6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-1 Lecture 25 - Frequency Response of Amplifiers (III) Other Amplifier Stages December 8, 2005 Contents: 1. Frequency response of common-drain amplifier 2. Cascode amplifier Reading assignment: Howe and Sodini, Ch. 9, §9.3.3; Ch. 10, §§10.5, 10.7 Announcement: Final exam: December 19, 1:30-4:30 PM, duPont; open book, calculator required; entire subject under examina- tion but emphasis on lectures #19-26. 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-2 Key questions • Do all amplifier stages suffer from the Miller effect? • Is there something unique about the common drain stage in terms of frequency response? • Can we make a transconductance amplifier with a large bandwidth? 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-3 1. Frequency response of common-drain am- plifier VDD signal source RS signal vs + load iSUP R vOUT L VGG - VSS Features: • voltage gain 1 • high input resistance • low output resistance •⇒good voltage buffer 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-4 High-frequency small-signal model: Cgd G D + vgs Cgs gmvgs gmbvbs ro S - - Cdb RS vbs Csb + vs + - B + r oc RL vout - vbs=0 Cgs + vgs - + RS v + Cgd gmvgs Cdb ro//roc//RL=RL' out vs - - gmRL ≤ Av,LF = 1 1+g mRL 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-5 Compute bandwidth by open-circuit time constant tech- nique: 1. shut-off all independent sources, 2. compute Thevenin resistance RTi seen by each Ci with all other C’s open, 3. compute open-circuit time constant for Ci as τi = RTiCi 4. conservative estimate of bandwidth: 1 ωH Στi 2 First, short vs: Cgs + vgs - + RS Cgd gmvgs Cdb RL' vout - 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-6 2 Time constant associated with Cgs: v i + t • 1 t 2 + + vgs - RS gmvgs RL' vout - node 1: vt + vout it − =0 RS node 2: − − vout gmvgs it =0 RL also vgs = vt Solve for vout in 1 and plug into 2: 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-7 vt RS + RL RTgs = = it 1+g mR L Time constant: RS + RL τgs = Cgs 1+g mR L 2 Time constant associated with Cgd: + vgs - + it + RS vt gmvgs RL' vout - - RTgd = RS τgd = CgdRS 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-8 2 Time constant associated with Cdb: + vgs - it + RS gmvgs RL' vt - it + gm RL' vt - 1 R L RTdb = //RL = gm 1+g mRL RL τdb = Cdb 1+g mRL Notice: RTdb = Rout//RL 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-9 2 Bandwidth: 1 1 ωH = + τ + τ + τ RS RL RL gs gd db Cgs 1+ + CgdRS + Cdb 1+ gmRL gmRL 2 If back is not connected to source: VDD signal source RS VSS signal load vs + iSUP vOUT RL - VGG VSS 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-10 Small-signal equivalent circuit: Cgd G D + vgs Cgs gmvgs gmbvbs ro RS - S - Cdb + + vs vbs Csb roc RL vout - - + B Cgs + - + vgs - RS v v + Cgd gmvgs gmbvbs bs Csb ro//roc//RL=RL' out vs - + - Cgs + + vgs - RS v + Cgd gmvgs Csb RL'//(1/gmb)=RL'' out vs - - gmRL ” Av,LF = 1+g mRL ” 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-11 Csb shows up at same location as Cdb before, then band- width is: 1 ωH RS+RL ” RL ” Cgs + CgdRS + Csb 1+gmRL ” 1+gmRL ” Simplify: • CD amp is about driving low RL from high RS ⇒ RS RL”, and 1 ωH Cgs RL ” RS ( + Cgd)+C sb 1+gmRL ” 1+gmRL ” • CD stage operates as voltage buffer with Av,LF ⇒ 1 gmRL ” 1, and 1 ω H Csb C R + gd S gm Since Cgd and 1/gm are small, if RS is not too high, ωH can be rather high (approach ωT ). 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-12 2 What happened to the Miller effect in CD amp? 1 ωH Cgs RL ” RS ( + Cgd)+C sb 1+gmRL ” 1+gmRL ” Miller analysis of Cgs: g R ” 1 − − m L Cgs = Cgs(1 Av )= Cgs(1 )= Cgs 1+g mRL ” 1+g mRL ” agrees with above result. → → Note, since Av 1, Cgs 0. See in circuit: iin C + + + vin Avvin vout - - - CM = C(1 − Av) if Av 1 ⇒ CM 0: bbootstrappingootstr apping 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-13 2. Cascode amplifier Common-source stage: excellent transconductance am - plifier, but bandwidth hurt by Miller effect. What’s a circuit designer to do? Consider CS-CG stage: VDD VDD iSUP1 iSUP2 signal source iOUT signal load RS vOUT1 VG2 VSS RL vs iOUT1 VG1 IBIAS VSS VSS How does this address the problem? • Rin2 very small ⇒ iOU T 1 can change a lot with vOU T 1 changing little ⇒ small voltage gain in CS stage ⇒ no Miller effect ⇒ high bandwidth • CG stage also has high bandwidth 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-14 Before analyzing CS-CG amp, notice that if we make iSUP1 = iSUP2 = iSUP , amplifier drastically simplified: VDD VDD iSUP iSUP signal source iOUT signal load RS vOUT1 VG2 VSS RL vs iOUT1 VG1 IBIAS VSS VSS VDD iSUP iOUT signal load VG2 VSS RL signal RS source vs VG1 VSS 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-15 VDD iSUP iOUT signal load VG2 VSS RL signal RS source vs VG1 VSS Small-signal equivalent circuit model: (gm2+gmb2)vgs2 RS Cgd1 + + - ro2 vs vgs1 Cgs1 gm1vgs1 Cdb1 ro1 vgs2 Cgs2+Csb2 Cgd2+Cdb2 roc//RL=RL ' - + - Time constants associated with Cgs1 and Cgd2 +Cdb2 have not changed. Time constant associated with Cdb1 + Cgs2 + Csb2 small (looking into Rin2 1/gm). 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-16 Focus on time constant associated with Cgd1: vt + - + it RS vgs1 gm1vgs1 gm2+gmb2 - From Lecture 24: 1 gm1 τgd1 =[ + RS (1 + )]Cgd1 gm2 + gmb2 gm2 + gmb2 If transistors identical (gm1 = gm2): τgd1 2RSCgd1 Much smaller than in single stage CS tansconductance amp: τgd =[Rout + RS (1 + gmRout)]Cgd CascoCascode: de: excellent transconductance amplifier with high bandwidth. 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 25-17 Key conclusions • Common-drain amplifier: – Voltage gain 1, Miller effect nearly completely eliminates impact of Cgs (bootstrapping) – if RS is not too high, CD amp has high bandwidth • Cascode amplifier: – effective sharing of current source – Miller effect minimized by reducing voltage gain of CS stage as a result of low input impedance of CG stage – transconductance amplifier with high bandwidth .