6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-1 Lecture 23 - Frequency Response of Amplifiers (I) Common-Source Amplifier December 1, 2005 Contents: 1. Introduction 2. Intrinsic frequency response of MOSFET 3. Frequency response of common-source amplifier 4. Miller effect Reading assignment: Howe and Sodini, Ch. 10, §§ 10.1-10.46.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-2 Key questions • How does one assess the intrinsic frequency response of a transistor? • What limits the frequency response of an amplifier? What is the ”Miller effect”? •6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-3 1. Introduction Frequency domain is a major consideration in most ana-log circuits. Data rates, bandwidths, carrier frequencies all pushing up. Motivation: • Processor speeds ↑ Traffic volume data rates • ↑⇒ ↑ • More bandwidth available at higher frequencies in the spectrum ( ) 0 0 4 2 8 MMDS 3G Skybridge Video WirelessMAN LMDS Teledesic Spacewav WE Datacom 'V Band' DOM Radio BW MHzFrequency 20 25 40 50 60 20 40 45 100 155 500 Figure by MIT OCW.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-4 2. Intrinsic frequency response of MOSFET � How does one assess the intrinsic frequency response of a transistor? ft ≡ short-circuit current-gain cut-off frequency [GHz] Consider MOSFET biased in saturation regime with small-signal source applied to gate: VDD iG=iin iD=ID+iout vs VGG vs at input ⇒ iout: transistor effect ⇒ iin due to gate capacitance ioutFrequency dependence: f ↑⇒ iin ↑⇒ |iin |↓ ioutft ≡ frequency at which =1|iin |6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-5 Complete small-signal model in saturation: G S D+ -vgs Cgs Cgd Cdb Csb gmvgs gmbvbs ro + vbs -iout vs + -iin B vbs=0 ++ --vgs gmvgs ioutiin vs Cgs Cgd1 2 node 1: iin − vgsjωCgs − vgsjωCgd =0 ⇒ iin = vgsjω(Cgs + Cgd) node 2: iout − gmvgs + vgsjωCgd =0 ⇒ iout = vgs(gm − jωCgd)� 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-6 Current gain: iout gm − jωCgdh21 = = iin jω(Cgs + Cgd) � Magnitude of h21: g2 + ω2C2 |h21| = m gd ω(Cgs + Cgd) • For low frequency, ω �gm ,Cgd gm |h21|�ω(Cgs + Cgd) • For high frequency, ω �gm ,Cgd < 1|h21|�CgsC+ gdCgd6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-7 log |h21| log ωωT 1 Cgd Cgs+Cgd -1 h21| becomes unity at:|gmωT =2πfT = Cgs + Cgd Then: gmfT = 2π(Cgs + Cgd)� 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-8 � Physical interpretation of fT: Consider: 1 Cgs + Cgd Cgs= 2πfT gm � gm Plug in device physics expressions for Cgs and gm: = 23 1 Cgs LW Cox L = W gm LµCox(VGS − VT) µ 32 VGS −VT L 2πfT or 1 L L = = τt2πfT �µ<Echan > <vchan > τt ≡ transit time from source to drain [s] Then: 1 fT �2πτt fT gives an idea of the intrinsic delay of the transistor: good first-order figure of merit for frequency response.� 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-9 To reduce τt and increase fT: L : trade-off is cost • ↓ ID ↑: trade-off is power • (VGS − VT) ↑⇒ • µ ↑: hard to do • note: fT independent of W Impact of bias point on fT: gm W LµCoxIDLµCox(VGS − VT)2W fT = = = 2π(Cgs + Cgd) 2π(Cgs + Cgd) 2π(Cgs + Cgd) fT fT 00 VT VGS0 ID In typical MOSFET at typical bias points: fT ∼ 5 − 50 GHz6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-10 3. Frequency response of common-source amp VDD vs VGG vOUT iSUP RS RL signal source + -signal� load VSS Small-signal equivalent circuit model (assuming current source has no parasitic capacitance): RS Cgd ++ --vgs + -voutgmvgsvs Cgs RLrocroCdb 'Rout Low-frequency voltage gain: voutAv,LF = = −gm(ro//roc//RL)= −gmR�out vs6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-11 ++ --vgs + -voutgmvgsvs Cgs Cgd1 2 Rout ' RS Cdb node 1: vs−vgs vgsjωCgs − (vgs − vout)jωCgd =0RS −node 2: (vgs−vout)jωCgd−gmvgs−voutjωCdb−vout =0R�out Solve for vgs in 2: 1jω(Cgd + Cdb)+ R�vgs = vout out jωCgd − gm Plug in 1 and solve for vout/vs: −(gm −jωCgd)R�Av = out DE N with 1 DE N =1 + jω{RSCgs + RSCgd[1 + R�+ gm)] + R�out ( outCdb}RS −ω2RSR�outCgs(Cgd + Cdb) [check that for ω =0, Av,LF = −gmR�out]6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-12 Simplify: 1. Operate at ω � ωT = gm Cgs+Cgd ⇒ gm � ω(Cgs + Cgd) >ωCgs,ωCgd 2. Assume gm high enough so that 1 RS + gm � gm 3. Eliminate ω2 term in denominator of Av worst-case estimation of bandwidth ⇒ Then: −gmR�outAv �1+ jω[RSCgs + RSCgd(1 + gmR� �]out)+ RoutCdbThis has the form: Av,LF Av(ω)= 1+ jωωH6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-13 log |Av| gmRout ' log ωωH -1 At ω = ωH: 1 Av(ωH)| = Av,LF ||√2|ωH gives idea of frequency beyond which |Avstarts rolling | off quickly ⇒ bandwidth For common-source amplifier: 1 ωH = RSCgs + RSCgd(1 + gmR� �out)+ RoutCdb Frequency response of common-source amplifier limited by Cgs and Cgd shorting out the input, and Cdb shorting out the output.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-14 Can rewrite as: 1 fH = 2π{RS[Cgs + Cgd(1 + Av,LF )] + R�outCdb}| |Compare with: gmfT = 2π(Cgs + Cgd) � In general: fH � fT due to • typically: gm �R1 S • Cdb enters fH but not fT • presence of Av,LF | in denominator |� To improve bandwidth, • Cgs,Cgd,Cdb ↓⇒small transistor with low parasitics • |Av,LF |↓⇒don’t want more gain than really needed but... why is it that effect of Cgd on fH appears to being am-plified by 1 + |Av,LF ??!!|6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 23-15 4. Miller effect In common-source amplifier, Cgd looks much bigger than it really is. Consider simple voltage-gain stage:
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