Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01Lecture 13: October 15, 2001Circuit Analysis with Dependent SourcesA)Node EquationsB) Equivalent Sources C)Amplifier Parameters:Gain, RIN, ROUTD)Non-Ideal Op-Amp ModelReading: Schwarz and Oldham 4.1 - 4.2The 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 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01GmVcdVoltage-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 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01EXAMPLE OF NODAL ANALYSIS WITH DEPENDENT SOURCESStandard technique, except an additional equation is needed if the dependent variable is an unknown current as here. Note Vb is redundant.R4 I2R2 I R3R1VaVb+-RmII2I = Va / R2+ (Va-Rm I2)/ R3and I2= Va / R2Solving:I = Va(1/R2+ 1/R3-Rm/R2 R3)So Va = IR2 R3/(R2+ R3- Rm )Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01THEVENIN EQUIVALENT WITH DEPENDENT SOURCESMethod 1: Use Vocand Iscas usual to find VTand RT(and INas well)This method also works when computing incremental signals such as a change in the source VS(given by ∆VSor vS) produces a change in VINor VOUT, (given by ∆VINor ∆VOUT also written vINand vOUT), and their ratio called the small-signal gain (∆VOUT/ ∆VS) or (vOUT/ vS)See examples in text (such as Example 4.3).Method 2: To find RTby the “ohmmeter method” turn off only the independent sources; let the dependent sources just do their thing.Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01EXAMPLE CIRCUIT WITH MULTIPLE SOURCESCircuit with independent sources turned to zeroRbVs RaRsVINVbGmVIN + - VDD-+++--VOUT VDD-+RORL Rbvs RaRs vIN GmvIN + - ++ - -vOUT RO RL Original circuitNote RLhas been rotated down.Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01EXAMPLE CIRCUIT: GAIN = (∆VOUT/ ∆VS)=(vOUT/vS)Input voltage divider and output current dividerreduce the gainRbvs RaRs vIN GmvIN + - ++--vOUT RORL babaINRRRRR+=sINSININvRRRv+=SLOLOINSINmLOLOINmOUTvRRRRRRRGRRRRvGv++−=+−=Copyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01Rbvs RaRs vIN GmvIN + - ++--vOUT RORL EXAMPLE CIRCUIT: INPUT/OUTPUT RESISTANCERINROUTbabaINRRRRR+=OOUTRR =Can circuit design improve RINand ROUT or do we need better devices?DeviceOutput does not feed back to inputAssume vS= 0 => vIN= 0 => no current in dependent sourceCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01EXAMPLE CIRCUIT: INCREASED INPUT RESISTANCERINvTEST vIN +-+-GmvIN +-vOUT = 0 ROiTEST RE vE Add resistor REAnalysis: apply iTESTand evaluate vTEST00=−−+TESTINmTESTEEEiRGiRvRvTESTININiRv =ETESTINTESTviRv+=KCLEINmINTESTTESTRRGRiv)1( ++=Check for special case for R0 infiniteIntuitive Explanation:REputs RINon a node whose voltage increases in response to current in RIN.The output has been assumed to be shortedFinish this in the homeworkCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01EXAMPLE CIRCUIT: INCREASED OUTPUT RESISTANCERINv = 0 vIN +-+-GmvIN +-vTEST ROiTEST REvE Add resistor REAnalysis: apply iTESTand evaluate vTESTUnknowns: iTEST, vTEST, vIN, vENeed 3 equations to find the ratio of iTEST/ vTESTvIN= -vE and is not zero!KCL at vEKVL at vOUTIntuitive Explanation: GmVINburps currentwhich has to also go through R0. This raises vTESTand the output impedance vTEST/iTESTThe input has been assumed to be shortedTry a bag. It is even easierFinish this in the homeworkCopyright 2001, Regents of University of CaliforniaEECS 42 Intro. electronics for CS Fall 2001 Lecture 14: 10/15/01 A.R. NeureutherVersion Date 10/16/01NON-IDEAL OP-AMPS JUST ANOTHER CASE OF ANALYSIS WITH DEPENDENT SOURCESCircuit (assume)RIN∞≅V0(+)(−)1KVIN9KR2R1+−)VV(A−+−⋅V0-+1KVIN9KR2R1Example:Analysis:∞→=+≅+++=A if 10VRRRVR1)R(A)RA(RVV IN121IN2121IN0Outline your circuit analysis strategy here.Answer:Hint: 1) Find V-in terms of V0, 2) plug into expression for V0and then 3) solve for V0 which appears on both sides of the
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