Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01Lecture 12: October 10, 2001Dependent Sources and Ideal Op AmpsA)Dependent Source ConceptB) Four Basic Dependent Source TypesC)Use in Amplifier ModelsD)Feedback and Ideal Op-Amp ModelE) Examples of Op-Amp CircuitsReading: Schwarz and Oldham 4.1 and 4.3 with ideal Op-Amp analysis onlyThe following slides were derived from those prepared by Professor Oldham For EE 40 in Fall 01Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01Dependent Voltage and Current SourcesA linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage. Example: you watch a certain voltmeter V1and manually adjust a voltage source Vsto be 2.5 times this value. V1+-Circuit ADigital VoltmeterVs=2.5 V1+-Circuit BYou set VsCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01Dependent Voltage Source ExampleThe voltage Vssource depends linearly on V1 (because you set it to 2.5 times V1, no matter what V1is. If you and the voltmeter are placed inside a box, the box functions as a voltage-dependent voltage source. V1+-Circuit ADigital VoltmeterVs=2.5 V1+-Circuit BYou set VsNote that the red box has two wires in (to read the input voltage) and two wires out (to deliver the output voltage).voltage-dependent voltage sourceCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01Dependent Voltage and Current Sources• A linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage. • We can have voltage or current sources depending on voltages orcurrents elsewhere in the circuit. A diamond-shaped symbol is used for dependent sources, just as a reminder that it’s a dependent source.Circuit analysis is performed just as with independent sources.+-cdVcd+-V= Avx VcdHere the voltage V is proportional to the voltage across the element c-d .Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01GmVcdVoltage-controlled current source … I = GmVcdAiIcCurrent-controlled current source … I = AiIc+-RmIcCurrent-controlled voltage source … V = Rm IcThe 4 Basic Linear Dependent SourcesVoltage-controlled voltage source … V = AvVcdAvVcd+-Parameter being sensedConstant of proportionalityOutputCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01WHY DEPENDENT SOURCES?EXAMPLE: MODEL FOR AN AMPLIFIERV0depends only on input (V+− V-) )VV(AV0 −+−=+−AV+V−V0Differential AmplifierAMPLIFIER SYMBOLinput outputAn actual amplifier has dozens (to hundreds) of devices (transistors) in it. But the dependent source allows us to model it with a very simple element.EXAMPLE: A =20 Then if input (V+-V-) = 10mV; Vo= 200mV.Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01EXAMPLE OF THE USE OF DEPENDENT SOURCE IN THE MODEL FOR 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.Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01OP-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−+V0VINEXAMPLEWe can show that that for A →∞and Ri→ ∞,121IN0RRRVV+⋅≅+−+−V0AV1-+V1RiR2Circuit ModelR1VINStable, finite, and independent of the properties of the OP AMP !Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01IDEAL OP-AMPS 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 CurrentsCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01IDEAL OP-AMPS ANALYSIS EXAMPLE #1Assumption 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 hereCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01IDEAL OP-AMPS ANALYSIS EXAMPLE #2R2I2VOUT-VRR1RLVIN021=−+−RVVRVVOUTRINR()RinROUTVVRRVV −−=12Voltage is VROnly two currents for KCLInverting Amplifier with reference voltageCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 12: 10/10/01 A.R. NeureutherVersion Date 10/09/01THE RAILS The output voltage of an amplifier is of course limited by whatever voltages are supplied (the “power supplies”). Sometimes we showthem explicitly on the amplifier diagram, but often they are left off.+−AV+V−)VV(A−+−V0=Differential AmplifierIf the supplies are 2V and 0V, the output cannot swing beyond these values. (You should try this experiment in the lab.) So in this case we have upper rail = 2V, lower rail = 0V.The rails cannot be larger than the supply voltages. For simplicity we will use the supply voltages as the rails.
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