Exercises for Differential Amplifiers. ECE 102, Fall 2012, F. Najmabadi

Transcription

1 Execises f iffeential mplifies ECE 0, Fall 0, F. Najmabai

2 Execise : Cmpute,, an G if m, 00 Ω, O, an ientical Q &Q with µ n C x 8 m, t, λ 0. F G 0 an B F G. epeat the execise f λ This execise shws that pecise biasing f Q an Q is nt necessay as ajusts itself autmatically. nclusin f channel-length mulatin es nt impact the bias pints f Q an Q which is set by the cuent suce. F. Najmabai, ECE0, Fall 0 7

3 gning channel-length mulatin λ 0 K: ssume atuatin 0 µ ncx O 4 0 O O m G O + t. G > 0 G O + & G 0.. > O atuatin G > G O 0 + & G > O atuatin F. Najmabai, ECE0, Fall 0 7 Nte that as the bias ltage f Q, G, changes, is ajuste autmatically t get the necessay O an

4 ncluing channel-length mulatin λ 0. K: m. ssume atuatin 0 O + 0. µ C n x O + λ n Nee t wite in tems f O : O + + G + O G t + t + G G F a gien G, we then substitute f in equatin which leas t a cubic equatin f O F. Najmabai, ECE0, Fall 0 47

5 ncluing channel- length mulatin λ 0.. O O + t G C G 0 O O 0. G O + t O O +.0 [ + 0. O +. G G O O +.0] O G O G O + t G G +. + O O + O 0. [ + 0. O +. O O +.0] O F. Najmabai, ECE0, Fall 0 7

6 Bias ltage f Q an Q G es nt affect as ajusts itself autmatically. G affects nly an an pecise biasing is NOT necessay. gne channel-length mulatin nclue channel-length mulatin O G O G.0 m m m m pecifie paametes nclusin f channel-length mulatin es nt impact the bias pints f Q an Q which is set by the Q cuent suce. F. Najmabai, ECE0, Fall 0 67

7 Execise : Fin the iffeential gain an f all tansists in the cicuit belw, Q & Q4 ae matche, Q & Q ae matche, all tansists hae O 0., µ n C x 400 µ, µ p C x 00 µ, an n p.6. gne channel-length mulatin in biasing calculatins. F symmetic cicuits:,,,,,,, F. Najmabai, ECE0, Fall 0 77

8 ince tansists ae matche an hae the same O : 4 00 µ µ n. C 6 0 µ p 0 4 C x x O O, g m, iffeential Me Half Cicuit g m O 0 6 k 6 k g m k 6 k F. Najmabai, ECE0, Fall 0 87

9 Execise : The iffeential amplifie belw shul achiee a iffeential gain f 40 with a pwe cnsumptin f m. ll tansists peate with the same O. Fin f all tansists, G, G4, an G. µ n C x 400 µ, µ p C x 00 µ, λ n 0., λ p 0., an tn tp 0.4. gne channel-length mulatin in biasing. Pwe Cnsumptin: P m 6 m F. Najmabai, ECE0, Fall 0 97

10 F. Najmabai, ECE0, Fall 0 07 iffeential Me Half Cicuit p n n p n p p n + λ λ λ λ λ λ λ λ O O n O m m g g λ,, m g

11 F. Najmabai, ECE0, Fall m 4 4 O O O O O C O x µ n C O x µ p C O x µ n G G tn O G G G tp O G

12 Execise 4: The cicuit belw is fabicate with n p.6, µ n C x 00 µ & µ p C x µ. ll tansists peate with O. Fin f all tansists an the iffeential gain f the cicuit. F. Najmabai, ECE0, Fall 0 7

13 F. Najmabai, ECE0, Fall k m O m m m O O O O g g g λ µ p n λ λ NMO: Q, Q, Q, & Q4: C O x µ n PMO: Q, Q6, Q7, & Q8: C O x µ p

14 Meth : Use fmula f Casce mplifie n ectue et 6, slie 4 which assumes g m >> :, g 0.4 0,, m, g m g m... g... 8 m8 0.4 m 6 k iffeential Me Half Cicuit Meth : Use multistage amplifie calculatins simila t ectue et 6, slie 4 but nt assuming g m >> : + gm Q i + gm Q, g m 7 6 k 90k k g m i 90 k 6 k 40.6k 7.6 g m >> is a g appximatins QQ 0.8 F. Najmabai, ECE0, Fall 0 47

15 Execise : ssume Q an Q4 as well Q an Q ae ientical. Cmpute the iffeential gain. This is a pactice pblem in cnstucting half-cicuit. F. Najmabai, ECE0, Fall 0 7

16 Half-cicuit f iffeential Gain Ze ltage at symmety line eplace Q by Elementay fms, g m, P F. Najmabai, ECE0, Fall 0 67

17 Execise 6: Cmpute the iffeential gain. This pblem has it all, half cicuit, cnstucting esistances fm elementay fm, an Casce amplifie. F. Najmabai, ECE0, Fall 0 77

18 iffeential-me half-cicuit [ + gm 7 p ] + 7 p ince p alue is nt gien, we cannt simplify expessin using g m >>. + Q, gm i Q gm i F. Najmabai, ECE0, Fall gm g g Q Q m m i

19 Execise 7: hat is the input cmmn-me ange in the cicuit belw. Q an Q ae entical an 00. Use µ n C x 8 m, t an G. The input cmmn-me leel is the ange f C alues that can be applie t the gate f Q an Q bias + signal f which tansists emain in satuatin. Basically we ae lking f ange f C ltages i.e., bias that can be applie t Q an Q while keeping them in satuatin. Then, f any gien bias ltage, we can calculate the ange f cmmn-me signals that can be applie t the cicuit. Thee ae tw limits: f Q an Q emain in satuatin, f Q t emain in satuatin. t is staight fwa t exten this t actie las. F. Najmabai, ECE0, Fall 0 97

20 ssume Q an Q in atuatin µ C 0 n x O 4 0 O O G O + t. O G t G t F Q in satuatin: O +.. F QQ in satuatin: O.. G CM. CM CM CM F. Najmabai, ECE0, Fall 0 07

21 Execise 8: Cicuit belw is esigne t peate at ze bias ltage at the gate f Q an Q Q & Q ae matche an λ 0. The pactical cicuit, hwee inclues a slight mis-match f an + is small. f 0, fin iffeential C ltage at the utput. B F what alues f O, the C utput ltage will be ze. gne channel-length mulatin. N amplifie chip can be manufactue with pefect symmety. Mis-matches nt nly affect CM but C ltages. iffeential C ltage at the utput an the input ffset ltage, O, ae imptant specs. Chips typically inclue pins f feeback t ze ut these ltages. Nte: an ae C alues in this pblem, they can be iewe eithe as mis-matche bias an n signal an signal but with a matche ze bias. F. Najmabai, ECE0, Fall 0 7

22 F. Najmabai, ECE0, Fall 0 7 ince tansists ae matche an G G because : Output Offset ltage f 0, fin iffeential C ltage at the utput: + 0. &. 0

23 B F what alues f O, the C utput ltage will be ze. gne channel-length mulatin. 0. Output Offset ltage 0. Meth : iewing O as the signal. The bias ltages emain at ze an has the abe alue. iffeential signal O is applie t the cicuit leaing t a iffeential utput,,. e want t fin O such that, + 0 O an + O,, g g m m O + O + g m g m O O g,,, m, g g O O F. Najmabai, ECE0, Fall 0 7 m m, O g [ m + O O O ] nput Offset ltage O O

24 Meth : iewing O as the bias ltage: F: Fin: 0 µ C G G G n x O + s an G s such that 0 µ C µ C µ C n n n x x x O O O O O 0. O O O O µ C O n x O O O O pping O tems by assuming O << O O O + O O + 0 O O + O O F. Najmabai, ECE0, Fall 0 47

25 Execise 9: Cnsie the cicuit belw with µ n C x 90 µ, µ p C x 0 µ, tn pn 0.7 an n p 0. The cicuit is t peate such that all tansists peate at O, 4 ef 0. m, an 6. a esign the cicuit i.e., fin f all tansists. b Fin the iffeential gain. c Fin the cmmn me espnse at i.e., CM. Fin the input cmmn-me ange e Fin the allwable ange f the utput ltage. gne channel-length mulatin in biasing calculatins. F. Najmabai, ECE0, Fall 0 7

26 Q6: Piing efeence ltage cuent f Q Q: Biasing cuent mi Q & Q: PMO iffeential amplifie 4 Qef: The efeence leg f cuent mi f the cicuit 6 Q7: Piing ef f Q6 Q& Q4: cuentsuceactie las F. Najmabai, ECE0, Fall 0 67

27 a Fin f all tansists 4 ef 0. m, an 6. tep : Cmpute all cuents m m m tep : Cmpute s NMO: Qef, Q, Q4, an Q ef µ C ef 7.8 n x ef O ef 4 ef 0. m 4 ef ef 0.4 m 7 ef.6 F. Najmabai, ECE0, Fall 0 77

28 PMO: Q, Q, Q, an Q µ p C x O m m 6 07 mall signal paametes: g m g m 4 O F. Najmabai, ECE0, Fall k 00 k 00 k

29 b Fin the iffeential gain: c Fin cmmn me espnse, :, g m 00k 00k 40, c, c c, c c c gm + g , c c m F. Najmabai, ECE0, Fall 0 97

30 Fin input cmmn me ange: CM O + tp. CM +. The abe equatin inicates changes an tacks CM as CM changes. is limite by tw citeia belw: Q in satuatin:. O. QQ in satuatin:..0 O O + O +. O CM CM Nte that the equiement n QQ in satuatin is usually me estictie than abe as QQ nt usually each satuatin tgethe calculatin abe epesents the best case. Hwee, cect slutin equies that we inclue channel-length mulatin an calculate the elatinship between & same aguments apply t pat e. F. Najmabai, ECE0, Fall 0 07

31 e Fin allwable ange f utput ltage: Q in satuatin:. O. + QQ in satuatin: O O + +. O..0. F. Najmabai, ECE0, Fall 0 7

32 Execise 0: Cnsie the cicuit belw with µ n C x 400 µ, µ p C x 00 µ, an tn pn 0.4. ll tansists peate at O 0. an 4 6 ef 0. m a esign the cicuit i.e., fin f all tansists b Fin the input cmmn-me ange c Fin the iffeential gain λ 0. - F. Najmabai, ECE0, Fall 0 7

33 QQ4: asymmetic actie la f iffeential amplifie Q6: PMO C amplifie n stage 4 Qef: The efeence leg f cuent mi f the cicuit 6 Q7: cuentsuceactie la f Q6 C amplifie Q: Cuentmi bias f iffeential Q & Q: NMO iffeential amplifie with single-ene utput st stage F. Najmabai, ECE0, Fall 0 7

34 a Fin f all tansists. tep : Cmpute all cuents. 4 6 ef 0. m m m tep : Cmpute s 0. NMO: Qef, Q, Q, an Q7 all hae same an O 0. 0 ef µ ncx ef O ef 7 ef 0. m 7 ef ef 0.4 m ef 0 PMO: Q, Q4, an Q6 all hae same an O 0. 0 µ p Cx O F. Najmabai, ECE0, Fall m

35 b Fin input cmmn me ange: CM G O + tn CM 0.6 imila t pblem 9, we lk at limits: Q in satuatin: 0. O 0.8 QQ an QQ4 in satuatin because the cicuit is NOT symmetic, we nee t cnsie bth cases an chse the mst estictie ne. QQ B QQ4 G O + tp G6 G6 O 6 + G6 tp 0.6 G O O CM CM 0.6 F. Najmabai, ECE0, Fall 0 7

36 c Fin the iffeential gain λ 0. - : m m m g m g m O k λ k λ k λ g m6 6 λ O λ k k F. Najmabai, ECE0, Fall 0 67

37 x Q & Q: NMO iffeential amplifie with single-ene utput st stage x x g m 0 k k x x Q6: PMO C amplifie n stage i g 0 m6 6 7 k k F. Najmabai, ECE0, Fall 0 77 x x 6