Slide 1EE100 Summer 2008 Bharathwaj MuthuswamyChapter 5• OUTLINE– Op-Amp from 2-Port Blocks– Op-Amp Model and its Idealization– Negative Feedback for Stability– Components around Op-Amp define the Circuit FunctionSlide 2EE100 Summer 2008 Bharathwaj MuthuswamyThe Operational Amplifier• The operational amplifier (“op amp”) is a basic building block used in analog 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 3EE100 Summer 2008 Bharathwaj MuthuswamyHigh Quality Dependent Source In an AmplifierV0depends only on input (V+− V-) )VV(AV0−+−=+−AV+V−V0Differential AmplifierAMPLIFIER SYMBOL+−+−V0AV1+−V1RiCircuit Model in linear regionAMPLIFIER MODELSee the utility of this: this Model when used correctly mimics the behavior of an amplifier but omits the complication of the many many transistors and other components.Slide 4EE100 Summer 2008 Bharathwaj MuthuswamyOp 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 +V –Inverting input v2Non-inverting input v1positive power supplynegative power supplyv0outputSlide 5EE100 Summer 2008 Bharathwaj MuthuswamyModel for Internal Operation• A is differential gain or open loop gain• Ideal op amp– Common mode gain = 00ioARR→∞→∞=v1v2Ri+–RovoA(v1–v2)i1i2io+_• Circuit Model()121212,2(),0cm docmcmddocmvvvvvvvAv AvSince v A v v A+==−=+=− =Slide 6EE100 Summer 2008 Bharathwaj MuthuswamyModel 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 terminalsv1v2Ri+–RovoA(v1–v2)i1i2io+_• Circuit ModelSlide 7EE100 Summer 2008 Bharathwaj MuthuswamyOp-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.Negative feedback ⇒ Stabilizes the outputR2R1−+V0VINWe can show that that for A →∞and Ri→ ∞,121IN0RRRVV+⋅≅+−+−V0AV1-+V1RiR2Circuit ModelR1VINStable, finite, and independent of the properties of the OP AMP !Hambley Example pp. 644 for Power SteeringSumming PointSlide 8EE100 Summer 2008 Bharathwaj MuthuswamySumming-Point Constraint• Check if 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 9EE100 Summer 2008 Bharathwaj MuthuswamyIdeal Op-Amp Analysis TechniqueAssumption 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 CurrentsApplies only when Negative Feedback is present in circuit!Slide 10EE100 Summer 2008 Bharathwaj MuthuswamyIdeal Op-Analysis: Non-Inverting AmplifierAssumption 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.021=−+RvvRvoutinininoutvRRRv121+=KCL with currents in only two branchesNon-inverting AmplifierVINappears hereYes Negative Feedback is present in this circuit!Slide 11EE100 Summer 2008 Bharathwaj MuthuswamyNon-Inverting Amplifier• Ideal voltage amplifier_+vin+-R2R1RLv2v012 1202221121,02.()(0)()ovininoininvClosed loop gain AvvvviiUse KCL At NodevvviRRvRRAvRvInput impedancei==== ==−−==+===→∞2Slide 12EE100 Summer 2008 Bharathwaj MuthuswamyIdeal Op-Amp Analysis: Inverting AmplifierR2I2VOUT-VRR1RLVIN021=−+−RVVRVVOUTRINR()RinROUTVVRRVV −−=12Voltage is VROnly two currents for KCLInverting Amplifier with reference voltageYes Negative Feedback is present in circuit!Slide 13EE100 Summer 2008 Bharathwaj MuthuswamyInverting Amplifier• Negative feedback Æchecked• Use summing-point constraint12 1222122110, 02.()( )ovinin outooinvClosed loop gain Avvv iiUse KCL At Nodevv v viRRRvvRvInput impedance Ri==== ==−−===−==Ideal voltage source – independent of load resistor_+vin+-R2R1RLv1v0v2i2Slide 14EE100 Summer 2008 Bharathwaj MuthuswamyVoltage Follower_+vin+-RLv2v0210222112 2110()(0)()11oinRRvvviRRvRR RAvR R=→∞−−==+== =+=Slide 15EE100 Summer 2008 Bharathwaj MuthuswamyExample 1• Switch is open121 313124502502,0 0()00()1,inininoininvvi ivvivvviiRvvivvvRvARv==→=−=→== →=→=−=→==== →∞v1v2vin+-RRLv02R_+i1i2Ri5i3i4Slide 16EE100 Summer 2008 Bharathwaj MuthuswamyExample 1• Switch is closedv1v2vin+-RRLv02R_+i1i2Ri5i3i412 1 32024500, 0 0() ()1,2ininoininvv i ivv vviiRRvvvRARv===→=−−===−=−==− =Slide 17EE100 Summer 2008 Bharathwaj MuthuswamyExample 2• Design an analog front end circuit to an instrument system– Requires to work with 3 full-scale of input signals (by manual switch): V– For each input range, the output needs to be V– The input resistance is 1MΩ0 1,0 10,0 100±± ±∼∼ ∼010±∼_+vinR2R1RLv2v02bacvbvav1211111(1 )oinabinabcainabcRvvRv v Switch at cRRv v Switch at bRRRRv v Switch at aRRR=+=+=++=++Slide 18EE100 Summer 2008 Bharathwaj MuthuswamyExample 2 (cont’d)21212121110 (1 )1(1) 0.10.1 (1 ) 0.0110 , 90 , 9009in a b cvab abvabc abcaavabc abcabcRRRRMRMax A Switch at cRRR RRRA Switch at bRRR R RRRRRRA Switch at aRRR R RRRRkRkR kRR=++=Ω==+++== + ∴ =++ ++== + ∴ =++ ++∴=Ω=Ω= Ω=Slide 19EE100 Summer 2008 Bharathwaj MuthuswamySumming Amplifier_+v3+-v0R1R2+-+-R3R0v2v1Slide 20EE100 Summer 2008 Bharathwaj MuthuswamyDifference Amplifier_+v2+-v0R4R1+-R3R2v1Slide 21EE100
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