EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSUniversity of CaliforniaBerkeleyCollege of EngineeringDepartment of Electrical Engineeringand Computer ScienceRobert W. BrodersenEECS140Analog Circuit Design LecturesonOP AMPSEECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-1M1v1-VddRcv2νOUTM13M5M6M12-Vdd-VddM2M4M3Vd2Vd1VDDMiller Op Ampν2ν1Vd1Vd2EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-2Miller Op Amp (Cont.)-+ν1ν2νOUT+-ROUTaννid⋅νidνOUTRid∞=ROUTro5ro6||=νd2νid------νOUTνd2---------⋅νOUTνid---------=gm2ro2ro4||()⋅ gm5ROUT⋅EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-3Miller Op Amp (Cont.)What is the DC voltage at Vd2?IDS 1IDS 2IDS 3IDS4===IDS 3k'2---WL----- VSG3VT–()21 λ VSD3⋅+()⋅⋅⋅=IDS 4k'2---WL----- VSG4VT–()21 λ VSD4⋅+()⋅⋅⋅=IDS 3IDS 4=VSG3VT–()21 λ VSD3⋅+()⋅ VSG4VT–()21 λ VSD4⋅+()⋅=VSG3VSG4=VSG3VT–()21 λ VSD3⋅+()⋅ VSG3VT–()21 λ VSD 4⋅+()⋅=VD1VDDVSG3– VDDVTVDSAT3–– VD2===VSD3VSD4VSG 3VTVDSAT3+===EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-4Miller Op Amp (Cont.)To set offset at output or 2nd stage M5, M6 to near zero,set IDS5 = IDS6IDS5IDS6ISD5k'2---WL-----5VSG 5VT–()21 λ VSD5⋅+()⋅⋅⋅=ISD6k'2---WL-----6VGS 6VT–()21 λ VDS6⋅+()⋅⋅⋅=Since VSD 4VSG3VSG5==ISD612--- ISD13⋅= if WL-----132WL-----⋅6=ISD5IDS3= if WL-----5WL-----3=then IDS6IDS5 or,=IDS 5IDS 3-------WL-----5WL-----3------------WL-----6WL-----132⁄--------------------2WL-----6⋅WL-----13-------------------===EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-5Miller Op Amp (Cont.)M 1M 2I1I2What happens if I1α I2⋅=k'2---WL-----1VSG1VT–()21 λ VSD1⋅+()⋅⋅⋅αk'2---WL-----2VSG2VT–()21 λ VSD'2⋅+()⋅⋅⋅⋅=1 λ VSD1⋅+ α 1 λ VSD2⋅+()⋅=VSD21λ---VSD1+α------------------1λ---–=α 1= VSD2VSD1=1002VSD1 Big Offset⋅+=λ 0.01=α12---= VSD2100 VSD 1+12⁄------------------------100–=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-6Miller Op Amp (Cont.)νdsνid-----gm 1– ro4ro2||()⋅=νOUTνd2---------gm5– ro6ro5||()⋅=Aνgm1gm5ro4ro2||()ro5ro6||()⋅⋅⋅=Gain :First StageSecond StageOverallEECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-7Miller Op Amp (Cont.)Aν2 IDS1⋅VDSAT1--------------2 IDS5⋅VDSAT5--------------1λnλp+()IDS1⋅--------------------------------1λnλp+()IDS 5⋅--------------------------------⋅⋅⋅=4VDSAT1()VDSAT5()λnλp+()2⋅⋅-----------------------------------------------------------------=Aν42 ISD 1⋅k'nWL⁄()1⋅----------------------------12---2 IDS 5⋅k'PWL⁄()5⋅----------------------------12---λnλp+()2⋅⋅-------------------------------------------------------------------------------------------------------=2 k'nk'P⋅()12---WL-----112---WL-----12---5⋅⋅⋅λnλp+()2ISD1IDS 5⋅()12---⋅----------------------------------------------------------------=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-8Miller Op Amp (Cont.)ROUTro5ro6||1λpλn+()IDS5⋅--------------------------------==Add output stage if this is too high.M1M2RLVINVOUTWhat is theoutput resistance of this ?EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPS OP-9Miller Op Amp (Cont.)You need to choose an operating point since the Rout is very non-linear.ROUT1gm1------VINVTn>=1gm2------VINVTp–<=gm2WL----- k' IDS⋅⋅⋅12---2WL----- k' IOUT⋅⋅⋅12---==2WL----- k'VOUTRL---------⋅⋅⋅12---=EECS140 ANALOG CIRCUIT DESIGN INTRODUCTIONh OP-10 Empty SlideEECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSOP-11+-νiddc offset VidVDD–5V–VDD+4V4V–W/L << 1How to connect these?4V4–()VYou could use a level shifterEECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSOP-12DIFF PAIR - GATE VOLTAGE SWEEP96 / 10 / 03 18:13:444.504.03.503.02.502.01.501.0500.0M0.-500.0M-1.0-1.50-2.0-2.50-3.0-3.50-4.0-4.50-5.0-10.0M -5.0M 0. 5.0M 10.0MVOLTS [LIN]OP1.SW0 VOUT2∆VOUT1VOLTLINEECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSOP-13WL0.5µ1.5µ 0.51+()× 2.25µ2=WL1µ2+〈〉× TransistorArea≈Area Calculation (L=.5 micron minimum channel Length)W/L=31.0µ0.5µResistorResistor Area = # of squares * 1.0 µ2 EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSOP-14LTWSheet ResistanceConductance 1Resiscetan----------------------------WT⋅L------------ σ mhoscm3-------------⋅==RLW----- ρbl⋅={ohms ⁄ρ1σ T⋅=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON OP AMPSOP-15Sheet Resistance (Cont.)11 1 1 11111115.51 1 11W}}W Wcount as 1/2 squareTOP VIEW15 SQUARESR 15 ρbl⋅=ρ1100Ω1----=R
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