Question

Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 112 192 112 VAD 1 H 1F Figure 1

Answer 1

Q in lu + Vis) IH If IH Vort) Lay Deteo mise the state space Taking Laplace-transform. lu representation Ta IL lu Iw Is Hill + Vich eeee 12 eeee hl Tois) Wote kel @ node 1, 2 Iz + I3 Vi (8) - 4 %-o er, a f L V;s)- v 2 teri-2 (5) 2 tu, tu, L. Vi (5) a (2+ & Jr, a la ris Again, write kel@ node U₂ Iza 14+ Is

ح) - ه- V - 0 ( و ) ح) - = (2 ح/ ) (+/ حا / ا ة + . f | = v ( 5+ - /+ک الم (ره) + (۱) ) 5 ,۷ (+1) 1+1+5+5 tys د / 2 ) /*/) 2 + 2 + 2ی V, * 2 ( s(541) رشید from eam is & cris ا - (22) (1) = ( : (۴/ 2 2م ) - (دم) 22 /// د (2) :t (1+ 20ی يتر و م 3ی د U .'. 2+ 6 +2ی 4 2ی (5) . (??

Now, Appusing voltage- division to find ( م / /ا 2 د (ک) /.. 7 7 (+/) estes د ( ی) ملخ . ام خامنه ای و مو + 9 ) دی 3ی (2) = 22 هی هی هی هی هی لای لای ه (5) مک 7 158 159/ 1433 + + ) 2ی می lors) د . 2) ح 8 + 2 2ی 0 s2 +ه می Hence, the state-space represents tion is. ? Q 10 0 O 7 Q X2 ) ( [2] + | * } -/o 5 - 2

24 & I 1 [o]o ar * Y-too (6) Fransfer functions Vo() Tif.. 52/ set 1) '. 7.7.2 34+553+ los²+85+2