6.012 - Microelectronic Devices and Circuits Lecture 24 - Intrin. Freq. Limits - Outline • Announcements Final Exam - Tuesday, Dec 15, 9:00 am - 12 noon • Review - Shunt feedback capacitances: Cµ and Cgd Miller effect: any C bridging a gain stage looks bigger at the input Marvelous cascode: CE/S-CB/G (E/SF-CB/G work, too - see µA741) large bandwidth, large output resistance used in gain stages and in current sources Using the Miller effect to advantage: Stabilizing OP Amps - the µA741 • Intrinsic high frequency limitations of transistors General approach MOSFETs: fT biasing for speed impact of velocity saturation design lessons BJTs: fβ, fT, fα biasing for speed design lessons Clif Fonstad, 12/8/09 Lecture 24 - Slide 1Summary of OCTC and SCTC results • OCTC: an estimate for ωHI log !log |Avd|!b!c!d!a!LO!LO*!4!5!2!1!3!HI*!HIMid-band Range1. ωHI* is a weighted sum of ω's associated with device capacitances: (add RC's and invert) 2. Smallest ω (largest RC) dominates ωHI * 3. Provides a lower bound on ωHI • SCTC: an estimate for ωLO 1. ωLO * is a weighted sum of w's associated with bias capacitors: (add ω's directly) 2. Largest ω (smallest RC) dominates ωLO * 3. Provides a upper bound on ωLO Clif Fonstad, 12/8/09 Lecture 24 - Slide 2The Miller effect (general) +-vin(1-Av)vinCmvout = Avvin+-+-iinConsider an amplifier shunted by a capacitor, and consider how the capacitor looks at the input and output terminals: Note: Av is negative vout+-Cmvin+-Av! iin= Cmd 1" Av( )vin[ ]dt= 1" Av( )Cmdvindt+-voutCm+-vin(1-Av)CmCin looks much ! Cm1" Av( )Av# Cmbigger than Cm Cout looks like Cm Clif Fonstad, 12/8/09 Lecture 24 - Slide 3The cascode when the substrate is grounded: High frequency issues: L.E.C. of cascode: can't use equivalent transistor idea here because it didn't address the issue of the C's! ro2vgs1gm1vgs1ro1+-(gm2+gmb2)vgs2+-vgs2+-voutrlCdb1+Cgs2+Cbs2Cgd2+Cbd2Cgd1Cgs1g1d1,s2,b2d2s1,b1,b2s1,b1,g2,b2g2,b2Voltage gain ≈ -1 so Voltage gain ≈ g rl,mminimal Miller effect. without Miller effect. Common-source gain without the Miller effect penalty! Clif Fonstad, 12/8/09 Lecture 24 - Slide 4Multi-stage amplifier analysis and design: The µA741 Figuring the circuit out: Emitter-follower/Current mirror load Simplified schematic Push-pulloutput common-base "cascode" differential gain stage EF CB The full schematic © Source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Darlington common-emitter gain stage © Source unknown. All rights reserved. Clif Fonstad, 12/8/09 This content is excluded from our Creative Commons license. Lecture 24 - Slide 5 For more information, see http://ocw.mit.edu/fairuse.Multi-stage amplifier analysis and design: Understanding the µA741 input "cascode" Begin with the BJT building-block stages: +-voutvt+-rtioutiingmv!+-vin +-voutgoce ebCommon emitterioutg!+-v! vin+-vin +-vout gsl + !/(rt+r!)eccbEmitter followeriinioutr" + !/gl+- iin+-vin +-voutdg,bg,bsCommon base ! go/!iiniout !(gm+g!)+-vinrl = 1/gliinRelative sizes: gm: large gπ: medium go: small gt, gl: cannot generalize Clif Fonstad, 12/8/09 Lecture 24 - Slide 6Multi-stage amplifier analysis and design: Two-port models Two different "cascode" configurations, this time bipolar: +-voutvt+-rtiout+-vinrl = 1/gliiniingmv!+-vin +-voutgoce ebCommon emitterioutg!+-v! +-voutvt+-rtiout+-vinrl = 1/gliiniingmv!+-vin +-voutgoce ebCommon emitterioutg!+-v! iin+-vin +-voutdg,bg,bsCommon base ! go/!iiniout !(gm+g!)+-vinrl = 1/gliin iin+-vin +-voutdg,bg,bsCommon base ! go/!iiniout !(gm+g!)+-voutvt+-rtiout!vin+-vin +-vout! !/(rt+r!)eccbEmitter followeriinioutr" + !/gl+-In a bipolar cascode, starting with an emitter follower still reduces the gain, but it also gives twice the input resistance, which is helpful. Clif Fonstad, 12/8/09 Lecture 24 - Slide 7Multi-stage amplifier analysis and design: MOSFET 2-port models Reviewing our building-block stages: +-voutvt+-rtioutgmvin+-vin +-voutgm+go+gls,bddgSource followeriiniout (gm+ gmb)vin+-vin +-vout gogtgm+gmb+gtdg,bg,bsCommon gategm+gmbiinioutiingmvin+-vin +-voutgods,gs,ggCommon sourceiout+-vinrl = 1/gliinRelative sizes: large gm, gmb: go: small gt, gl: cannot generalize Clif Fonstad, 12/8/09 Lecture 24 - Slide 8Multi-stage amplifier analysis and design: Two-port models Two different "cascode" configurations: +-voutvt+-rtiout+-vinrl = 1/gliiniingmvin+-vin +-voutgods,gs,ggCommon sourceiout+-voutvt+-rtiout+-vinrl = 1/gliin (gm+ gmb)vin+-vin +-vout gogtgm+gmb+gtdg,bg,bsCommon gategm+gmbiinioutiingmvin+-vin +-voutgods,gs,ggCommon sourceioutgmvin+-vin +-voutgm+go+gls,bddgSource followeriiniout+-voutvt+-rtiout+-vinrl = 1/gliin (gm+ gmb)vin+-vin +-vout gogtgm+gmb+gtdg,bg,bsCommon gategm+gmbiinioutWith MOSFETs, starting a cascode with a source follower costs a factor of two in gain Clif Fonstad, 12/8/09 because rout for an SF is small, so it isn't very attractive. Lecture 24 - Slide 9Multi-stage amplifier analysis and design: The µA741 The circuit: a full schematic The monolithic capacitor made the µA741"complete" and a big success. Why is itneeded? What does it do? C1 is in a Miller position across Q16 Clif Fonstad, 12/8/09 Lecture 24 - Slide 10 © Source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.Multi-stage amplifier analysis and design: The µA741 Why is there a capacitor in the circuit?: the added capacitorintroduces a low frequency polethat stabilizes the circuit. Without it the gain is still greater than 1 when the phase shift exceeds 180˚ (dashed curve). This can result in positive feedback and instability. With it the gain is less than 1 by the time the phase shift exceeds 180˚ (solid curve). Lowfrequencypole Clif Fonstad, 12/8/09 Lecture 24 - Slide 11Intrinsic performance - the best we can do We've focused on ωHI, the upper limit of mid-band, but even when ω > ωHI the |Av| > 1, and the circuit is useful. For example, for the common source stage we had ! Avj"( )=#gtgm# j"Cgd( )j"( )2CgsCgd+ j"gl+ go( )Cgs+ gl+ go+ gt+ gm( )Cgd[ ]+ gl+ go( )gt{ }gm /(gl+go)log |Av,oc|log !!1! 2! 31!1gm /(gl+go)A Bode plot of Av is shown to the right: this and ask how high can a device in isolation have provide voltage or current gain? When we look for a metric to compare the ultimate performance limits
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