EE201 Lecture 29 P 1 First Order Op amp Circuits RC Capacitors can be added to op amp circuits for increased control of circuit outputs However there are subtleties concerning this approach 1 All resistors do not determine time constant 2 Op amp circuits may deviate from ideal response 3 Stray capacitances a capacitance between a conductor and ground may influence results EE201 Lecture 29 P 2 Example Find vo t for the op amp circuit shown assuming ideal op amp behavior C ic R iR vo t v s Input characteristics for op amp v v 0 Initial condition for capacitor voltage vc 0 vc 0 vo 0 vo t vc t vc 0 ic t iR t 1 t ic d 0 C Property of ideal op amp i 0 1 EE201 Lecture 29 iC t vs t R P 3 put this into 1 t 1 v d vo t vc 0 0 s RC xample Find vout t assuming vc 0 0 1k 0 1 F 5u t V v t 1k 1k Step 1 Find voltage across capacitor vout t v Solution for voltage across capacitor vc t vc vc 0 vc exp t RTHC vout t EE201 Lecture 29 P 4 Since i 0 resistors and capacitor are in series RTH 2 k RTHC 0 2 x 10 3sec vC 0 vC 0 0 vC 5V vC t 5 5e 5000t V Step 2 Find current through 1k resistor between capacitor and ground Differentiate voltage across capacitor d vC t iC C 0 1 F 5000 5e 5000t dt iC t 2 5 x 10 3 e 5000t A EE201 Lecture 29 Step 3 Calculate vout t from iC t vout t 1k iC t vout t 103 2 5x10 3 e 5000t vout t 2 5 e 5000t Because properties of op amp v v vout t does not depend on load resistor P 5 EE201 Lecture 29 P 6 Example Find vout t for the op amp circuit shown assuming ideal op amp behavior i1 vin t 0 01 F 100k if i2 100k 100k Step 1 Realize v vTherefore i1 i2 if i1 i2 vin t 2R Also v v vin 2 vout t EE201 Lecture 29 P 7 Step 2 Find feedback current from capacitor equation vin if C d dt d dt vout vin 2 vout t vin t 2 2RC Step 3 Solve for vout t d vout t dt d vin t 2dt Integrating vin t vout t 2 vin t vout t 2 vin 2RC 1 2RC tt v d 0 in tt 500 0 vin d
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