Basic Building Blocks for Analog Design

Transcription

1 ICTP Micopocesso Laboatoy Second Cental Aeican eional Couse on Adanced VLSI Des Techniques Beneéita Uniesidad Autónoa de Puebla, Puebla, Mexico 9 Noebe 7 Decebe 004 Basic Build Blocks fo Analo Des Gioanni Anelli CEN - Euopean Oanization fo Nuclea eseach Physics Depatent Micoelectonics Goup CH- Genea 3 Switzeland Gioanni.Anelli@cen.ch

2 Instuctions fo use This lectue deals with the basis of analo des. I hae decided to pepae the ateial a ate foal way, dei alost all the necessay foulas. This was done to ty to ie you soe coplete and pecise ateial fo futue efeence. We will not need to assiilate all the foulas today. The ipotant th is that we econize each foula which ae the ipotant paaetes and tends.

3 Analo des tade-offs NOISE LINEAITY POWE DISSIPATION INPUT/OUTPUT IMPEDANCE ANALOG DESIGN OCTAGON GAIN SUPPLY VOLTAGE SPEED VOLTAGE SWINGS Behzad azai, CMOS Technoloy Chaacteization fo Analo and F Des", IEEE JSSC, ol. 34, no. 3, Mach 999, p. 68.

4 Analo des ethodoloy Defe specifications Choose achitectue Siulate scheatic Extact scheatic fo layout Layout Vesus Scheatic (LVS) check Siulate scheatic ay T,, pocess paaetes Extacted scheatic siulations Masks layout Des ules Check (DC) BLOCK DONE! In a coplex des, this will be epeated fo eey block of the des hieachy.

5 Outle Sle-stae aplifies The diffeential pai The cuent io Diffeential pai actie cuent io Opeational aplifie (op ap) des B. azai, Des of Analo CMOS Inteated Cicuits, McGaw-Hill Intenational Edition, 00. P.. Gay, P.J. Hust, S.H. Lewis,.G. Meye, Analysis and Des of Analo Inteated Cicuits, J. Wiley & Sons, 4 th edition, 00.. Geoian, Intoduction to CMOS Op-Aps and Copaatos, J. Wiley & Sons, 999..L. Geie, P.E. Allen and N.. Stade, VLSI Des Techniques fo Analo and Diital Cicuits, McGaw-Hill Intenational Edition, 990. D.A. Johns and K. Mat, Analo Inteated Cicuit Des, J. Wiley & Sons, 997.

6 Outle Sle-stae aplifies Coon-souce Stae Coon-da Stae (Souce Followe) Coon-ate Stae Cascode Stae Folded cascode Stae The diffeential pai The cuent io Diffeential pai actie cuent io Opeational aplifie (op ap) des

7 Coon-Souce Stae (CSS) β Vout VDD D (V VT ) DC chaacteistic n D V out Sall sal a G V V out D β (V n V T ) D V Sall sal a (with channel lenth odulation) G ( // ) 0 D 0 D 0 D Sall sal odel satuation V G S D V GS D o V out The aboe esults could also hae been obtaed diectly fo the sall sal odel

8 CSS Siulation - DC 3.5E-0 Vout [ V ] Vout Ids.0E-0.5E-0.0E-0 5.0E-03 IDS [ A ], [ S ] W 00 µ L 0.5 µ 00 Ω The axiu sall sal a is only.8!!! V [ V ] 0.0E00

9 CSS Siulation - DC Inceas the alue of the load esisto to kω we hae 3.E-0.5 Vout Ids.0E-0 W 00 µ L 0.5 µ Vout [ V ] E E E-03.0E-03 IDS [ A ], [ S ] 000 Ω The axiu sall sal a is now V [ V ] 0.0E00

10 CSS Siulation Sall Sal V [ V ] t [ s ] Ids [ A ] 000 Ω 9.6 S We ject at the put a susoid with fequency khz, peak to peak aplitude V AND dc offset 0.9 V. V [ V ] t [ s ] Vout [ V ] The DC offset is ipotant to be the iht bias pot. The put oltae is coneted a cuent by the tansisto and then a oltae aa by the esisto.

11 Diode-connected tansisto A MOS tansisto behaes as a sall sal esisto when ate and da ae shoted. A tansisto this confiuation is efeed to as diode-connected tansisto. The deice is always satuation. To calculate the ipedance of this deice we use the sall-sal equialent cicuit and a test oltae eneato ( ed). The atio between the oltae x applied and the cuent i x ies the ipedance. G, D i x V GS o x S i x i x x x 0 x 0 The calculation show that the ipedance is ien by the paallel of two esistos, / and 0.

12 Diode-connected tansisto Ipedance seen look to the souce. G, D V GS o b V BS B i x x S i x x x i x x 0 b x i x x b 0 b In this case we hae thee esistances paallel: /, / b and 0.

13 Diode-connected tansisto Ipedance seen look to the da with a esisto S between the souce and ound. G, D i x V GS o V b BS x x i x S B S S i x i x x S ( x ix S ) bix S 0 i x x b 0 0 Without bulk effect ( b ) and the channel lenth odulation ( 0 ) we would see the seies of / and S. If S 0 we fd aa /. S b S

14 CSS with diode-connected load Sall sal a ( // ) G out D S V T T V out G b 0 0 Fo T and T ston esion G n b n ( W /L) ( W / ) L The equations aboe can be obtaed thee diffeent ways: Us the esults found fo sle tansistos (as we hae done) Stat fo the DC equations and do soe atheatics (bo ) Us the sall sal equialent cicuit (see next slide) In an N-well CMOS pocess, the bulk contacts of all the NMOS ae connected toethe to ound (substate). On the othe hand, each bulk contact of the PMOS (each well) can be connected to a desied sal.

15 Sall sal cicuit G, D i out 0 V GS o b V BS i out out 0 b out S, V out i G D out b 0 0 V V GS 0 B S B G out b 0 0

16 CSS with diode-connected load Substitut the NMOS load with a PMOS load, we et id of the bulk effect. T Sall sal a G 0 0 V T V out In ston esion, we hae G µ µ n ( W /L) W /L p ( ) Dawbacks of this confiuation: It is difficult to hae hih a V out_ax V GS. To hae a, (W/L) is ade salle than (W/L). This will liit the axiu output oltae, sce V GS will be quite hihe than V T.

17 CSS with Cuent Souce load To cease the a, we can use the output esistance of a tansisto. T poides the DC cuent bias to T, and has a hih output ipedance. The bias cuent is deteed by V b. V b T Sall sal a G ( // ) V T V out This solution ies a uch hihe a than the othe solutions and has a bette DC output sw, sce V out_ax V DS_sat and V out_ V DS_sat. The output of the cicuit shown is an undefed state (hihipedance node). This cicuit needs theefoe an extenal syste to fix its output DC bias pot (we need a feedback netwok!).

18 CSS with CSL Siulation - DC CSS-CSL Coon Souce Stae with Cuent Souce Load Input Tansisto W 00 µ L 0.5 µ Load Tansisto W 800 µ L 4 µ 3.E-04.4E E-04.E E-05.0E-03 Vout [ V ].5 6.0E-05 IDS [ A ] [ S ] 8.0E E E E Vout Ids.0E-05.0E V [ V ] 0.0E00 0.0E V [ V ]

19 CSS-CSL Siulation Sall S. V [ V ] V [ V ] Sall sal siulations t [ s ] t [ s ] Ids [ µa ] Vout [ V ] We ject at the put a susoid with fequency khz, peak to peak aplitude V and DC offset V. The DC offset is ipotant to be the iht bias pot (especially fo the output!) With a cuent of just 00 µa and the sae put tansisto diensions as the case of the CSS with load esisto, we hae a a of 373. N.B. The output cuent is salle than what it should be. The bias pot is so citical that the siulato has soe pobles

20 CSS with Tiode load This cicuit is the sae as the CSS with Cuent Souce load, but the ate bias of tansisto T is low enouh to ake sue that T woks the lea eion and theefoe it behaes as a esisto. V b T Sall sal a G µ P C ox W L ( V V V ) DD b TP V T V out To hae T the lea eion, we ust hae V b < V out V TP (whee V TP is a positie nube). If we can not take V b < 0 V, we can take it 0 V. In this case we ust hae V out > V TP. The pcipal dawback of this cicuit is that the sall-sal a depends on any paaetes.

21 CSS with Souce Deeneation V D V out S In soe applications, the squae-law dependence of the da cuent upon the ate oedie oltae toduces excessie non leaity. S soothes this effect sce it takes a potion of the ate oedie oltae. At the liit, fo S >> /, the sall sal a does not depend on (and theefoe on I DS ) anyoe. It is teest to note that the appoxiated sall sal a (which can be easily calculated with the sall sal equialent cicuit) can also be calculated as if S and / wee two esistos seies. Sall sal a (appoxiation) G D S S D

22 CSS with Souce Deeneation The appoxiated sall sal oltae a can also be seen as the poduct of the sall sal equialent tansconductance of the deeneated CS Stae ultiplied by the total esistance seen at the output ( D ). To calculate the exact sall sal oltae a we need the exact sall sal equialent tansconductance and the output esistance of the deeneated CS Stae. Both these quantities can be calculated with the equialent sall sal cicuits. D Sall sal a (appoxiation) G S D _ eq D V out V S Exact sall sal equialent tansconductance (with channel lenth odulation and bulk effect) _ eq S 0 0 ( b ) S 0 DO IT YOUSELF AS AN EXECISE!

23 CSS with Souce Deeneation Calculation of the output esistance of the deeneated CS Stae. G D V i x V GS o V b BS x x i x S B S S i x out _ CSS _ de s i x x x 0 s 0 b S s i s x ( b ) 0 S S

24 CSS with Souce Deeneation Exact sall sal a of the deeneated CS Stae. Appoxiated sall sal a G app. S D _ eq D D V out Output esistance of the deeneated CS Stae out out _ CSS _ De // D V out _ CSS _ de 0 S ( b ) 0 S S Exact sall sal a G _ eq out _ eq S 0 0 ( b ) S 0 Execise: ty to obta the sae equation with the coplete sall sal cicuit

25 Souce Followe (SF) The analysis of the Coon Souce Stae (CSS) with cuent souce load deonstated that to hae a hih oltae a we hae to hae a hih load ipedance. If we want to use a CSS to die a low ipedance load, we hae to put a buffe between the CSS and the load. The siplest buffe is the Souce Followe (also called Coon Da Stae). V How do we obta the sall sal a? We could use the sall sal equialent cicuit o we can be clee and euse what we hae seen up to now! V out G V V out S // b / 0 S G b 0 S S ( b ) S The a of ou buffe is nee one! It is, the best case, /n

26 Souce Followe (SF) The Souce Followe with a esisto is hihly non lea, sce the da cuent T is a ston function of the put DC leel. We can theefoe eplace the esisto with a cuent souce. G // SF _ NMOS V 0 DD b / 0 b / 0 / 0 V V b T T V out The a is this case close to /n (still not ). The cicuit is still non lea due to the body effect (non lea dependence of V T upon the souce potential). This can be soled us a PMOS Souce Followe, which both the tansistos hae the body (well) connected to the souce. In this case, we hae: SF _ PMOS G 0 // / 0 / The a can be this case ey close to one! 0 / 0

27 Souce Followe dawbacks G L // 0 // / 0 / 0 / 0 / L G / L L L / V b T V T L V out If the souce followe has to die a low ipedance, we isk to hae a a which is sificantly salle than one. Anothe ipotant dawback is that souce followes shift the sal by one V GS. This is a dawbacks especially low oltae cicuit, whee this causes a liitation the oltae headoo. On the othe hand, if the powe supply oltae is hih enouh, souce followes can be used as oltae leel shiftes.

28 Coon-Gate Stae (CGS) In Coon-Souce Staes and Souce Followes the put sal is applied to the ate. We can also apply it to the souce, obta what is called a Coon-Gate Stae (CGS) out out _ CGS // D out _ CGS 0 D D b /0 0 D 0 ( b ) 0 EXECISE! V b V V out G G D out _ D 0 D ( // ) ( / ) 0 0 D ( ) D b 0 b 0 n D The put ipedance of a CGS is elatiely low, but this only if the load ipedance low. The a is slihtly hihe to the one of a CSS, sce we apply the sal to the souce. N.B. We hae calculated the sall sal a us diffeent ethods (ed and blue). The esults ae identical!

29 Coon-Gate Stae (CGS) With the esults obtaed, it is now ey easy to study the ost eneal case, which cludes the ipedance S of the sal souce, the channel odulation effect and the bulk effect. Let s call the esistance seen by the ideal oltae souce. D 0 S D out ( b ) 0 D out D ( b ) 0 G D S [ ( b ) 0 ] D 0 V out V b S This esult is ey siila to the one of a Coon Souce Stae with souce deeneation. The a hee is still slihtly hihe due to the body effect. It is now also easy to calculate the esistance seen to the output. // out D out _ CSS _ de V out _ CSS _ de 0 S ( b ) 0 S

30 Cascode Stae (CascS) The cascade of a Coon-Souce Stae (V-I conete) and of a Coon-Gate Stae is called a Cascode. D out 0 ( ) 0 D 0 b 0 D EMINDE I T V out V b G 0 ( ) 0 D 0 b 0 D V T The a is pactically the sae as the case of a Coon-Souce Stae. D I I

31 Cascode Stae Output esistance One nice popety of the cascode stae can be discoeed look at the esistance seen the da of T. This is quickly done if we look at T as a Coon-Souce Stae with a deeneation esisto 0. out ( ) S out _ CSS _ de 0 S b 0 V b T out _ CascS 0 0 ( b ) 0 0 ( b ) 0 0 V T Copaed to a CSS, the output ipedance is boosted by a facto ( b ) 0. The disadantae of the cascode confiuation is that the iu output oltae is now the su of the satuation oltaes of T and T. It ust theefoe be used with cae low oltae cicuits.

32 CascS with cuent souce load To fully pofit of the hih output ipedance of the cascode stae, it sees natual to load it with a hih ipedance load, like a cuent souce. out _ CascS 0 0 ( b ) 0 0 V b V b V T out out _ CascS 03 T 3 T V out G out // If 03 is not hih enouh, we can use the cascode pciple to boost the output ipedance of the cuent souce as well. N.B. eebe that the DC output leel hee is not well defed, and that we will need a feedback loop.

33 Folded Cascode Stae (FCascS) V D I b T V out T V b V T T V b V out I b D This solution is has a lowe output ipedance than the standad CascS and consues oe cuent fo the sae pefoance.

34 Outle Sle-stae aplifies The diffeential pai Diffeential sal adantaes The diffeential pai Coon Mode Analysis Lae Sal Analysis Sall Sal Analysis Coon Mode ejection atio (CMM) Diffeential pai with MOS loads Diffeential Pai Misatch The cuent io Diffeential pai actie cuent io Opeational aplifie (op ap) des

35 Sle-Ended s Diffeential A sle-ended sal is defed as a sal easued with espect to a fixed potential (usually, ound). A diffeential sal is defed as a sal easued between two nodes which hae equal and opposite sal excusions. The cente leel diffeential sals is called the Coon-Mode (CM) leel. The ost ipotant adantae of diffeential sals oe sle-ended sals is the uch hihe iunity to enionental noise. As an exaple, let s suppose to hae a distubance on the powe supply. D D D V out_se V out V out -

36 Sle-Ended s Diffeential The Coon-Mode distubances disappea the diffeential output. Vdd Vout_SE Vout Vout - Vout_diff V out _ diff V out V out

37 Diffeential Pai (DP) V,CM V D D V V out V out V out V V V out,cm I SS V out t The cuent souce has a ey ipotant function, sce it akes the su of the cuents the two banches (I I I SS ) dependent fo the put coon ode oltae. The output coon ode oltae is then ien by: out,cm V DD D I SS

38 Diffeential Pai V out V out D D V out V out - D I SS V V V -V V out -V out D I SS I SS N.B. The sall sal a is the slope of this plot V -V - D I SS

39 DP Coon ode analysis To bette undestand what can be the axiu oltae excusion of the put, we substitute the ideal cuent souce with a eal one.,cm _ VGS (VGS3 VT3 ) VGS VDS _ SAT3 D D ISS V V, V V out V out,cm _ ax DD D T DD V T T V And what can be the axiu excusion of the output? V b T 3 V out _ DS _ SAT V DS _ SAT3 out _ ax V DD

40 DP - Lae sal analysis With the basic tansisto equations, soe patience and soe atheatics we can obta the equation fo the plot shown. D I SS V out -V out V li li V -V -V li I - D I SS ISS β /n out out out ID ID V V I D out Fo V < li I I SS Fo < V < li li I β V n 4ISS β /n V Fo V > li I I SS

41 Diffeential pai tansconductance Dei the cuent diffeence as a function of the put oltae diffeence we obta the tansconductance G of the diffeential pai. I G I SS V V -V li V li -V li V li G I V β n 4ISS V β /n 4ISS V β /n 0 G β n I SS

42 DP sall sal a Fo the tansconductance G of the diffeential pai when the diffeential stae is balanced ( 0), we obta the sall sal a G. G β n I I G SS out D D G out D β n I SS The te cicled ed looks suspiciously failia to us It is the tansconductance ston esion of a tansisto cay a cuent I SS /! So we can wite G D

43 DP sall sal a Now that we know it, is is quite obious to econize it look aa at the cicuit scheatic. D D We can see the cicuit as two coon souce staes with deeneated esisto, and supeipose the effects. V V out T T P V out V O, een bette, we can ealize that the pot P is (ideally) AC ounded. out D V b T 3 out D out out D ( )

44 DP Coon Mode a We hae seen that ideally a diffeential pai the output oltae does not depend on the coon ode put oltae. But fact the non fite output ipedance 03 of the cuent souce has an fluence, sce the pot P do not behae as an AC ound anyoe. The syety this cicuit suests that we can see it as two identical half cicuits paallel. This akes the analysis uch easie. D D D What do we hae hee? A CSS with souce deeneation. Easy V V out T T P V out V V out V,CM T G CM out,cm D / 0 V b T 3 03

45 Coon Mode ejection atio The aiation of the coon ode output oltae with the coon ode put oltae is eneally sall and not so woy. MUCH MOE concen is when we hae a diffeential output as a consequence of a coon ode aiation at the put! This can happen if the cicuit is not fully syetic (isatch!). Let's call G CM-DM the a of this coon-ode to diffeential-ode conesion. A diffeence the tansconductances of the two tansistos, fo exaple, would ie: D GCM DM ( ) We see that it is essential to hae a ood cuent souce (ey hih 03 ). To ake possible a eanful copaison between diffeent diffeential cicuit, we want to copae the undesiable diffeential output ien by a coon ode put aiation and the wanted diffeential output ien by a diffeential put. 03 We defe the Coon Mode ejection atio (CM) as: Tak to account ONLY the tansconductance isatch, we obta CM ( 03) CM G G CM DM

46 Diffeential Pai with MOS loads To analyze the two cicuits we can now ake use of the half-cicuit concept and pofit fo all the esults obtaed up to now. G N P // 0N // 0P N P G N ( // ) 0N 0P T 3 T 4 V b T 3 T 4 V b V out V out V out V out V T T V V T T V I SS I SS

47 Cascode Diffeential Pai And, of couse, the a can be boosted us coon-ate staes. T 7 T 8 V b3 V b3 G ( // ) V out V b T 3 T 4 V b V out T 5 T 6 V b V b Cascode staes wee used a lot the past, when the supply oltaes wee elatiely hih (few olts). V T T V In deep subicon technoloies they ae used with oe cae. I SS

48 Diffeential pai isatch The two tansistos hae the sae da cuent σ V GS σ V th σ β / β I σ V GS [V] σ β / β σ V T.4 % 4.5 V 0 8 I σ VT E-0.E-0.E00.E0.E0.E03 I.C.

49 Outle Sle-stae aplifies The diffeential pai The cuent io Standad Cuent Mio Cascode Cuent Mio Low-oltae Cascode Cuent Mio Cuent Mio Output Ipedance Cuent Mio Misatch Diffeential pai actie cuent io Opeational aplifie (op ap) des

50 Cuent io (CM) We suppose that all the tansistos hae the sae µ, C ox and V T. λ is the sae if the tansistos hae the sae L I EF I I W ( λ V ) W W W L L L GND I I EF L W L ( λ V ) To hae an exact eplica of the efeence cuent, we hae to ake the tansisto identical AND they ust hae the sae V DS. When this is not possible, choos lon deices educes the effect of λ. Pecise cuent atios can be obtaed play with the atio between the tansisto widths (not the lenths!). DS DS

51 Cuent io siulation 0.5 µ technoloy,.5 V, I EF 00 µa, W W 00 µ, L L I [ A ] V DS SI V DS WI µ C V DS [ V ] ox 4nφ I n(w /L t ) L 0 u L 0.5 V DS.5 V T L 0.5 [µ] L 0 [µ] I D [µa] β [A/V ] [S] V T [V] V GS [V] V DS_sat [V] out [MΩ]

52 Cascode cuent io (CCM) V G3 ust be fixed so that V D V D. I EF V D V G3 I 3 V D3 W 3 L 3 V D W L W L GND Mak L L and theefoe ha λ λ, we obta that the cuent I 3 pactically does not depend on the oltae V D3. Of couse, all the deices ust be satuation (the cicuit is not suitable fo low oltae applications). V I D 3 I EF W /L W /L ( 3 b3 ) 03 V Ipotant: L 3 can be diffeent fo L and L. P How do we fix V G3 so that V D V D?

53 Cascode cuent io (CCM) I EF I 3 VD3 W 4 L 4 W 3 L 3 V D V D Tansisto 4 does the job hee! Tansistos & decide the cuent atio. Tansistos 3 & 4 fix the bias V D V D. These esults ae alid een if tansistos 3 & 4 suffe fo body effect. I 3 I EF W /L W /L W L W L GND W /L W /L W W 3 4 /L /L 3 4 The poble of this cuent io is that V D3 > V DS3 V GS.

54 Cascode cuent io siulation 0.5 µ technoloy,.5 V, I EF 00 µa I3 [ A ] W W 00 µ L L 0.5 µ W 3 W 4 50 µ L 3 L 4 µ V D3 [ V V D3.5 V T T3 I D [µa] β [A/V ] [S].676. V T [V] V GS [V] V DS_sat [V] out [MΩ]

55 Low Voltae CCM (LVCCM) I EF I 3 VD3 The a diffeence of this cuent io copaed to the standad cascode cuent io is that hee we can lowe the oltaes V D and V D to the liit of the satuation of tansistos T and T. V B V D W 4 W 3 L L 3 4 V D I 3 I EF W /L W /L W W L L GND W /L W /L W W 3 4 /L /L 3 4 The iu output oltae (V D3 ) hee is just two satuation oltaes.

56 Low Voltae CCM siulation () 0.5 µ technoloy,.5 V, I EF 00 µa I3 [ A ] W W 00 µ L L 0.5 µ W 3 W 4 50 µ L 3 L 4 µ V D3 [ V V D3.5 V T T3 I D [µa] β [A/V ] [S] V T [V] V GS [V] V DS_sat [V] out [MΩ] 0.0.6

57 Low Voltae CCM siulation () 0. I3 [ A ] This plot shows that we can lowe the oltae V B until it eaches the V B [ V ] I EF I 3 V B V D W 4 W 3 L L 3 4 liit V GS3 V DS_sat W W L L GND V D3 V D

58 Cuent ios: copaison IOUT [ A ] V out_ CM - L u LVCCM CCM V OUT [ V ] Pecision CM V DS_sat Poo (unless lae L) CCM V GS V DS3_sat Good LVCCM V DS_sat V DS3_sat Good

59 Cuent io output ipedance Standad CM CCM LVCCM V out V out I EF I EF V out I out I out I EF Iout W 4 L 4 W 3 L 3 W 4 L 4 V b W 3 L 3 W L W L GND W L W L GND W W L L GND out 0 out 0 03 ( 3 b3 ) 003

60 Cuent io isatch The two tansistos hae the sae ate oltae σ I/I I σ β / β σ V th I σ I/I [%] σ β / β σ V T.4 % 4.5 V 6 4 σ β / β 0.E-0.E-0.E00.E0.E0.E03 I.C.

61 Outle Sle-stae aplifies The diffeential pai The cuent io Diffeential pai actie cuent io Coon ode, sall sal and lae sal analysis Noise Offset Opeational aplifie (op ap) des

62 Diffeential Pai Actie CM Cuent ios can also pocess a sal, and they can theefoe be used as actie eleents. A diffeential pai with an actie cuent io is also called a diffeential pai with actie load. The cuent io hee has also the ipotant ole to ake a diffeential to sle-end conesion! Coon Mode Analysis T 3 T 4,CM _ VGS VDS _ SAT5 V out ( V V V, V ),CM _ ax DD GS3 T DD V T T Maxiu output excusion V out _ DS _ SAT V DS _ SAT5 V b T 5 out _ ax V DD V DS _ SAT4

63 Diffeential Pai Actie CM Let s now calculate the sall-sal behaio, nelect the bulk effect fo siplicity. The cicuit is NOT syetic, and theefoe we can not use the halfcicuit pciple hee. As a fist appoxiation, we can conside the coon souces of the put tansistos as a itual ound. The sall-sal a G can be seen as the poduct of the total tansconductance of the stae and of the output esistance. T 3 T 4 i out T T V out i out G G G out i out out 0 // 04,, I SS G, ( // ) 0 04

64 Diffeential Pai Actie CM In eality, the cuent souce is not ideal, and this has an effect on the a we hae just calculated. This effect is eneal neliible. What is not neliible is the effect of 05 on the coon ode a. Fo a coon ode put sal the cicuit can be seen syetic! It can be shown that een fo a pefectly syetic cicuit (no isatch) a CM sal at the put (,CM ) eneates an unwanted sal at the output ( out ). Coon Mode Ga (nelect bulk effect and 0, ) V,CM T 3 T 4 T T V b T 5 V out G CM V V out,cm, 05, 3,4 3,4, // 03,4 05

65 Noise a DP Actie CM I I tot i out i out load load tot _ load _ load

66 Noise a DP Actie CM K a _ Ka _ load µ load L tot _ / f CoxWL f Ka _ µ Lload f I tot Make W L bi and L > load L tot _ th 4kTnγ µ C ox W L I µ load µ W L W L load f Make W L > W L load

67 Offset of a DP Actie CM ANDOM OFFSET (WOST CASE) I off I β, β3,4 3,4 V T, VT3, 4, β, β3,4 I SYSTEMATIC OFFSET V off T T V out The diffeence the da oltaes of T and T ies oi a diffeence the DC cuents the two banches. T 3 T 4 COMMON MODE OFFSET As we hae aleady seen, a coon ode sal at the put ies a non zeo output oltae sal.

68 List of Aconys CSS: CSS-CSL: SF: CGS: CascS: FCascS: DP: CM: CCM: LVCCM: CM: Coon-Souce Stae Coon-Souce Stae with Cuent Souce Load Souce Followe (also called Coon-Da Stae) Coon-Gate Stae Cascode Stae CSS CGS Folded Cascode Stae Diffeential Pai Cuent Mio Cascode Cuent Mio Low-Voltae Cascode Cuent Mio Coon Mode ejection atio soy

69 Outle Sle-stae aplifies The diffeential pai The cuent io Diffeential pai actie cuent io Fequency analysis of an aplifie Opeational aplifie (op ap) des Sle-stae op aps Two-stae op aps

70 Op-ap application exaples NONINVETING CONFIGUATION INVETING CONFIGUATION V V out V V out BUFFE V V out V G G G The aboe equations ae alid only if the a of the op-ap is ey hih!

71 Sle-stae Op Ap V b T 7 T 8 T 5 T 6 V b Seeal diffeent solutions can be adopted to ake a Sle-stae aplifie. If hih as ae needed, we can use, fo exaple, cascode stuctues. V b V T 3 T 4 T T V b V out With sle-stae aplifies it is difficult to obta at the sae tie hih a and oltae excusion, especially when othe chaacteistics ae also equied, such as speed and/o pecision. Two-stae confiuations this sense ae bette, sce they decouple the a and oltae sw equieents. I SS

72 Two-stae Op Ap G 8, (0, // 03,4 ) 5,6(05,6 // 07, ) The second stae is ey often a CSS, sce this allows T 3 T 4 the axiu oltae sw. T 5 V b T 6 V T T The output oltae sw this case is - V DS_SAT V out V out I SS V b T 7 T 8

73 G Two-stae Op Ap { [( ) )]//[( ) )] } ( // ), 3,4 b3,4 03,4 0, 5,6 b5,6 05,6 07,8 9,0 09,0 0, V b3 V b T 7 T 8 T 5 T 6 V b3 V b To cease the a, we can aa ake use, the fist stae, of cascode stuctues. T 9 T 0 V b T 3 T 4 V b V out T T V out V V b4 T T I SS V b4

74 Two-stae Op Ap G, (0, // 03,4 ) 6(06 // 08 ) V T 3 T 4 T 5 V b T 6 T T Two-stae op aps can also hae a sle-ended output. In this case, we kept the diffeential behaio of the fist stae, and is the cuent io T7-T8 which does the diffeential-to-sle ended conesion. V out I SS T 7 T 8