EE40 Lecture 23 Venkat Anantharam 3 21 08 Reading Chap 14 Operational Amplifiers EE40 Spring 2008 Slide 1 Venkat Anantharam The Operational Amplifier The operational amplifier op amp is a basic building block used in circuits Its behavior is modeled using a dependent source When combined with resistors capacitors and inductors it can perform various useful functions amplification scaling of an input signal sign changing inversion of an input signal addition of multiple input signals subtraction of one input signal from another integration over time of an input signal differentiation with respect to time of an input signal analog filtering nonlinear functions like exponential log sqrt etc Isolate input from output allow cascading EE40 Spring 2008 Slide 2 Venkat Anantharam Op Amp Terminals 3 signal terminals 2 inputs and 1 output IC op amps have 2 additional terminals for DC power supplies Common mode signal v1 v2 2 Differential signal v1 v2 V Inverting input v2 Non inverting input v1 positive power supply v0 output V negative power supply EE40 Spring 2008 Slide 3 Venkat Anantharam Model for Internal Operation A or Ad or AOL is differential gain or open loop gain Ideal op amp Circuit Model A Ri v1 Ro 0 i1 Ro io Common mode gain 0 vcm v1 v2 2 Ri v2 vd v1 v2 vo Acm vcm Ad vd i2 vo A v1 v2 Since vo A v1 v2 Acm 0 EE40 Spring 2008 Slide 4 Venkat Anantharam Model and Feedback Negative feedback Circuit Model connecting the output port to the negative input port 2 Positive feedback connecting the output port to the positive input port 1 Input impedance R looking into the input terminals Output impedance Impedance in series with the output terminals EE40 Spring 2008 v1 i1 Ro io Ri v2 Slide 5 i2 vo A v1 v2 Venkat Anantharam Op Amp and Use of Feedback A very high gain differential amplifier can function in an extremely linear fashion as an operational amplifier by using negative feedback R1 R2 VIN V0 Summing Point Negative feedback Stabilizes the output We can show that that for A and Ri V 0 V IN EE40 Spring 2008 R1 R 2 R1 Stable finite and independent of the properties of the OP AMP Slide 6 Venkat Anantharam Summing Point Constraint Check if we are under negative feedback Small vi result in large vo Output vo is connected to the inverting input to reduce vi Resulting in vi 0 Summing point constraint v1 v2 i1 i2 0 Virtual short circuit Not only voltage drop is 0 which is short circuit input current is 0 This is different from short circuit hence called virtual short circuit EE40 Spring 2008 Slide 7 Venkat Anantharam Ideal Op Amp Analysis Technique Applies only when Negative Feedback is present in circuit Assumption 1 The potential between the op amp input terminals v v equals zero Assumption 2 The currents flowing into the op amp s two input terminals both equal zero No Potential Difference R2 R1 No Currents VIN V0 EXAMPLE EE40 Spring 2008 Slide 8 Venkat Anantharam Voltage Follower v0 v2 vin RL R2 0 R1 v0 v2 v2 0 i R2 R1 vo R1 R2 R2 A 1 1 vin R1 R1 EE40 Spring 2008 Slide 9 Venkat Anantharam
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