EECE488: Analog CMOS Integrated Circuit Design. 3. Single-Stage Amplifiers
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1 EECE488: Analo CM Inteated Cicuit esin 3. inle-tae Aplifies hahia Miabbasi epatent of Electical and Copute Enineein Uniesity of Bitish Colubia Technical contibutions of Peda Lajeadi in eisin the couse notes ae eatly acknowleded. M et 3: inle-tae Aplifies eiew. Why Aplifies?. Aplifie Chaacteistics 3. Aplifie Tade-offs 4. inle-stae Aplifies 5. Coon ouce Aplifies. esistie Load. iode-connected Load 3. Cuent ouce Load 4. Tiode Load 5. ouce eeneation M et 3: inle-tae Aplifies
2 eiew 6. Coon-ain (ouce-followe Aplifies. esistie Load. Cuent ouce Load 3. Voltae iision in ouce Followes 7. Coon-Gate Aplifies 6. Cascode Aplifies M et 3: inle-tae Aplifies 3 eadin Assinents eadin: Chapte 3 of azai s book In this set of slides we will study low-fequency sall-sinal behaio of sinle-stae CM aplifies. Althouh, we assue lon-channel M odels (not a ood assuption fo deep subicon technoloies the techniques discussed hee help us to deelop basic cicuit intuition and to bette undestand and pedict the behaio of cicuits. Most of the fiues in these lectue notes ae esin of Analo CM Inteated Cicuits, McGaw-Hill, 00. M et 3: inle-tae Aplifies 4
3 Why Aplifies? Aplifies ae essential buildin blocks of both analo and diital systes. Aplifies ae needed fo aiety of easons includin: To aplify a weak analo sinal fo futhe pocessin To educe the effects of noise of the next stae To poide a pope loical leels (in diital cicuits Aplifies also play a cucial ole in feedback systes We fist look at the low-fequency pefoance of aplifies. Theefoe, all capacitos in the sall-sinal odel ae inoed! M et 3: inle-tae Aplifies 5 Aplifie Chaacteistics - Ideally we would like that the output of an aplifie be a linea function of the input, i.e., the input ties a constant ain: y x y αx In eal wold the input-output chaacteistics is typically a nonlinea function: M et 3: inle-tae Aplifies 6 3
4 Aplifie Chaacteistics - It is oe conenient to use a linea appoxiation of a nonlinea function. Use the tanent line to the cue at the ien (opeatin point. y The lae the sinal chanes about the opeatin point, the wose the appoxiation of the cue by its tanent line. x This is why sall-sinal analysis is so popula! M et 3: inle-tae Aplifies 7 Aplifie Chaacteistics - 3 A well-behaed nonlinea function in the icinity of a ien point can be appoxiated by its coespondin Taylo seies: n f ''( x0 f ( x0 n y f ( x0 f '( x0 ( x x0 ( x x0 L ( x x0! n! f n Let α ( x 0 n to et: n! y α 0 α( x x0 α ( x x0 L α n ( x x0 If x-x 0 x is sall, we can inoe the hihe-ode tes (hence the nae sall-sinal analysis to et: y α ( 0 α x x0 α 0 is efeed to as the opeatin (bias point and α is the sall-sinal ain. 0 0 y y f ( x y α α x n M et 3: inle-tae Aplifies 8 4
5 Aplifie Tade-offs In pactice, when desinin an aplifie, we need to optiize fo soe pefoance paaetes. Typically, these paaetes tade pefoance with each othe, theefoe, we need to choose an acceptable copoise. M et 3: inle-tae Aplifies 9 inle-tae Aplifies We will exaine the followin types of aplifies:. Coon ouce. Coon ain (ouce Followe 3. Coon Gate 4. Cascode and Folded Cascode Each of these aplifies hae soe adantaes and soe disadantaes. ften, desines hae to utilize a cascade cobination of these aplifies to eet the desin equieents. M et 3: inle-tae Aplifies 0 5
6 Coon ouce Basics - In coon-souce aplifies, the input is (soehow! connected to the ate and the output is (soehow! taken fo the dain. We can diide coon souce aplifies into two oups:. Without souce deeneation (no body effect fo the ain tansisto:. With souce deeneation (hae to take body effect into account fo the ain tansisto: M et 3: inle-tae Aplifies Coon ouce Basics - In a siple coon souce aplifie: ate oltae aiations ties ies the dain cuent aiations, dain cuent aiations ties the load ies the output oltae aiations. Theefoe, one can expect the sall-sinal ain to be: A M et 3: inle-tae Aplifies 6
7 Coon ouce Basics - 3 iffeent types of loads can be used in an aplifie:. esistie Load. iode-connected Load 3. Cuent ouce Load 4. Tiode Load The followin paaetes of aplifies ae ey ipotant:. all-sinal ain. Voltae swin M et 3: inle-tae Aplifies 3 esistie Load - Let s use a esisto as the load. The eion of opeation of M depends on its size and the alues of V in and. We ae inteested in the sall-sinal ain and the headoo (which deteines the axiu oltae swin. We will calculate the ain usin two diffeent ethods. all-sinal odel. Lae-sinal analysis M et 3: inle-tae Aplifies 4 7
8 esistie Load - Gain Method : all-inal Model This is assuin that the tansisto is in satuation, and channel lenth odulation is inoed. The cuent thouh : utput Voltae: all-sinal Gain: A i UT i UT M et 3: inle-tae Aplifies 5 esistie Load - 3 Gain Method : Lae-inal Analysis If V <V TH, M is off, and V UT V V. V UT V A UT As V becoes slihtly lae than V TH, M tuns on and oes into satuation (V V > V G -V TH 0. VUT Vdd i Vdd W µ C ( V V n ox TH L W UT A µ C ( V n ox L VTH 0 i V As V inceases, V deceases, and M oes into tiode when V -V TH V UT. We can find the alue of V that akes M switch its eion of opeation. VUT Vdd i Vdd W µ C ( V V ( V n ox TH L VTH M et 3: inle-tae Aplifies 6 8
9 esistie Load - 4 Gain Method : Lae-inal Analysis (Continued As V inceases, V deceases, and M oes into tiode. W V VUT V i V µ n Cox ( V VTH VUT L UT W UT UT µ n Cox ( V VTH VUT VUT L We can find A fo aboe. It will depend on both V and V UT. If V inceases futhe, M oes into deep tiode if V UT << (V -V TH. UT V V UT UT W V i V µ n Cox ( V V L V V W µ n Cox ( V VTH L N TH V V UT N N M et 3: inle-tae Aplifies 7 esistie Load - 5 Exaple: ketch the dain cuent and of M as a function of V. depends on V, so if V chanes by a lae aount the sallsinal appoxiation will not be alid anyoe. In ode to hae a linea aplifie, we don t want ain to depend on paaetes like which depend on the input sinal. M et 3: inle-tae Aplifies 8 9
10 esistie Load - 6 Gain of coon-souce aplifie: W V W V V A µ ncox ( V VTH µ ncox L I L I Veff To incease the ain:. Incease by inceasin W o V (C potion o bias. Eithe way, I inceases (oe powe and V inceases, which liits the oltae swin.. Incease and keep I constant ( and powe eain constant. But, V inceases which liits the oltae swin. 3. Incease and educe I so V eains constant. If I is educed by deceasin W, the ain will not chane. If I is educed by deceasin V (bias, the ain will incease. ince is inceased, the bandwidth becoes salle (why?. Notice the tade-offs between ain, bandwidth, and oltae swins. M et 3: inle-tae Aplifies 9 esistie Load - 7 Now let s conside the siple coon-souce cicuit with channel lenth odulation taken into account. Channel lenth odulation becoes oe ipotant as inceases (in the next slide we will see why!. Aain, we will calculate the ain in two diffeent ethods. all-sinal Model. Lae inal Analysis M et 3: inle-tae Aplifies 0 0
11 esistie Load - 8 Gain Method : all-inal Model This is assuin that the tansisto is in satuation. The cuent thouh : i utput Voltae: UT i ( ( o o all-sinal Gain: A UT ( o M et 3: inle-tae Aplifies esistie Load - 9 Gain Method : Lae-inal Analysis As V becoes slihtly lae than V TH, M tuns on and oes into satuation (V V > V G -V TH 0. W VUT V I V µ n Cox ( V VTH ( λ VUT L UT W ( UT µ n Cox ( V VTH λ VUT ( V VTH λ L W µ n Cox ( V VTH ( λ VUT L A W I µ n Cox V V λ ( TH λ L o o ( o o M et 3: inle-tae Aplifies
12 esistie Load - 0 Exaple: Assuin M is biased in actie eion, what is the sall-sinal ain of the followin cicuit? I is a cuent souce and ideally has an infinite ipedance. A UT ( o o This is the axiu ain of this aplifie (why?, and is known as the intinsic ain. How can V chane if I is constant? W I λ n ox TH L µ C ( V V ( V Hee we hae to take channel-lenth odulation into account. As V chanes, V UT also chanes to keep I constant. UT M et 3: inle-tae Aplifies 3 iode Connected Load - ften, it is difficult to fabicate tihtly contolled o easonable size esistos on chip. o, it is desiable to eplace the load esisto with a M deice. ecall the diode connected deices: Body Effect (when λ 0 (when λ0 N o YE o b b M et 3: inle-tae Aplifies 4
13 iode Connected Load - Now conside the coon-souce aplifie with two types of diode connected loads:. PM diode connected load: (No body effect. NM diode connected load: (Body effect has to be taken into account M et 3: inle-tae Aplifies 5 iode Connected Load - 3 PM iode Connected Load: Note that this is a coon souce confiuation with M bein the load. We hae: UT A ( o o o Inoin the channel lenth odulation ( o o, we can wite: W µ n Cox I L A W µ p Cox I L I VG VTH VG VTH A I VG VTH VG VTH W µ n L W µ p L M et 3: inle-tae Aplifies 6 3
14 NM iode Connected Load: iode Connected Load - 4 Aain, note that this is a coon souce confiuation with M bein the load. We hae: UT A ( o o o b Inoin the channel lenth odulation ( o o, we can wite: A b b ( η W L VG V A TH η W η VG V TH L M et 3: inle-tae Aplifies 7 iode Connected Load - 5 Fo a diode connected load we obsee that (to the fist ode appoxiation:. The aplifie ain is not a function of the bias cuent. o, the chane in the input and output leels does not affect the ain, and the aplifie becoes oe linea.. The aplifie ain is not a function of the input sinal (aplifie becoes oe linea. 3. The aplifie ain is a weak function (squae oot of the tansisto sizes. o, we hae to chane the diensions by a consideable aount so as to incease the ain. M et 3: inle-tae Aplifies 8 4
15 iode Connected Load The ain of the aplifie is educed when body effect should be consideed. 5. We want M to be in satuation, and M to be on (M cannot be in tiode (why?: 6. The oltae swin is constained by both the equied oedie oltaes and the theshold oltae of the diode connected deice. M: VUT > VG VTH Veff, M : VUT < V VTH 7. A hih aplifie ain leads to a hih oedie oltae fo the diode connected deice which liits the oltae swin. M et 3: inle-tae Aplifies 9 iode Connected Load - 6 Exaple: Find the ain of the followin cicuit if M is biased in satuation and I s 0.75I. UT A ( Is o o o o o Inoin the channel lenth odulation ( o o we et: A A W µ n L W µ p L VG VTH 4 VG VTH W µ n Cox I L W µ p Cox I L I VG V TH I VG VTH M et 3: inle-tae Aplifies 30 5
16 Exaple (Continued: iode Connected Load - 7 We obsee fo this exaple that:. Fo fixed tansisto sizes, usin the cuent souce inceases the ain by a facto of.. Fo fixed oedie oltaes, usin the cuent souce inceases the ain by a facto of Fo a ien ain, usin the cuent souce allows us to ake the diode connected load 4 ties salle. 4. Fo a ien ain, usin the cuent souce allows us to ake the oedie oltae of the diode connected load 4 ties salle. This inceases the headoo fo oltae swin. M et 3: inle-tae Aplifies 3 Cuent ouce Load - Note that cuent souce M is the load. ecall that the output ipedance of M seen fo V out : o i A UT ( ( o Fo lae ain at ien powe, we want lae o and o λ I W L L Incease L and W keepin the aspect atio constant (so o inceases and I eains constant. Howee, this appoach inceases the capacitance of the output node. We want M to be in satuation so o o L W V V VUT > VG VTH Veff VUT < V Veff M et 3: inle-tae Aplifies 3 6
17 Cuent ouce Load - We also want M to be in satuation: V V > V V V V > V UT G TH eff UT eff Thus, we want V eff and V eff to be sall, so that thee is oe headoo fo output oltae swin. Fo a constant I, we can incease W and W to educe V eff and V eff. The intinsic ain of this aplifie is: A o In eneal, we hae: W L, o L W A L But since cuent in this case is ouhly constant: µ C n W I L ox W L, o λ I L A LW M et 3: inle-tae Aplifies 33 Tiode Load We econize that this is a coon souce confiuation with M bein the load. ecall that if M is in deep tiode, i.e., V <<(V G - V TH, it behaes like a esisto. M If V N << ( V V G TH W µ C p ox L : ( V V µ C ( V V V, G TH p ox W L et 3: inle-tae Aplifies dd b TH A ( V b should be low enouh to ake sue that M is in deep tiode eion and usually equies additional coplexity to be pecisely eneated. N depends on µ p, C ox, and V TH which in tun depend on the technoloy bein used. In eneal, this aplifie with tiode load is difficult to desin and use! Howee, copaed to diode-connected load, tiode load consues less headoo: M : VUT > VG VTH Veff, M : VUT V N 34 o 7
18 ouce eeneation - The followin cicuit shows a coon souce confiuation with a deeneation esisto in the souce. We will show that this confiuation akes the coon souce aplifie oe linea. We will use two ethods to deie the ain of this cicuit:. all-sinal Model. Usin the followin Lea Lea: In linea systes, the oltae ain is equal to G out. M et 3: inle-tae Aplifies 35 ouce eeneation - Gain Method : all inal Model i UT UT i UT b UT UT A B UT b UT UT i ( ( b UT b, B UT, i UT i UT UT UT UT UT M et 3: inle-tae Aplifies 36 8
19 9 et 3: inle-tae Aplifies 37 M ouce eeneation - 3 Gain Method : Lea The Lea states that in linea systes, the oltae ain is equal to G out. o we need to find G and out.. G : ecall that the equialent tansconductance of the aboe Cicuit is: ( ( b b i G UT ] [ et 3: inle-tae Aplifies 38 M ouce eeneation - 4 Gain Method : Lea (Continued. UT : We use the followin sall sinal odel to deie the sall sinal output ipedance of this aplifie: ( ( ( ( ( ( ( ( ( ( b b UT b b b B b B i i i i i i i i i ( ( (, ince typically >> : ( ( ( b b b ( (
20 0 et 3: inle-tae Aplifies 39 M ouce eeneation - 5 Gain Method : Lea (Continued ( ( ( ( ( b b b b UT G A ( ( ( ( b b UT ( ( ( b G ( et 3: inle-tae Aplifies 40 M ouce eeneation - 6 If we inoe body effect and channel-lenth odulation: Method all-sinal Model: UT G A ( ( ( ( ( ( b b b b UT b o li 0 ( ( b b G b o li 0 UT G G G G UT A, Method Takin liits:
21 ouce eeneation - 7 btainin G and out diectly assuin λγ0:. G : i G, G G G i G. UT : G UT 0 i G i G A G UT G M et 3: inle-tae Aplifies 4 ouce eeneation - 8 If we inoe body effect and channel-lenth odulation: G, A UT We Notice that as inceases G becoes less dependent on : s li G li s i UT That is fo lae : G i UT Theefoe, the aplifie becoes oe linea when is lae enouh. Intuitiely, an incease in tend to incease I, howee, the oltae dop acoss also inceases. This akes the aplifie less sensitie to input chanes, and akes I soothe! The lineaization is achieed at the cost of losin ain and oltae headoo. M et 3: inle-tae Aplifies 4
22 ouce eeneation - 9 We can anipulate the ain equation so the nueato is the esistance seen at the dain node, and the denoinato is the esistance in the souce path. A The followin ae I and of a tansisto without. I and of a tansisto considein ae: When I is sall such that <<, G. When I is lae such that >>, G /. M et 3: inle-tae Aplifies 43 Altenatie Method to Find the utput-esistance of a eeneated Coon-ouce Aplifie M et 3: inle-tae Aplifies 44
23 Why Buffes? Coon ouce aplifies needed a lae load ipedance to poide a lae ain. If the load is sall but we need a lae ain (can you think of an exaple? a buffe is used. ouce-followe (coon-dain aplifies can be used as buffes., 0, A UT V Ideal Buffe:. : the input cuent is zeo; it doesn t load the peious stae.. UT 0: No oltae dop at the output; behaes like a oltae souce. M et 3: inle-tae Aplifies 45 esistie Load - We will exaine the ouce followe aplifie with two diffeent loads:. esistie Load. Cuent ouce Load esistie Load: As shown below the output (souce oltae will follow the input (ate oltae. We will analyze the followin cicuit usin lae-sinal and sall-sinal analysis. M et 3: inle-tae Aplifies 46 3
24 esistie Load - Lae inal Analysis: The elationship between V and V UT is: W V I µ C ( V V ( λ V UT n ox G TH L W V µ C V V V λ V λ V UT n ox UT TH L iffeentiate with espect to V : W UT µ C n ox UT L V TH V TH W µ C n ox L TH 0 γ TH UT ( ( UT UT TH ( V V V ( λ V ( Φ V Φ F B F UT ( V V ( λ G TH TH γ Φ V F B UT Need to find the deiatie of V TH with espect to V :, UT V B V UT η UT M et 3: inle-tae Aplifies 47 esistie Load - 3 Lae inal Analysis (Continued: The sall sinal ain can be found: UT A V ( η I λ UT b b o o If channel-lenth odulation is inoed ( o we et: A V UT ( b M et 3: inle-tae Aplifies 48 4
25 esistie Load - 4 all inal Analysis: We et the followin sall sinal odel: UT UT UT A ( ( ( ( ( UT A G b UT B b b b, UT b G, UT ( B UT b M et 3: inle-tae Aplifies 49 esistie Load - 5 Gaph of the ain of a souce-followe aplifie:. M nee entes the tiode eion as lon as V <V.. Gain is zeo if V is less than V TH (because is As V inceases, inceases and the ain becoes: A b η 4. As V UT inceases, η deceases, and theefoe, the axiu ain inceases. 5. Een if, the ain is less than one: A < V b o 6. Gain depends heaily on the C leel of the input (nonlinea aplifie. M et 3: inle-tae Aplifies 50 5
26 Cuent ouce Load In a souce followe with a esistie load, the dain cuent depends on the C leel of V, which akes the aplifie hihly nonlinea. To aoid this poble, we can use a cuent souce as the load. The output esistance is:, M o I o UT M I b o b o If channel lenth odulation is inoed ( o o : UT b b b Note that the body effect educes the output ipedance of the souce followe aplifies. M et 3: inle-tae Aplifies 5 Voltae iision in ouce Followes - When Calculatin output esistance seen at the souce of M, i.e., M,, we foce to zeo and find the output ipedance: M o b Howee, if we wee to find the ain of the aplifie, we would not suppess. Hee, we would like to find an equialent cicuit of M, fo which we can find the ain. Conside the sall-sinal odel of M : M et 3: inle-tae Aplifies 5 6
27 7 et 3: inle-tae Aplifies 53 M Voltae iision in ouce Followes - Fo sall-sinal analysis B, so b B dependant cuent souce can be eplaced by a esisto (/ b between souce and dain. Note that, when lookin at the cicuit fo the souce teinal, we can eplace the G dependant cuent souce with a esisto (of alue / between souce and ate. iplified cicuit: et 3: inle-tae Aplifies 54 M Voltae iision in ouce Followes - 3 Exaple: Find the ain of a souce followe aplifie with a esistie load. We daw the sall sinal odel of this aplifie as shown below to et: b b UT b b UT A b b b b b A We can show that this is equal to what we obtained befoe:
28 Voltae iision in ouce Followes - 4 Exaple: Find the ain of a souce followe aplifie with a cuent souce load. all-sinal odel of this aplifie is: UT b b A UT b b If we inoe channel lenth odulation: UT b b A UT b b M et 3: inle-tae Aplifies 55 Voltae iision in ouce Followes - 5 Exaple: Find the ain of a souce followe aplifie with a esistie load and biased with a cuent souce. all-sinal odel of this aplifie is: UT L L b b A UT L L b b M et 3: inle-tae Aplifies 56 8
29 Voltae iision in ouce Followes - 6 Exaple: Find the ain of a souce followe aplifie with a esistie load. all-sinal odel of this aplifie is: UT b b b b A UT b b b b M et 3: inle-tae Aplifies 57 Adantaes and isadantaes -. ouce followes hae typically sall output ipedance.. ouce followes hae lae input ipedance. 3. ouce followes hae poo diin capabilities.. 4. ouce followes ae nonlinea. This nonlineaity is caused by: Vaiable bias cuent which can be esoled if we use a cuent souce to bias the souce followe. Body effect; i.e., dependence of V TH on the souce (output oltae. This can be esoled fo PM deices, because each PM tansisto can hae a sepaate n-well. Howee, because of low obility, PM deices hae hihe output ipedance. (In oe adanced technoloies, NM in a sepaate p-well, can be ipleented that potentially has no body effect ependence of o on V in subicon deices. M et 3: inle-tae Aplifies 58 9
30 Adantaes and isadantaes - 5. ouce followes hae oltae headoo liitations due to leel shift. Conside this cicuit (a coon souce followed by a souce followe: If we only conside the coon souce stae, V >V G -V TH. If we only conside the souce followe stae, V >V G3 -V TH3 V G. Theefoe, addin the souce followe will educe the allowable oltae swin at node. The C alue of V UT is V G lowe than the C alue of V. M et 3: inle-tae Aplifies 59 Coon-Gate A ( b ( η M et 3: inle-tae Aplifies 60 30
31 Coon-Gate A ( b o o ( b o M et 3: inle-tae Aplifies 6 Coon-Gate A ( b o o ( b o fo 0 : A ( b( o M et 3: inle-tae Aplifies 6 3
32 Coon-Gate Input Ipedance in o o ( ( ( b o in ( ( b o o b o b b o M et 3: inle-tae Aplifies 63 Coon-Gate Input Ipedance Input ipedance of coon-ate stae is elatiely low only if is sall Exaple: Find the input ipedance of the followin cicuit. M et 3: inle-tae Aplifies 64 3
33 Exaple Calculate the oltae ain of the followin cicuit: A ( b o M et 3: inle-tae Aplifies 65 Coon-Gate utput Ipedance {[ ( ] } out b o M et 3: inle-tae Aplifies 66 33
34 Exaple Copae the ain of the followin two cicuits (λγ0 and 50Ω tansission lines! M et 3: inle-tae Aplifies 67 Cascode tae Cascade of a coon-souce stae and a coon-ate stae is called a cascode stae. out {[ ( [( b b o o ] o o ] } o A V {[ o o ( b ] ]} M et 3: inle-tae Aplifies 68 34
35 Cascode tae A V [( o o ( o3 o4 3 ] M et 3: inle-tae Aplifies 69 utput Ipedance Copaison M et 3: inle-tae Aplifies 70 35
36 hieldin Popety M et 3: inle-tae Aplifies 7 Boad Notes M et 3: inle-tae Aplifies 7 36
37 Tiple Cascode What is the output esistance of this cicuit? Poble? M et 3: inle-tae Aplifies 73 Folded Cascode M et 3: inle-tae Aplifies 74 37
38 utput Ipedance of a Folded Cascode out [ ( b o ]( o o 3 o M et 3: inle-tae Aplifies 75 38
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