R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyLecture 11• Last time:– MOS common-source amplifier• Today :– MOSFET small-signal model:transconductance and output resistanceR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyWhy Find an Incremental Model?• Signals of interest in analog ICs are often of the form:vGS(t) = VGS+ vgs(t)Direct substitution into iD= f(vGS, vDS) is tedious AND doesn’t include charge-storage effects … pretty rough approximationR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyWhich Operating Region?R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyChanging One Variable at a Time vGS0.5 1 1.5 2 iD Assumption: VDS> VDS,SAT= VGS– VTn(square law)R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyThe Transconductance gmDefined as the change in drain current due to a changein the gate-source voltage, with everything else constantDSVGSVDSGSGSDVVGSDmvivig,,∂∂=∆∆=Square-law: MOSFET saturation region)1()()2/(2DSnTnGSoxnDvVvCLWiλµ+−=R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyAnother Way to Find gmR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyEvaluating gmSquare-law characteristic: H&S 1stEditiongm= Linear characteristic: better for submicron CMOS )1)((, DSnTnGSoxsatSATDvVvWCviλ+−=R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyOutput Resistance roDefined as the inverse of the change in drain current dueto a change in the drain-source voltage, with everythingelse constantR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyEvaluating ro1,−∂∂=DSGSVVDSDovirTypical value:R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyPutting Together a Circuit Model drainsourcegate id vgsvds - + + -R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyRole of the Substrate PotentialNeed not be the source potential, but VB< VSEffect: changes threshold voltage, which changes the drain current … substrate acts like a “backgate”QBSDQBSDmbvivig∂∂=∆∆=Q = (VGS, VDS, VBS)R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyBackgate TransconductanceResult:=∂∂∂∂=∂∂=QBSTnQTnDQBSDmbvVVivigR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyFour-Terminal Small-Signal ModelR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyMOSFET Capacitances in SaturationGate-source capacitance: channel charge is not controlled by drain in saturation.R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyGate-Source Capacitance CgsWedge-shaped charge in saturation Æ effective area is (2/3)WL(see H&S 4.5.4 for details)ovoxgsCWLCC+= )3/2(Overlap capacitance along source edge of gate ÆoxDovWCLC=(Underestimate due to fringing fields)R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyGate-Drain Capacitance CgdNot due to change in inversion charge in channelOverlap capacitance Covbetween drain and sourceis CgdR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyJunction CapacitancesDrain and source diffusions have (different) junctioncapacitances since VSBand VDB= VSB+ VDSaren’t the sameComplete model (without interconnects)R. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleySmall-Signal PMOS ModelR. T. HoweEECS 105 Spring 2005 Lecture 11Dept. of EECSUniversity of California, BerkeleyMOSFET SPICE ModelMany “levels” … we will use the square-law “Level 1” modelSee H&S 4.6 for
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