Question

a. (10) For the circuit below, draw the s-domain equivalent circuit and show that H(S) = 2 2 . 2321H 0.5F V b. (10) Using Inverse Laplace Transforms, find the impulse response (1)

Answer 1

Tal an - Vi FO.SF V Converting circuit to s-domain IL) two- - 22 IS + - Vils) Vous) 1 - 0.5 Vils) - IU) 2+5+ oogs] Vous I ) Vous Viv) IL) 10:55 IV) (2 + s + %.55] H ) = 2/3 25+52 + 2 H6 = Voll vils) 2 52+25+2 T

(6) HY) - 2 s2+28+2 2 (5+152 + 1 we know that e-at sin Wat ut) - Lot wo (sta) two? so 2_ (5+1 2+1 I.2oT, I.LT 2 e-t sint UCH) ht) = 2 e-t sint UCH)

(6) What is impulse response Impulse response gives the characteristics of an LTI system. 37 Impulse gresponse of a LTI system is Zined for a given system. It does not change with change of input. Impulse response is generally a small duration time domecin siqnal. Impulse response of the system is given by the system transfer function. gmpulse response of a system is zero state response. (d) Vit = 2e-3t applying laplence transform Vils) = 2 | e-at Lot L ) 5+3 1 ste HIS): Voy). vils) .2 +2 5 2

Vous) Vils). 2 (52+25+2) St3 ²4 25+2 (5+3) (32+25+2) Vols : A. & BSTC 5+3 824 25+2 A($+ 25+ 2) + (BS+C)(5+3) (5+3)($2+25+2) 4 - (5+3) (3² + 2+2) As?+ 2 AS + 2 A + Bš? + 3 BS +C5 +3. (5+3) (+25+2) ,2A +30 = dya . A+B=0, 2 A + 3B+C =0 By solving this A = 0,8 , B=-0.8, C=0.8 " So, Vol). 0.8 3+3 -0.85 tong 52+25+2

No + 0.8 5+3 0.8 -0.85-0-8+0.8 (5+1)2+1 adding and subtrafeting 0-8 = 0.8 - 0 - :8 (Stv? 0.8(6+1) 5+3 (5+1241 Stult, - applying Inverse Z-transform Volt) = Qes ud ooge-3t ut) + 16 e-t sint ult? -0.8 e-t cost uct) Volt) : 0.8 [ 2-3+ + 2e-tsint - et cost Juet) volts e convolution h(t)- impulse response of system a(t) input of the system. y (t) a output of the system Laplace Transform of h(t) LoL, HUS) act) 2013 Xu), y(t) 2013 YUS) than y(t) = n(t) * hlt) n(t) . Londblution that taking laplece transform than it becomes YU)= XUS) X HU) s multiplication.