Execises f iffeential mplifies ECE 0, Fall 0, F. Najmabai
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 0. -. 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
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 0. 0. > 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
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
ncluing channel- length mulatin λ 0.. O 0. + + O + t G C G 0 O 0.448 O 0. G O + t O +. + 0 O +.0 [ + 0. O +. G G O O +.0] 0 0.948 0 0.948 0.948.0 + O.448 0.948 +.0 G O 0.467 G O + t G G +. + O O + O 0. [ + 0. O +. O O +.0] 0 0.967.0 0.967 + 0.0.0 + O.467 0.0+.0 F. Najmabai, ECE0, Fall 0 7
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 00 0.00.0.00.0 m 00.0 0.0.0.0 m 0.448 0 0.948.448.0.0 m 0.467.0 0.0.467.0 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
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
ince tansists ae matche an hae the same O : 4 00 µ 00 00 6 0 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 - - 0 6 k 6 k 0 8 0 8 F. Najmabai, ECE0, Fall 0 87
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.8 0 4.m 6 m F. Najmabai, ECE0, Fall 0 97
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 0.67 40 0. + O O n O m m g g λ,, m g
F. Najmabai, ECE0, Fall 0 7 0.67 6 m 4 4 O O O O O 00 0.67 0 400 0 6 6 C O x µ n 400 0.67 0 00 0 6 4 6 C O x µ p 00 0.67 0 400 0. 6 C O x µ n 67 0 67 67 0.4 0.67 + + + + G G tn O G. 67.8 67 0.4 0.67 + + G G tp O G
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
F. Najmabai, ECE0, Fall 0 7 6 k 0 00 0.78... 0.4 m 0 00...... 00... 6 8 6 8 9 8 9 8 O m m m O O O O g g g λ µ 0.78.6 p n λ λ NMO: Q, Q, Q, & Q4: 8 0 00 0 00 4 6 6 C O x µ n PMO: Q, Q6, Q7, & Q8: 0 0 00 6 7 8 6 6 C O x µ p
Meth : Use fmula f Casce mplifie n ectue et 6, slie 4 which assumes g m >> :, g 0.4 0,, m, 6 0 04 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 7 + 6 0 Q i + gm Q, 0.4 0 + 0.4 0 + 0.4 6 + 6 0 g m 7 6 k 90k.6 40.6 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
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
Half-cicuit f iffeential Gain Ze ltage at symmety line eplace Q by Elementay fms, g m, P F. Najmabai, ECE0, Fall 0 67
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
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 0 87 + gm g g Q Q m m i
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
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
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
F. Najmabai, ECE0, Fall 0 7 ince tansists ae matche an G G because : + 0. 0. Output Offset ltage f 0, fin iffeential C ltage at the utput: + 0. &. 0
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 + + 0. O O ] nput Offset ltage O O
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 + 0. + 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
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
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
a Fin f all tansists 4 ef 0. m, an 6. tep : Cmpute all cuents. + 6 6 0.4 0.4 m m 7 6 0.4 m tep : Cmpute s NMO: Qef, Q, Q4, an Q7 0. 0 ef µ C ef 7.8 n x ef O 90 0-6 ef 4 ef 0. m 4 ef 7.8 7 ef 0.4 m 7 ef.6 F. Najmabai, ECE0, Fall 0 77
PMO: Q, Q, Q, an Q6 0. 0. µ p C x O 0 0-6 0. m. 6 0.4 m 6 07 mall signal paametes: g m g m 4 O 0. 0 8 0 0 0. 0 0.4 0 F. Najmabai, ECE0, Fall 0 87 0 0. 0 4 0 0 k 00 k 00 k
b Fin the iffeential gain: c Fin cmmn me espnse, :, 8 0 4 g m 00k 00k 40, c, c c, c c c gm + g 4 8 0 00 0 4 + 8 0 0 0, c c m + 80 0.98 + 80 + + F. Najmabai, ECE0, Fall 0 97
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.. +..0 CM.7 0.8 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
e Fin allwable ange f utput ltage: Q in satuatin:. O. + QQ in satuatin: O O + +. O..0. F. Najmabai, ECE0, Fall 0 7
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
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
a Fin f all tansists. tep : Cmpute all cuents. 4 6 ef 0. m + 7 6 0.4 0. 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 0 47 00 4 6 0. m 4 6 00
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 0.6 0.4 G6 G6 O 6 + G6 tp 0.6 G6 0.4 0. 0.4 O 0. 0. 0.4 O 0. 0.8 0. 0.8 CM 0.6 0. 0. CM 0.6 F. Najmabai, ECE0, Fall 0 7
c Fin the iffeential gain λ 0. - : 4 6 0. m + 0.4 m 6 7 0. m g m g m O 0. 0 0. 0 k λ 0. 0. 0 k λ 0. 0. 0. k λ 0. 0.4 0 4 g m6 6 λ O 6 0. 0 0. 0. 0. 0 6 6 λ 0. 0. 0 7 7 0 k k F. Najmabai, ECE0, Fall 0 67
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