Lecture 14ANNOUNCEMENTS•Midterm #1 results (undergrad scores only):253810•Midterm #1 results (undergrad. scores only): • N=74; mean=62.8; median=63; std.dev.=8.42• You may pick up your exam during any TA office hour.OUTLINE• Regrade requests must be made before you leave with your exam.• The list of misunderstood/forgotten points has been updated.OUTLINE• Frequency Response (cont’d)–CE stage (final comments)– CB stage– Emitter follower– Cascode stageEE105 Fall 2007 Lecture 14, Slide 1Prof. Liu, UC BerkeleyReading: Chapter 11.4‐11.6CE Stage Pole Frequencies, for VA<∞()()()ωCrRgCRinp++≈11,()()()µCrRgCRoCminThev++1⎞⎛⎞⎛≈ωt1()()⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛++µωCrRgCrRoCmoutoCoutp11,EE105 Fall 2007 Lecture 14, Slide 2Prof. Liu, UC BerkeleyNote that ωp,out> ωp,inI/O Impedances of CE Stage()()[]πrCRCjZin||11++≈[]oCoutrRCCZ||||1=()()[]µπωCrRgCjoCm1++[]oCCSoutCCj||||+µωEE105 Fall 2007 Lecture 14, Slide 3Prof. Liu, UC BerkeleyCB Stage: Pole Frequencies• Note that there is no capacitance between input & output nodesÆNo Miller multiplication effect!ÆNo Miller multiplication eff ect!Y1=ωCB stage with BJT capacitances shownYCYpCR,ωCSYCCC+=µ∞=orTXpωω>⎞⎛=11,TXmSXpCgR⎟⎟⎠⎞⎜⎜⎝⎛1||,EE105 Fall 2007 Lecture 14, Slide 4Prof. Liu, UC BerkeleyπCCX=Emitter Follower• Recall that the emitter follower provides high input impedance and low output impedance, and is used as a voltage buffer.p p, gFollower stage with BJT capacitances shown• CLis the load capacitanceCircuit for small-signal analysis(Av)∞=r∞=orEE105 Fall 2007 Lecture 14, Slide 5Prof. Liu, UC BerkeleyAC Analysis of Emitter Follower πvvvoutX+=• KCL at node X:011=++++−+ππππvvvvRvvvoutinout•KCL at output node:11ππµωωCjrCjRSoutvvgvvππ=++•KCL at output node:CRLmCjvgCjrωωπππ11=++ 1)()()(1 2+++≅⇒ωωωπjbjajgCvvmiout()LSLLmSCRCCRbCCCCCCgRa⎞⎜⎜⎛++=ππµπµ1EE105 Fall 2007 Lecture 14, Slide 6Prof. Liu, UC Berkeley1)()(++ωωjbjavinmLSmSgrgCRb⎠⎜⎜⎝+++=ππµ1Follower: Zero and Pole Frequencies )(1+ωπjgCv()LLmSCCCCCCgRa ++=πµπµ1)()(2++≅ωωjbjagvvminoutmLSmSgCrRgCCRb⎟⎟⎠⎞⎜⎜⎝⎛+++=ππµ1• The follower has one zero:TmzfCgπω2==• The follower has two poles at lower frequencies:TzfCπ⎞⎛⎞⎛⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛+=++2121 11)()(ppjjjbjaωωωωωωEE105 Fall 2007 Lecture 14, Slide 7Prof. Liu, UC BerkeleyEmitter Follower: Input Capacitance• Recall that the voltage gain of an emitter follower isLvRRA1+=∞=orFollower stage with BJT capacitances shownmLgR+• CXYcan be decomposed into CdCh i d()CCAC1πCXand CYat the input and output nodes, respectively:()LmvXRgCAC+=−=11ππCCCπ−=⎞⎜⎜⎛−=11CCC+=πLmvYRgCACπ=⎠⎜⎜⎝−=1()RrR1++=βEE105 Fall 2007 Lecture 14, Slide 8Prof. Liu, UC BerkeleyLminRgCC++=1µ()LinRrR1++=βπEmitter Follower: Output ImpedanceCircuit for small-signal analysis (Rout)∞=or()⎞⎜⎛1()Rvgivv++−=()⎟⎠⎞⎜⎜⎝⎛+−=ππππωCjrvgivmX1()()()πππππππωωββωωjCrRRrjRrjCrRrjCrRivZSSSSSXXout1/111++⋅++=++++=≡()SmxxRvgivvππ++=EE105 Fall 2007 Lecture 14, Slide 9Prof. Liu, UC Berkeley()()ππππβββωCrjjCriX/1111+++++Emitter Follower as Active Inductor()()()πππππππωββωjCrRRrjRrRrjCrRvZSSSSSXout/1++⋅+=++=≡CASE 1:RS<1/gmCASE 2:RS>1/gm()()ππππβωββωCrjjCriXout/1111+++++CASE 1: RS 1/gmCASE 2: RS 1/gmcapacitive behavior inductive behavior• A follower is typically used to lower the driving impedanceÆRS>1/gmso that the“active inductor”characteristic on theEE105 Fall 2007 Lecture 14, Slide 10 Prof. Liu, UC BerkeleyÆRS 1/gmso that the active inductor characteristic on the right is usually observed. Cascode Stage• Review:– A CE stage has large Rinbut suffers from the Miller effect.– A CB stage is free from the Miller eff ect, but has small Rin.• A cascode stage provides high Rinwith minimal Miller effect.111−≈⎠⎞⎜⎜⎝⎛−=≡mXXYvgvA∞=or21,⎠⎜⎝mmYXYvggvCC2≈⇒XYXCC2 ≈⇒EE105 Fall 2007 Lecture 14, Slide 11 Prof. Liu, UC BerkeleyCascode Stage: Pole Frequencies1Cascode stage with BJT capacitances shown(Miller approximation applied)()()111,2||µππωCCrRSXp+=1∞=or()1212,211µπωCCCgCSYp++=2gm 222,2TmYpfCgπωπ=≈Note that(),1ωCCRoutp+=EE105 Fall 2007 Lecture 14, Slide 12 Prof. Liu, UC Berkeley()22µCCRCSL+Cascode Stage: I/O Impedances∞=oro()11121||µππωCCjrZin+=()221||CSLoutCCjRZ+=µωEE105 Fall 2007 Lecture 14, Slide 13 Prof. Liu, UC BerkeleySummary of Cascode Stage Benefits• A cascode stage has high output impedance, which is advantageous foradvantageous for– achieving high voltage gain–use as a current source• In a cascode stage, the Miller effect is reduced, for improved performance at high frequencies.EE105 Fall 2007 Lecture 14, Slide 14 Prof. Liu, UC BerkeleyImpedance of Parallel RC CircuitEE105 Fall 2007 Lecture 14, Slide 15 Prof. Liu, UC
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