime]);
% Define the integrand as a function handle
integrand = @(z) Kernel_handle(z, loop_z_prime);
% Integrate using the defined function handle
Z(i,j) = integral(integrand, loop_lower_z, loop_upper_z);
Below is complete implementation of your code using the above arguments
%% Starting Timer and Clearing Plots/Command Line
tic
close all; clc;
%% Fixed Variables and Parameters
% Value of j
j = 1i;
% Speed of light = c = 3*10^8 m/s
c = 3*10^8;
% Frequency = 300 MHz = 300*10^6 Hz = 3*10^8 Hz
f = 3*10^8;
% Value of lambda = c / f
lambda = c/f;
% Wavenumber value = k
k = (2*pi)/lambda;
% Intrinsic Impedance Value = eta
eta = 120*pi;
% Radius of the wire
a = 0.005*lambda;
% Length of the dipole antenna
L = 0.5*lambda;
% Number of segments
N = 3;
% Number of columns
M = N;
% Declaring "z" and "z_prime" as symbolic variables
syms z z_prime;
%% Calculating the Kernel Factor
% R equation
R = sqrt(a^2 + (z - z_prime)^2);
% Factor_1 = (-j*eta) / k
F_1 = (-j*eta) / k;
% Factor_2 = (exp(-j*k*R)) / (4*pi*(R)^5)
F_2 = exp(-j*k*R) / (4*pi*(R)^5);
% Factor_3 = 1 + jkR
F_3 = 1 + (j*k*R);
% Factor_4 = 2*R^2 - 3*a^2
F_4 = (2*R^2) - (3*a^2);
% Factor_5 = (k*a*R)^2
F_5 = (k*a*R)^2;
% Kernel function
Kernel = F_1 * F_2 * (F_3 * F_4 + F_5);
% Convert Kernel to a function handle
Kernel_handle = matlabFunction(Kernel, 'Vars', [z, z_prime]);
% Upper and lower z integration boundaries
delta_z = L / N;
upper_z = 0 : delta_z : L - delta_z;
lower_z = delta_z : delta_z : L;
% Start and stop values for z_prime
z_prime_start = L / (2*N);
delta_z_prime = L / N;
z_prime_end = L - z_prime_start;
z_prime = z_prime_start : delta_z_prime : z_prime_end;
% Pre-allocating the Z Matrix into an N x N Matrix
Z = zeros(N, N);
for i = 1:N
for j = 1:M
loop_z_prime = z_prime(i);
loop_upper_z = upper_z(j);
loop_lower_z = lower_z(j);
% Define the integrand as a function handle
integrand = @(z) Kernel_handle(z, loop_z_prime);
% Integrate using the defined function handle
Z(i,j) = integral(integrand, loop_lower_z, loop_upper_z);
end
end
toc
disp(Z)
Refer to the following references for further help.
- https://www.mathworks.com/help/matlab/ref/integral.html?s_tid=doc_ta#btbbkta-3
- https://www.mathworks.com/help/matlab/matlab_prog/creating-a-function-handle.html
Hope this answers your query.
