EE201 Lecture 28 29 P 1 Thevenin Equivalent Circuits with Op Amps and First Order Op amp Circuits RC Thevenin and Norton Equivalent Circuits for Op Amps Consider the following op amp circuit Assuming ideal op amp behavior find its Norton and Thevenin equivalents i 2k 200 10V i200 2k 1k A 3k vOC EE201 Lecture 28 29 P 2 Step 1 Find the node voltage VA v v 0 i200 10 V 200 0 05 A i2k VA 0 2000 i200 VA 100 V Step 2 Find vOC Using voltage division vOC 3k 4k 100 V 75 V Step 3 Find iSC From Ohm s law iSC VA 1 k 0 1 A Step 4 Calculate RTH from vOC and iSC RTH vOC iSC 750 EE201 Lecture 28 29 The Norton equivalent network is 0 1 A 750 The Thevenin equivalent network is 750 75 V P 3 EE201 Lecture 28 29 P 4 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 28 29 P 5 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 28 29 iC t vs t R P 6 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 vout t 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 EE201 Lecture 28 29 P 7 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 28 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 8 EE201 Lecture 28 29 P 9 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 2R Also v v vin 2 vout t EE201 Lecture 28 29 P 10 Step 2 Find feedback current from capacitor equation vin d if C 2RC d dt vout vin 2 vout vin 2 dt Step 3 Solve for vout t d vout d vin dt vin 2dt Integrating vin vout 2 vout vin 2 2RC t 1 2RC v d 0 in t 500 0 vin d
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