1EE105 - Fall 2005Microelectronic Devices and CircuitsLecture 10MOS TransistorSmall-Signal Model2AnnouncementsHomework 5 due next TuesdayLab 3 this week, Lab 4 next weekReading: Chapter 4 (4.5-4.6), 8.3Midterm 1 in two weeksOctober 13, 6:30-8pm, Sibley23Lecture MaterialLast lectureSample and holdMOS amplifier exampleThis lectureMOSFET small-signal model4Large-Signal AnalysisVDDvIN= vGS0vO= vDStt35There is a Better Way!What’s missing: didn’t include device output impedance or charge storage effects (must solve non-linear differential equations…)Approach 2. Do problem in two steps.DC voltages and currents (ignore small signals sources): set bias point of the MOSFET ... we had to do this to pick VGSalreadySubstitute the small-signal model of the MOSFET and the small-signal models of the other circuit elements …This constitutes small-signal analysis6An MOS AmplifierDSIGSVsvDRDDVGS GS svVv=+ovInput signalOutput signalSupply “Rail”47Small-Signal AnalysisStep 1. Find DC Bias – ignore small-signal sourceVGSwas found inLecture 9IDS,Q859Step 2: Small-Signal ModelingWhat are the small-signal models of the DC supplies?10Small-Signal Models of Ideal SuppliesSmall-signal model:supplysupplysupplyigv∂==∞∂supply0r =supplysupplysupply0igv∂==∂supplyr =∞shortopen611The Transconductance gmDefined as the change in drain current due to a change in the gate-source voltage, with everything else constant,,()(1)GS DS GS DSDDmoxGSTDSGS GSVV VViiWgCVV Vvv Lµλ∆∂=== −+∆∂2,()(1)2oxDSsat GS T DSCWIVVVLµλ=−+()moxGSTWgCVVLµ=−0≈22DSmox oxDSoxIWWgCCIWLLCLµµµ==2()DSmGS TIgVV=−Gate BiasDrain Current BiasDrain Current Bias and Gate Bias12Output Resistance roDefined as the inverse of the change in drain current due to a change in the drain-source voltage, with everything else constantNon-Zero SlopeDSVδDSIδ713Evaluating ro1,GS DSDoDSVVirv−⎛⎞∂⎜⎟=⎜⎟∂⎝⎠2()(1)2oxDGS T DSCWiVVVLµλ=−+021()2oxGS TrCWVVLµλ=−01DSrIλ≈14Total Small Signal Current()DSDSdsit I i=+DS DSds gs dsgs dsiiivvvv∂∂=+∂∂1ds m gs dsoigv vr=+TransconductanceConductance815Putting Together a Circuit Model1ds m gs dsoigvvr=+16MOS AmplifierDSIGSVsvDRDDVov1: DC solutionID= 0.1mAVGS= 1.32V, VDS= 2.5V2: Small signalmA/V625.02=−=TnGSDSmVVIg∞→λ=DSoIr191718MOS Amplifier: Small-Signalvgs= vsid= gmvgsvo= - idRd||ro= - gmvsRdAv= -15.6dmsoVRgvvA −==1019MOS AmplifierOutput resistance: typical value λ = 0.05 V-1Voltage gain:()20.125|| 200 14.30.32vA⋅⎛⎞=− =−⎜⎟⎝⎠Ω=λ= kIrDSo2001Output resistance lowers voltage gain20Input and Output WaveformsOutput small-signal voltage amplitude: 14 x 25 mV = 350Input small-signal voltage amplitude: 25 mV1121What Limits the Output Amplitude?1. vOUT(t) reaches VDDor 0 … or 2. MOSFET leaves constant-current region and enterstriode regionVDDvIN0vo,max= VDDvo,min= VDS, SAT= VGS–VTn= 0.32VVo,max= VDD–(VGS– VTn) = 2.18VOptimum bias point Vo
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