EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 University of CaliforniaBerkeleyCollege of EngineeringDepartment of Electrical Engineeringand Computer ScienceRobert W. BrodersenEECS140 Fall,2002Analog Circuit Design Moreon Op AmpsTELESCOPIC and FOLDED CASCODEEECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-1+-+-+-VddVdd–Vdd–M13M12M11M10M9M8M7M6M5M4M3M2M1Vid2------Vid2------IREFI2I1RCVicVG8VG6νOUTTelescopic - OP AMPCircuit 1 (Poor Bias41⁄101⁄ν2ν1101⁄21⁄21⁄21⁄21⁄21⁄21⁄21⁄21⁄21⁄21⁄ Strategy)EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-2Circuit 1 :Telecopic OP AMP with “BAD” Bias of cascode :The currents are balanced so that all transistors have,IDSIREF=except for M13 which has,Since,IDS132 IREF⋅=then,This also implies that,similarily,So if the input has, I1I2IREf==VGS3VGS4VGS9==VDS4VDS3=VDS5VDS6=Vid0=(all W/L’s are equal also)EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-3then,The gate of M8 is also at,due to its connection to M11, so,The swing in the positive direction will be,But since,this means the swing is only 1 VT in the positive direction. In the negative direction,but since,the swing is only VT again.VOUTVDD2 VTo2 VDSAT⋅–⋅– VG6 (if γ 0)===VDD2 VTo2 VDSAT⋅–⋅–VOUTVG6VG8==VOUTMAX +, VG6VT+=VOUTVG6=VOUTMIN --,VG8VT–=VOUTVG8=EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-4Thus the total swing is only 2VT ... not too good.In the positive direction we could use a high swing configurationas was described for the cascoded current source.On the low side we can use a better circuit.Circuit 2 :Telescopic with a cascode bias that gives a better swing in the negative direction.Maximum voltage in the positive direction is given by M6 goinglinear when,Negative swing is limited by M8 going linear,Set VA so that M1 & M2 are at the edge of saturationVOUTMAX + ,VDDVGS3VDSAT6––>VOUTMIN, --VAVT8–=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON MOS DEVICE MODELSROBERT W. BRODERSEN LECTURE 2 FALL,1998MOA-5Circuit 2 (Better Bias)M13M12M9M8M7M6M5M4M3M2M1IREF2-------IbRCIREF2-------VAVSd12d9d5d4d3d2d1νOUTIREFTelescopic - OP AMP21⁄ 21⁄21⁄21⁄21⁄21⁄21⁄21⁄101⁄101⁄230⁄ν1ν2VDD–Vdd– 5V–=Vdd5V=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON MOS DEVICE MODELSROBERT W. BRODERSEN LECTURE 2 FALL,1998 MOA-6Telescopic Op AmpRCM1 M2M3M4M5 M6M7M8M9M12 M13VDDVDD–VDD–VDDVT∆V+()–VDD2 VT∆V+()⋅–VDD2 ∆VVT–⋅–gmro2⋅gmro2⋅Max swing positive :VDD2 ∆VVT–⋅–EECS140 ANALOG CIRCUIT DESIGN LECTURES ON MOS DEVICE MODELSROBERT W. BRODERSEN LECTURE 2 FALL,1998Telescopic Op Amp (Cont.)VAVSVDSAT9VT9++=VDS2VDSAT2 for setting M2 at EOS=VDS2VAVT8VDSAT8VS–––=VSVDSAT9VT9VT8VDSAT8VS–––++=VDS2VDSAT9VDSAT8– VDSAT2 for EOS==VDSAT9VDSAT2VDSAT8+=WL-----8WL-----7=WL-----1WL-----2= MOA-7EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-8This means that,Since this will set,To calculate the (W/L)9 and IB to do this we set,since,If we say,thenVAVSVDSAT2VT8VDSAT8+++=VDS2VDSAT2=VDS 9,VAVS– VDSAT2VT8VDSAT8++==VDS 9,VT9VDSAT9+=VDSAT9VT8VT9–()VDSAT2VDSAT8++=VT8VT9≈2 IB⋅k'nWL-----9⋅----------------------12/2 IDS2⋅k'n--------------12/1WL-----812/---------------1WL-----212/---------------+2⋅=EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-9so,if,WL-----9IBIS---WL-----812/–WL-----212/–+2⋅=WL-----210=WL-----82=IB0.79µA= IS10.5µA=then,WL-----9115------≈Gain and RoutGMgm1 (cascoding has no effect on gm)=ROUTgm6ro4⋅()ro6⋅[]gm8ro2⋅()ro8⋅[]||=Aνdgm1gm6gm8ro4ro6ro2ro8⋅⋅⋅()⋅⋅gm6ro4ro6gm8ro2ro8⋅⋅+⋅⋅--------------------------------------------------------------⋅=EECS140 ANALOG CIRCUIT DESIGN MORE ON OP AMPS TELESCOPIC AND FOLDED CASCODEROBERT W. BRODERSEN LECTURE 22 MOA-10To see the current dependence let,and,gmgm1gm6==roro4ro6ro2ro8====Aνdgm2ro2⋅IDSIDS2-----1IDS-----∼∼≈Gain keeps increasing as we decrease the current.gm6ro4ro6⋅⋅2 IDS⋅VDSAT6-------------1λpIDS⋅---------------1λpIDS⋅---------------⋅⋅=Aνd2 IDS⋅VDSAT1-------------2IDS-----1VDSAT6λp2⋅----------------------1VDSAT8λn2⋅----------------------||⋅⋅=4VDSAT1------------1VDSAT6λp2VDSAT8λn2⋅+⋅--------------------------------------------------⋅=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON MOS DEVICE MODELSROBERT W. BRODERSEN
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