6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-1Lecture 25 - Frequency Response ofAmplifiers (III)Other Amplifier StagesDecember 8, 2005Contents:1. Frequency response of common-drain amplifier2. Casco de amplifierReading assignment:Howe and Sodini, Ch. 9, §9.3.3; Ch. 10, §§10.5, 10.7Announcement:Final exam: December 19, 1:30-4:30 PM, duPont; openbook, calculator required; entire subject under examina-tion but emphasis on lectures #19-26.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-2Key questions• Do all amplifier stages suffer from the Miller effect?• Is there something unique about the common drainstage in terms of frequency response?• Can we make a transconductance amplifier with alarge bandwidth?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-31. Frequency response of common-drain am-plifiervsVGGvOUTVDDVSSiSUPRSRLsignal source+-signalloadFeatures:• voltage gain ' 1• high input resistance• low output resistance•⇒good voltage buffer6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-4High-frequency small-signal model:GBSD+vs+-vgs+--vbsvbs=0+-vgs+-voutgmvgsroRLRS+-voutgmvgsro//roc//RL=RL'rocCgdCgsCsbgmbvbsCdbCgsCgdCdb+vs-RSAv,LF=gmR0L1+gmR0L≤ 16.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-5Compute bandwidth by open-circuit time constant tech-nique:1. shut-off all independent sources,2. compute Thevenin resistance RTiseen by each Ciwithall other C’s open,3. compute open-circuit time constant for Ciasτi= RTiCi4. conservative estimate of bandwidth:ωH'1Στi2 First, short vs:+-vgs+-voutgmvgsRL'CgsCgdCdbRS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-62 Time constant associated with Cgs:+-vgs+-voutgmvgsRL'RS+-vtit12node 1:it−vt+ voutRS=0node 2:gmvgs− it−voutR0L=0alsovgs= vtSolve for voutin 1 and plug into 2:6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-7RTgs=vtit=RS+ R0L1+gmR0LTime constant:τgs= CgsRS+ R0L1+gmR0L2 Time constant associated with Cgd:+-vgs+-voutgmvgsRL'RS+-vtitRTgd= RSτgd= CgdRS6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-82 Time constant associated with Cdb:+-vgsgmvgsRL'RS+-vtitRL'gm+-vtitRTdb=1gm//R0L=R0L1+gmR0Lτdb= CdbR0L1+gmR0LNotice:RTdb= Rout//RL6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-92 Bandwidth:ωH'1τgs+ τgd+ τdb=1CgsRS+R0L1+gmR0L+ CgdRS+ CdbR0L1+gmR0L2 If back is not connected to source:vsVGGvOUTVDDVSSVSSiSUPRSRLsignal source+-signalload6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-10Small-signal equivalent circuit:GBSD+-vgs+-vbs+-vgs+-vbsgmvgsro+-vout+-voutgmvgsgmbvbsro//roc//RL=RL'rocCgdCgsCsbgmbvbsCdbCgsCgdCsb+vsvs-RS+-vgs+-voutgmvgsRL'//(1/gmb)=RL''CgsCgdCsb+vs-RS+-RSRLAv,LF=gmRL”1+gmRL”6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-11Csbshows up at same location as Cdbbefore, then band-width is:ωH'1CgsRS+RL”1+gmRL”+ CgdRS+ CsbRL”1+gmRL”Simplify:• CD amp is about driving low RLfrom high RS⇒RS RL”, andωH'1RS(Cgs1+gmRL”+ Cgd)+CsbRL”1+gmRL”• CD stage operates as voltage buffer with Av,LF'1 ⇒ gmRL” 1, andωH'1CgdRS+CsbgmSince Cgdand 1 /gmare small, if RSis not too high, ωHcan be rather high (approach ωT).6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-122 What happened to the Miller effect in CD amp?ωH'1RS(Cgs1+gmRL”+ Cgd)+CsbRL”1+gmRL”Miller analysis of Cgs:C0gs= Cgs(1−Av)=Cgs(1−gmRL”1+gmRL”)=Cgs11+gmRL”agrees with above result.Note, since Av→ 1, C0gs→ 0.See in circuit:++--vin+-voutAvvinCiinCM= C(1 − Av)if Av' 1 ⇒ CM' 0: bootstrapping6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-132. Cascode amplifierCommon-source stage: excellent transconductance am-plifier, but bandwidth hurt by Miller effect.What’s a circuit designer to do?Consider CS-CG stage:vsVG1VDDVSSiSUP1iOUT1vOUT1RSsignal sourceiOUTVDDVG2VSSVSSiSUP2IBIASRLsignalloadHow does this address the problem?• Rin2very small ⇒ iOUT1can change a lot with vOUT1changing little ⇒ small voltage gain in CS stage ⇒no Miller effect ⇒ high bandwidth• CG stage also has high bandwidth6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-14Before analyzing CS-CG amp, notice that if we makeiSU P1= iSU P2= iSU P, amplifier drastically simplified:vsVG1VDDVSSiSUPiOUT1vOUT1RSsignal sourceiOUTVDDVG2VSSVSSiSUPIBIASRLsignalloadvsVG1VSSRSsignalsourceiOUTVDDVG2VSSiSUPRLsignalload6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-15vsVG1VSSRSsignalsourceiOUTVDDVG2VSSiSUPRLsignalloadSmall-signal equivalent circuit model:++--vgs1gm1vgs1vsCgs1ro1RSCdb1+-vgs2ro2(gm2+gmb2)vgs2roc//RL=RL'Cgs2+Csb2Cgd2+Cdb2Cgd1Time constants associated with Cgs1and Cgd2+Cdb2havenot changed.Time constant associated with Cdb1+ Cgs2+ Csb2small(looking into Rin2' 1/gm).6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-16Focus on time constant associated with Cgd1:+-vgs1gm1vgs1gm2+gmb2RS+-vtitFrom Lecture 24:τgd1=[1gm2+ gmb2+ RS(1 +gm1gm2+ gmb2)]Cgd1If transistors identical (gm1= gm2):τgd1' 2RSCgd1Much smaller than in single stage CS tansconductanceamp:τgd=[R0out+ RS(1 + gmR0out)]CgdCascode: excellent transconductance amplifier with highbandwidth.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-17Key conclusions• Common-drain amplifier:– Voltage gain ' 1, Miller effect nearly completelyeliminates impact of Cgs(bootstrapping)– if RSis not too high, CD amp has high bandwidth• Cascode amplifier:– effective sharing of current source– Miller effect minimized by reducing voltage gain ofCS stage as a result of low input impedance of CGstage– transconductance amplifier with high
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