Question

Problem 1. Electrical Signal Filters Find the transfer function, G(s) = V., for each of the following systems. For full credit, use either impedance methods or the differential equation method. I would recommend doing both to prepare for the exam. a) Low-pass filter W R V(O) с V.O b) High-pass filter H! VO) V.) c) Band-pass filter HI R VO) C C2 = R2 V. ()

Answer 1

3 a) Impedance method R Vols) Vils) Applying Voltage divison rule Vols) = Ve(s) + . Vols) V (s) RCS + 1 bietet Differential eauation method R Volt) 5 i (4) Applying KNL to the loop Vs (t) = V6 (4) + i (+)R

Since it is the curerent furough the Cape Colore covole) Corise Ĉ () = dt Substituting in 6 V (t) V. (2) tre dvola) dt Applying Laplace dream forem to both sidly Ve (s) a Vo(s) +RCS Vo(s) Vols) Vals) RCS + 1 С Vn Volt) Impedance method Yes VE (3) R Vols) R (Voltage division Rule VL - V () R+ Ls RCS Vo (s). Vals) =; RCS + )

Differential equation method VSCH R Vo () ilo + KVL to the loop Applying Vs1+) = Volk) + = Since itt) is the leveret flowing through the registore i (t) dt с 714) = Volt) R Volt) + Vs It) še vous de Applying Laplace freausforem ation to both sicles RC . Vs (3) = Vo(s) + t Vols) a Rc No(s) Vi (s) s 1 It I RES Rest 1 RCS th R8 Volt) GI

impedance method Ri GS Ngle) R₂ Vole) C₂8 + V. (S) = 1 R2 Ve.cs). es (ab )=(2, 4 ás) ) CS 1 R₂ = X R₂ cs was the R₂ RGS+1 V. (5) V 15) Rawie w sid!!!! R₂ C2S + 1 R2 R245+1 + R, GS ti cis R₂GS RiRG2+ (A,G,ARGA GR) + +1

ditterential caration suchte ing 41 VM) ç dvolt dt Applying a kve on our loop vu) = vw = = Secunde + info iu = ication and is volt Rz V:(0) = Volt) + < scade.com You) de (solar, en À VOR Applying Larlau frecans fermention to both side Vs (1) z V. (1) + V, (s) + Vo(s) + GS Vols) + evolu) Vo(s) TRGS+ + - Voll) + RGS 1 Vils) LA + RGS FRGS + hu

RGS + R₂ C2 S + I + R, 4 Polys + RGS Volu Valo) RGS 1) R2GS R, GR 2 C2 ² + (R, G + R₂ (2+ R24)S +) VI