Question

e. We have a signal which function is Inoimbo V13 (t) = sin(0.1 2 * t) + sin(10 * 2 t) We will design a low-pass filter with cutoff of frequency = 0.5Hz to extract the 0.1Hz signal sin(0.1 * 2 * t) and filter 10HZ noise sin(10 * 2 * t) ). e.1(N) (3 pts) Please find a suitable value of Resistor R(N), where C=1.5915 * 10-6 (F) to implement a cutoff frequency 0.5Hz low-pass filter. e.2(N) (4 pts) Please use Isim to simulate the filter signal Vo3 (t) and plot Vi3(t) and Vo3(t) in the same figure.

Answer 1

Solusiny In order to pass the 0.1th component and fills component we needed to design the the lotte frequency filter as shown below a) tome vin (a) Time domain equivalent circuit (b) frequency domain equivalent circuit

Now, in figby Appy woltage ander arrous Free branch - jwe | Rtje) %= vin The magnitude of teja) - Migosl = JHCorey 2 Yo obrain we in equating to Homan at wawe Vit URCO2 squwning both sides + 2 = 1+(WRC)? {we= é radisec 2 RC for c= 1.5915 uf fe= 0.542 valce of 'R' required - r R= . . dicte R = 1 = 2x1052 2 x 0:15 X1.5915X100 10% R=0.2m2 . Using MATLAR we can pest the signal -

MATLAB CODE FOR SOLUTION clc close all clear all syms 3 R=200000; C=1.5915*10^-6; sys=tf ( [01],[(R*C) 1]) ; Define transfer function of the filter t =0:0.001:10; $ Time Vector Vi3 = 1*sin (2 pi*0.1*t) +1*sin (10*2*pi*t); Forcing Function Vo3 = lsim (sys, Vi3, t); Calculate output response figure (1) plot(t, Vi3, 'b') hold on plot(t, Vo3,'g') legend('input Vi_ _3','output Vo_ _3'); grid on

input Viz output Voz 1 HET -------------- FAHARI ---------- DOTATE -0.5 LKW WNMAALAALAAN -1.5 Steady state input and output response curve obtained using MATLAB