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+// Example 11.5

+// Design of a Lowpass Filter

+f_co=4000; // In Hertz

+R_L=200;

+R_s=50;

+// Using node equation in figure 11.10

+// (1/R_s+1/R_L+s*C)*V_out=(1/R_s)*V_s;

+// V_out/V_s=H(s)=(K*omega_co)/(s+omega_co)---equation (1)

+// Comparing equation (1) with low pass filter equation we get,

+K=(1/R_s)/(1/R_s+1/R_L);

+omega_co=2*%pi*f_co;

+C=1/(omega_co*(1/R_s+1/R_L));

+R_eq=(R_s*R_L)/(R_s+R_L);

+tau=R_eq*C;

+// design testing

+// Model for voice signal is 3kHz sinusoid with V_m=5V

+// so total input signal will become

+// v_s(t)=5*cos(omega1*t)+0.5*cos(omega2*t)

+omega1=2*%pi*3000;

+omega2=2*%pi*16000;

+// using equation for Low pass filter we get

+H_omega1=(K*omega_co)/(%i*omega1+omega_co);

+H_omega2=(K*omega_co)/(%i*omega2+omega_co);

+a_omega1=abs(H_omega1);

+theta1_r=atan(imag(H_omega1),real(H_omega1));

+a_omega2=abs(H_omega2);

+theta2_r=atan(imag(H_omega2),real(H_omega2));

+t=0:0.0001:0.01;

+v_out=a_omega1*5*cos(omega1*t+theta1_r)+a_omega2*0.5*cos(omega2*t+theta2_r);

+v_s=5*cos(omega1*t)+0.5*cos(omega2*t)

+plot(t,v_out,t,v_s,'-g')

+xlabel('t')

+ylabel('v_out(t)')

+title('Voltage Waveform')

+h1=legend(['v_out';'v_s'])

+disp("waveform Shows that whistle amplitude has been cut down to 3% of the voice signal at the input")