Question
Problem 4.1 For the circuit shown in Fig. 4.1, there is no initial energy storage. Draw...
Problem 4.1 For the circuit shown in Fig. 4.1, there is no initial energy storage. Draw and label the circuit in the s- domain and use it to determine H(s)=V_(s)/Vsrc(s). Using H(s) and given: (a) vsrc(t)= e'u(t) V, find vo(t) using the inverse Laplace Transforms. (b) vsrc(t)=2 cos 2t V, determine the steady state output volt). 0.502 122 1н + USRC 1 F V, 22 VO Fig. 4.1
Answers
Circuit diagram [s-domain] Apply Nod al At, A 0.5 Vn 1r S VA = Vn im Vs(s) 2r S Vols) S Vnxs + Vn-US + Vn-Vo = 0 Vn[s++1] - Vstuin Va[s1s+i] = SVstvo - Apply KUL; VS = 0.5 Va tvo Vx=(Us - Vo) x2 put in equ (Us-Vo) x2 x (s7s+) = s Vs + Vo Vs [25*+s+2] = V[25+25 +3] Vo = 2 s²+2573 Vs 25+5+2 H(S): 25+25+3 25+5+2 @j Vs (+)- etult) => Vs(s): 1 sti A + BS+C .: Vols): 25?+25+3 2s+s+2) XS+ A SI 25+5+2. put s:-1,A=1 B+c=1 S: 1, S-09 C=1 B=00.5 .: Vols) = 1 + 1 I + S+1 sti 252+5+2 8+4)*69 IC Take Inverse Laplace. Volt) [et --[et sin (1934) 2025t]4[+] Property used: Shifting 1 x(s-so) → esoty(t) lúj sin(at) → 52492 2 Vs(t) = 2 Cos (2+) L = 2 rad /sec 2 + H(w) = -2w2+3+2jw -2 w2+2 + jw Magnitude) (3-8) +9 ✓ 2-8)²+(22 => 1.0124 Angle » tano (4 tan- " (2) (3-8 2-3 - 20:22° :: Output ; Vo(t) = -2X1.0124 cos (2t -20-22°) volt): 2.0248 Cos (2t -20.22°)
![Circuit diagram [s-domain] Apply Nod al At, A 0.5 Vn 1r S VA = Vn im Vs(s) 2r S Vols) S Vnxs + Vn-US + Vn-Vo = 0 Vn[s++1] - V](https://i.imgur.com/Y9v8c4n.png)
![0.5 .: Vols) = 1 + 1 I + S+1 sti 252+5+2 8+4)*69 IC Take Inverse Laplace. Volt) [et --[et sin (1934) 2025t]4[+] Property used](https://i.imgur.com/MxNythP.png)
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