Question

Problem 2. Op-amp circuits to ODEs Find the governing equation(s) for the following op-amp circuits. Then find the transfer function, G(s) = Vol. Feel free to either use the impedance method or the time-domain methods. a) a R: R 1. R b) R C HE 1 M

Answer 1

RI w @ given circuit is RI Vo VOCs) V2 + V R V; (5) cs For an ideal op Amp the both input terminals have Level. so that v=V2 as shown same voltage in Figure Nodal Equation at node V2 gives V2 12-V (5) R + v =0 CS vi(5) R *+cs) Vz= v;($) { it.com] Nodal Equation at node vi gives V, RI + V;-Vo(s) RU VoCS) we know "=V2 Ri mi látkou) r(s) G+ Gtesi) [Botha vics) { itcas] Vols) Ri - Vo(s) 2 V.CS) GCS) Vics) IACRS CS Scanned with CamScanner

6 The given op - Amp circuit is 25 R2 At CI RI th Vo(s) Vils) CIS an ideal For Op-Amp Vi=v2 but given V2 SOV than Vi=ov, Nodal Equation at node vi giver (: Visov) Rit V - Vics) + V, Vols) R2 t CIS C₂S V:05) Ritius --Vo(s) R2t. (2S Cis. It GRIS cas vics) s ] vo(s) [ it C₂ R25 Vols) = GIS) -Gis (i+C2 R25) C2 S (it Cris) Vies) G15) -co (It C2 R25) C2 (1+CRIS) CS Scanned with CamScanner