Question

8. Consider the circuit: t=0 212 f(t)t 222 11 Pilt) 1F yt (a) Show that the transfer function of the circuit for t > 0 is † (s) = F(*) 452 +55+2 (b) What are the characteristic modes of the circuit (c) Determine the response y(t) for t > 0 if f(t) = 1, y(0-) = 1 V and i(0-) = 0.

Answer 1

Solution Vi ar for txo R2 flu If Tc Y/H) je yn) Z11) Les Zeld). ny Vils) 2 VIS) 2) Vils). (1+25) Y21) - le SR₂C Kee @VI SCY) + V-F V LJ 1 20 2 {s + ( 2 + ) ( 1+25)}Y15) = { [251 (114) (1 126) JYLL) FLS) 2) ns Y(s) FID 2 2+ 45² 455. 25+ 1 + 4 + 125 SP HI) YIS) FU) 45²15812.

Charaden egn 4 54 55 12 20 2 s= (-0.625 +1 0.33) Due to fit) flHal sest ta h B 2 1 so Y(S) 2 F(S) HIS). 452 45312 YO. ] 4 4 [st sur + [ en deur jou levou on) si (S+0.625+00:33) (5+0623-j 0.25) s+ 0.625-j 0.21 S+062 +10.3] 3. & e 110-627-30-33) -$10.65 tjonit e ant -0.6257 (10.33t - ej 0.33t - 2x3 1922-067 2) 28-0.6257 am 0.33t Que to enchal condition Now clo-) = 0 @tro 4 10.1) 1V so (c(0)=0 ý (0.00 so

T A (-0.625) e-0.6257 50 ylch A 6-0.62.17 fm (0.33t+0) @ tzo, y (o)- 1 60 Almor 1 0 A 0-0.625 € 0:33 froy (0.33410) dm 10.23170) @tro, ý (0)2 41 x 0.13 lond - 0.625 Ah and 20 0.33 losar 0.625 fm & ) Q: 2173 so A 2 2.1417 YH 2:1417 0:6287 fm (0.336 +27-33°) So So tolas off is Yalta y It) from 0 & ylts from 0.75 e 0.625+ Im 0.33+ + 2417 60.5t fm 10.324 50 YIH +27-82") A