Week 11: Differential Amplifiers

Transcription

1 ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture -

2 Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap of Jaeger and Blalock or hap , of Sedra and Smth Lecture -

3 BJT Dfferental Par Two dentcal transstors wth emtters shorted together, connectng to a resstor or a current source. Transstors operate n acte mode. Desgned to amplfy oltage dfference between the two nputs One of the most used crcut buldng blocks E.g., as the nput stage of opamps Lecture - 3

4 Lecture - 4 Large Sgnal Analyss BE T S e / T d T BE BE e e / ) / ( / BE T S e / α /α / E E α α d T e / + α d T e / + + α d B B BE BE where

5 Large Sgnal Analyss d B - B < T for use as a lnear amplfer For d > 4 T ( 00m), the tal current flows almost entrely n one of the two transstors Ths hgh senstty makes the dfferental par a fast current swtch The transstors are ether n acte mode or n cutoff mode Also contrbutes to hgh swtchng speed Lecture - 5

6 MOS Dfferental Par Lecture - 6

7 Lecture - 7 Large Sgnal Analyss Fg. 6.9 The MOSFET dfferental par. ' ' ) ( ) ( t n D t n D L W k L W k ) ( ) ( ' ' t n D t n D L W k L W k Assumng dentcal deces and neglectng the output resstance and body effect, the dran currents are d Snce, d n D D L W k ' We hae () D D + The current-source bas mposes the constran () + L W k L W k L W k L W k n d d n D n d d n D ' ' ' ' ) / ( ) / ( Solng eqs () & () yelds

8 Lecture - 8 Large Sgnal Analyss ( ) ' where orrespondngly, leadng to 0, pont, At the bas t n D D d L W k + / / t d d t D t d d t D

9 Large Sgnal Analyss For d / << D D + t (small sgnal approxmaton) t t d d Snce g m ( / ) t t We hae the sgnal component d of D as g / ) d m ( d At full swtchng stuaton (that s, D and D 0, or ce ersa), the alue of d s: d max ( t ) Lecture - 9

10 Large sgnal analyss Topcs to coer A analyss Half-crcut analyss Lecture - 0

11 Modelng nputs ommon-mode component: (the aerage) Dfferental-mode component: (the dfference) + c d Lecture -

12 Dfferental Mode nput 0 Analyze the crcut by superposton of DM and M sgnals Frst set the common-mode nput to 0: d Lecture -

13 A Analyss for Dfferental-Mode nput d gnorng r o, we hae d 3 g m g m r 4 π r π e e EE d 4 (g m+ )( + ) r 3 4 π e e EE ( g e m+ )( e ) e 0 Emtter A ground for DM nput. r π EE No bypass cap s needed! Lecture - 3

14 oltage Gan for Dfferental Output d / / 3 d 4 d g d m + g c m c Dfferental output: od c c g m d d e 0 Dfferental-mode gan s: A dd od d c g m 0 Lecture - 4

15 oltage Gan for Sngle-ended Output d g d m c e 0 + g d m c f ether c or c s used alone as output, output s sad to be sngleended. g A A c m dd dd d 0 c A dd c d c 0 g m A dd Lecture - 5

16 Dfferental-Mode nput esstance d Dfferental-mode nput resstance: e 0 d r d π b snce ( / ) d b r π Lecture - 6

17 Output esstances d e 0 Dfferental-mode output resstance s the resstance seen between and : ( r ) od o Sngle-ended output resstance s the resstance seen between (or ) and ground: od Lecture - 7

18 ommon Mode nput 0 0 Set dfferental-mode nput to 0: Lecture - 8

19 A Analyss for ommon-mode nput gnorng r o : (+ β ) e Output oltages are: Dfferental output 0 c b b r π e EE b β c c b rcut s symmetrcal c r π + (β +) EE r π β + (β + ) c EE c EE ommon-mode oltage gan for sngle-ended output Lecture - 9

20 Emtter oltage b r π c + (β +) EE e (β + ) b EE rcut s symmetrcal r π (β + ) EE + (β + ) c EE c Emtter not A ground for M nput. Lecture - 0

21 ommon-mode nput esstance rcut s symmetrcal M nput resstance s the resstance seen between the shorted bases ( c ) and ground: r π + (β + ) r c EE π + (β+ ) c EE b Two b are drawn from the nput oltage source consstng two parallel c. Lecture -

22 ommon-mode ejecton ato M s defned as M A A dm cm represents ablty of amplfer to amplfy desred DM nput sgnal and reject undesred M nput sgnal. For output defned dfferentally, the common-mode gan of a balanced amplfer s zero M s nfnte Many noses appear n common form to the nput and thus do not appear at the output Lecture -

23 Lecture - 3 esstor Msmatch onsder msmatches between (whch always exsts): c EE c c EE c c EE c EE c c od where represents fractonal msmatch ( ) / + M EE g m EE m g cm A dm A EE should be maxmzed for good M Δ+ -Δ

24 DM and M Gans Defne the DM and M outputs as od c c + c c oc Output and nput are related by the gan matrx: od oc A A dd dc A A cd cc d c where A dd dfferental-mode gan A cd common-mode to dfferental-mode conerson gan A cc common-mode gan A dc dfferental mode to common-mode conerson gan For deal symmetrcal amplfer, A cd A dc 0. A dd od 0 A oc 0 cc d c Purely dfferental-mode nput ges purely dfferental-mode output and ce ersa. Lecture - 4

25 Large sgnal analyss Topcs to coer A analyss Half-crcut analyss Lecture - 5

26 Half-rcut Analyss edraw the dfferental amplfer n a fully symmetrcal form power supples are splt nto two equal hales n parallel emtter resstor s separated nto two equal resstors n parallel For dfferental mode sgnals, ponts on the lne of symmetry are grounds for ac analyss and EE are A grounds e s A ground as proen preously For common-mode sgnals, ponts on lne of symmetry are replaced by open crcuts b/c no current flows across the lne of symmetry Lecture - 6

27 Dfferental-mode Half-crcuts Drect analyss of the half-crcuts yeld: c c o g m +g m c c d d g m d The two power supply lnes and emtter become ac grounds / r d d b π ( od r o ) The half-crcut represents a -E amplfer stage Lecture - 7

28 ommon-mode Half-crcut For D For A Half crcut All ponts on lne of symmetry become open crcuts Lecture - 8

29 ommon-mode nput oltage ange The M nput sgnal range for small-sgnal assumpton to be ald s smlar to that of an emtter-degenerated E amplfer: c 5m ( + gm EE ) EE s ery large n most cases Wde common-mode nput range Lecture - 9

30 M nput oltage ange Another condton s that BJT must be n acte mode: 0 B + α BE EE EE α EE BE α EE + EE For example, f EE, EE >> BE, and EE, 3 Lecture - 30

31 Basng wth urrent Source Dfferental amplfers based usng current sources has A more stablzed operatng pont A hgher effecte alue of EE to mproe M D 0 SS SS Equalent of ss Lecture - 3

32 D Analyss S SS /. D Half-crcut D K n + TN TN D K n TN + SS K n D 0 D DD D D and OD + DS D S DD D D Lecture - 3

33 Example Problem: Fnd Q-ponts of transstors n the dfferental amplfer and the upper lmt of nput M oltage. Gen data: DD SS, SS 00 µa, SS 500 kω, D 6 kω, λ , K n 5 ma/, TN Analyss: D SS 00µA 00µ A +.0 5mA/ DS -(00µ A)(6kΩ) +. 7 To mantan pnch-off operaton of M for nonzero, GD - - DD D D - + DD D D TN TN 6.8 Lecture - 33

34 Half rcut for Dfferental-mode nput ac ground Gan for DM output s A dd od d c g m D 0 Gan for sngle-ended output s g d m d D + g d m d D od g m D d Half rcut g A A d m D dd dd d 0 c A dd d + g m D A dd d 0 c DM nput and output resstance: d od D Lecture - 34

35 eference Equatons Lecture - 35

36 Half rcut for ommon-mode nput Half rcut ss Two ss n parallel ommon-mode half-crcut common-source amplfer wth SS as source resstor Lecture - 36

37 A Analyss for M nput Half rcut g m D d d + g m SS ommon-mode gan: A cc od oc c 0 d d c g m D D + g m 0 SS SS d M nput to DM output conerson gan 0 because ommon-mode nput resstance: c Lecture - 37

38 ommon-mode ejecton rato For DM output, M A A dm cm A dm 0 Msmatch wll result n fnte M as n the BJT dfferental par. For sngle-ended output, M A A dm cm A dd / Acc ( g m )/ D /( ) D SS g m SS SS should be maxmzed Lecture - 38

39 lass Exercse Draw the common-mode and dfferental-mode half crcuts for the dfferental par shown below. Lecture - 39

40 Summary Propertes of the dfferental par t amplfes dfference between nput oltages and reject ther common-mode component Most noses, such as power supply nose, appear to be common mode sgnal and not amplfed by the amplfer. M represents ts ablty to reject M nput sgnal. t can produce A ground (for DM nput) at emtter wthout usng bypass capactors nput common mode range s ery wde Half crcut analyss technque Ponts on the lne of symmetry are open-crcuts for M sgnal Ponts on the lne of symmetry are A grounds for DM sgnal Lecture - 40