% RC circuit (series configuration) works as a filter (low-pass filter)

clear all
close all
R=100;
C=100e-6;

% i-u representation, input u (source voltage), output y (voltage across C)
% u=RC*y_dot + y => y_dot +y/(R*C) =u/(R*C)

% ss representation
% x_dot=-x/(R*C) +u/(R*C)
% y=x

% then x_dot=a*x + b*u; y=c*x+d*u

a=-1/(R*C);
b=1/(R*C);
k=b/(-a); % =1;
tau=1/(-a);

% define the tf
s=tf('s');
W=k/(1+tau*s);


% plot the Bode diagrams
bode(W);
grid on
hold on

% plot the Bode asymptotic diagrams
bodeas(W)
grid on
hold on

% two inputs with different omega
omega_1=10;
omega_2=1000;
T2=2*pi/omega_2;

T1=2*pi/omega_1;
time1=0:T1/50:5*T1;
time2=0:T2/50:5*T2;

u1=sin(omega_1*time1);
u2=sin(omega_2*time2);
y1=lsim(W,u1,time1);
y2=lsim(W,u2,time2);

% plot u and y
figure
hold on
grid on
plot(time1,u1,'-b','linewidth',2)
plot(time1,y1,'-r','linewidth',2)
legend('u_1','y_1')

figure
hold on
grid on
plot(time2,u2,'-b','linewidth',2)
plot(time2,y2,'-r','linewidth',2)
legend('u_2','y_2')