clear
clc
R = 10000;  %Resistance (Ohms)
C = 0.0000001;   %Capacitance (F)
a = 350;   %Starting x-coordinate of figure
b = 100;   %Starting y-coordinate of figure
width = 1500;   %Width of figure
height = 1200;  %Height of figure
t1 = 0:0.000001:0.02;
t2 = 0:0.000001:0.012;
t3 = 0:0.000001:0.01;
w1 = 780;
w2 = 1200;
w3 = 2150;
u1 = sin(w1*t1);
u2 = sin(w2*t2);
u3 = sin(w3*t3);

num = 1;
den = [C^3*R^3 2*C^2*R^2 2*C*R 1];
sys = tf(num,den)

figure('pos', [a,b,width,height]);
subplot(3,3,1), step(sys), title('Butterworth Filter')
subplot(3,3,2), bode(sys), title('Bode plot of Butterworth Filter')
subplot(3,3,3), bodemag(sys, {30,220}), title('Bode Magnitude (Cornering Frequency)')
subplot(3,3,4), bodemag(sys, {750.1,900}), title('Bode Magnitude at 0.9 (-0.915 dB)')
subplot(3,3,5), bodemag(sys, {1169.4,1367.5}), title('Bode Magnitude at 0.5 (-6 dB)')
subplot(3,3,6), bodemag(sys, {1870.0,2186.7}), title('Bode Magnitude at 0.1 (-20 dB)')
subplot(3,3,7), lsim(sys,u1,t1), title('Response to sin at Magnitude 0.9')
subplot(3,3,8), lsim(sys,u2,t2), title('Response to sin at Magnitude 0.5')
subplot(3,3,9), lsim(sys,u3,t3), title('Response to sin at Magnitude 0.1')

[mag, phase, wout] = bode(sys);
wout
mag
wout(27:28)
wout(29:30)
wout(32:33)