Hi xin
When dealing with discrete data, plotting directly will inherently produce a step-like appearance. If the objective is to accurately reflect the continuous-time behaviour of the system, numerical integration methods should be considered that simulate continuous-time behaviour.
For a capacitor, the relationship between current i(t) and voltage u(t) is given by the differential equation: i(t) = C* (du/dt).
To solve a differential equation numerically, MATLAB's built-in numerical solvers like ode45, which are designed to handle ordinary differential equations (ODEs) can be used.
For detailed information regarding the ode45 solver, kindly refer the following documentation. https://www.mathworks.com/help/matlab/ref/ode45.html
This can be implemented as follows.
C = 100e-3;
T = 0.5;
f = 50;
u = @(t) sin(2 * pi * f * t);
differentialEquation = @(t, i) C * (2 * pi * f * cos(2 * pi * f * t)); % dy/dt = C * du/dt = C * (du/dt)
i0 = 0; % Initial condition for the current
tspan = [0 T];
[t, i] = ode45(differentialEquation, tspan, i0); % Solving the differential equation using ode45
plot(t, i);
title('Capacitive Current (Continuous-Time Simulation)');
xlabel('Time (s)');
ylabel('Current (A)');
ylim([-0.1 0.1])
By using ode45, the continuous-time behaviour of the capacitor can be simulated without manually discretizing the system, resulting in a smooth and accurate representation of the current.
I hope this helps.
