Question

Problem 1: /25 For the circuit shown below, use frequency-domain circuit analysis techniques to determine (a) the voltage transfer function Ho) of the circuit; (b) the magnitude response H(o) of the circuit; and (c) the phase response (0) of the circuit. (d) Based on the results of parts (a) - (c), identify the type of filter circuit shown. R + Vin(t) llll L Vout(t)

Answer 1

Solution : as considering s-domain analysis, R H * ot L Vin Vo Om s-domain, impeden dence of L= (L5) 11 of R = (R) so, Z = impedenee seen from inputside. Z= (R+ Ls) so, Vo = I (15) = Vin Z LS ES 5V; Vo Vin - SH(s) RALS Replacing sjw (jLW) LR+ < Ans) HIW) {R + fL WE

b) Magnitude of HW) (H(W) 1 = (LW) VR²+(2W) 2 Plotting lHWI vs (w) in MATLAB

Plot: (Considering L =1H , R = 1 ohm)

Bode Diagram Magnitude plot in log scale -10 -15 -20 Magnitude (dB) -30 -35 -40 -45 -50 102 10 10 104 100 Frequency (radisec)

قيا 20 tant (LW) - tant R Phase Angle of t(W) > ant (2) = (2) - tanit ( en ) Acnee, plotting to us w in MATLAB 2

Plot:

90 60 Phase (deg) 30 10 10 10° 10 102 Frequency (rad/sec)