EE40Lecture 23Venkat AnantharamThe Operational AmplifierOp Amp TerminalsModel for Internal OperationModel and FeedbackOp-Amp and Use of FeedbackSumming-Point ConstraintIdeal Op-Amp Analysis TechniqueVoltage FollowerSlide 1EE40 Spring 2008 Venkat AnantharamEE40Lecture 23Venkat Anantharam3/21/08 Reading: Chap. 14: Operational Amplifiers.Slide 2EE40 Spring 2008 Venkat AnantharamThe 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 cascadingSlide 3EE40 Spring 2008 Venkat AnantharamOp 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 v2Non-inverting input v1positive power supplyv0outputV –negative power supplySlide 4EE40 Spring 2008 Venkat AnantharamModel for Internal Operation•A (or Ad or AOL) is differential gain or open loop gain• Ideal op amp– Common mode gain = 00ioARR→∞→∞=• Circuit Modelv1Ri+–RoA(v1–v2)i1i2io+_vov2()121212,2(),0cm docmcmddocmvvvvvvAv AvSince v A v v A+===+=− =v−Slide 5EE40 Spring 2008 Venkat AnantharamModel and Feedback• Negative feedback– 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• Circuit Modelv1v2Ri+–RovoA(v1–v2)i1i2io+_Slide 6EE40 Spring 2008 Venkat AnantharamOp-Amp and Use of FeedbackA very high-gain differential amplifier can function in an extremely linear fashion as an operational amplifier by using negative feedback.R2R1−+V0VINSumming PointNegative feedback ⇒ Stabilizes the outputWe can show that that for A →∞and Ri→ ∞,Stable, finite, and independent of the properties of the OP AMP !121IN0RRRVV+⋅≅Slide 7EE40 Spring 2008 Venkat AnantharamSumming-Point Constraint• Check if we are under negative feedback–Small viresult in large vo–Output vois 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.Slide 8EE40 Spring 2008 Venkat AnantharamIdeal Op-Amp Analysis TechniqueApplies only when Negative Feedback is present in circuit!Assumption 1: The potential between the op-amp input terminals, v(+)–v(-), equals zero.R2R1−+V0VINEXAMPLEAssumption 2: The currents flowing into the op-amp’s two input terminals both equal zero.No Potential DifferenceNo CurrentsSlide 9EE40 Spring 2008 Venkat AnantharamVoltage Follower_+vin+-RLv2v0210222112 2110()(0)()11oinRRvvviRRvRR RAvR R=→∞−−==+==
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