Question

9.7 For the circuit shown in Fig. P9.7, determine (a) the transfer function H = V./V; and (b) the frequency w, at which H is purely real. Figure P9.7: Circuit for Problem 9.7.

Answer 1

Vin(s) Soluhon ? ay By converting the given the circuit we can conread find the H(S) = Vols) Virks ) Hou by applying voltage division law . Volpině (R271 (s) 11 () R1 +(R2)/18416) Sr R25L LR2 +SL ) "ciruit in naplace domain" vinas) Rys R2ts2 Rut er )/eriste + c)] et de contato [*. ( a 19 63] entrance A)] 1 LR2 C CR2152) SORI CR2FSL) C CR2FSL) + R2 ( R2 + S2+ SCR2SL) CCREASL) (R2+ SL + SC R2 SL) HS) = Vols) = LR2 ( R2 + 5Lt S²R2L2) 2 R2 ( Vin(s) (R2+54) (se?R, R2 + 52c2R1L) + (R2Z +SLR2+ SCR52) |H(S) = Vols) - S2RŽLC + SL2R2 + BLR,? Vin(s) S3 c²L²R14 S²(C²R, R241 & CRq²L) + 5 (LR2 + C² R1 R22) + R₂2 Lo Required Transfer functions.

(b) Nowfor getting H(5) Pweel, Recel: - Tank pakt - A purely Real Then Y6) = 5 + sctke ohne Z6) = t'sC++ - Estreet SLA Ngen zow) = La sem e t iure] иі z W) = P W L R2 ( R2-W2LR - GWL) 7 - L(R-W²L(P2) ²+ (WL) 2 T Now for making zie) Real then, Imag [zow)] = 9WL (R,W2LCR2) =0 so wzo er ² = FLER Tw=(ſheh