Frequency Response of Amplifiers

Transcription

1 類比電路設計 ( Frequency epne f Aplifier h-uan an Natinal hun-h Univerity epartent f Electrical Eneer Overview ead B azavi hapter 6 ntrductin n thi lecture, we tudy the repne f le-tae and differential aplifier the frequency da Fllw a review f baic cncept, we analyze the hih-frequency behavir f cn-urce and cn-ate tae and urce fllwer Next, we deal with cacde and differential aplifier Fally, we cnider the effect f active current irrr n the frequency repne f differential pair Anal-ircuit e 6- h-uan an / EE, NHU

2 Miller effect Applicatin f Miller effect t a flat ipedance That i, Anal-ircuit e 6- h-uan an / EE, NHU Aciatin f ple with nde acade f aplifier A A The verall tranfer functin can be written a ( N P We ay ay each nde the circuit cntribute ne ple t the tranfer functin The ple i detered by the ttal capacitance een fr each nde t rund ultiplied by the ttal reitance een at the nde t rund n eneral, the tranfer functin i iven a where each ple with ne nde f the circuit, ie, j τ j, where τ j i the prduct f the capacitance and reitance een at nde j t rund ( Aj Av j j j j Anal-ircuit e 6-3 h-uan an / EE, NHU

3 n-urce tae Hih-frequency del f a tae (Aue λ 0 and M perate aturatin At the put nde, the ttal capacitance een fr t rund i equal t G ( A v G, where A v The put ple i [ ( ] G (Miller ultiplicatin G At the put nde, the ttal capacitance een t rund i equal t B ( A v G B G The put ple i ( B G Anal-ircuit e 6-4 h-uan an / EE, NHU n-urce tae (cnt d Mdel fr calculatin f put ipedance (f i relative lare, the effect f i nelected The put ple: where eq G G eq G G G G G Thu, the put ple i ruhly equal t ( G G eq G B Fally, we urie that the tranfer functin i ( Anal-ircuit e 6-5 h-uan an / EE, NHU

4 n-urce tae (cnt d Equivalent circuit f tae ( ( G ξ G ( G [ ( ( ] ( G 0 where ξ G G G B G B G B 0 zer Nte the tranfer functin i f ecnd rder even thruh the circuit cnta three capacitr While the denatr appear rather cplicated, it can yield tuitive exprein fr the tw ple, p and p, if we aue p << p Writ the denatr a p p p p p p G G B ple Anal-ircuit e 6-6 h-uan an / EE, NHU n-urce tae (cnt d f p i uch farther fr p (ie, p << p, then We bta p p p p p p p p p ( ( p ( G G G G G f ( G G i neliible, then f G >> ( G ( G B /, B then G G B B ( G G ( G B ( G G p G [ ( ] G G p ( GG GB ( G B G B G B Anal-ircuit e 6-7 h-uan an / EE, NHU

5 n-urce tae (cnt d Feedfrward path thruh G The tranfer functin exhibit a zer iven by z / G cated the riht half plane, the zer arie fr direct cupl f the put t the put thruh G at very hih frequency Nte that a zer the riht half plane trduce tability iue feedback aplifier Anal-ircuit e 6-8 h-uan an / EE, NHU n-urce tae (cnt d alculatin f the zer a tae er: ( 0 z Fr a fite, thi ean that ( z 0 and hence the put can be hrted t rund at the frequency with n current Therefre, the current thruh G and M are equal and ppite: G z That i, z / G Anal-ircuit e 6-9 h-uan an / EE, NHU

6 n-urce tae (cnt d nput ipedance At hih frequency, the effect f the put nde ut be taken t accunt ( G B ( G B ( hence G At frequencie where ( G B << and B <<,, dicat that the put ( G ipedance i priarily capacitive G B n fact, if G i lare, it prvide a lw-ipedance path between the ate and dra f M, yield the equivalent circuit that / and appear parallel with the put Anal-ircuit e 6-0 h-uan an / EE, NHU urce fllwer urce fllwer G [ G ( G] Tranfer functin: ( G ( G GG G ( G G er: The tranfer functin cnta a zer the left half plane Thi i becaue the al cnducted by G at hih frequencie add with the ae plarity t the al prduced by the tric tranitr Ple: f the tw ple f the tranfer functin are aued far apart, then the da ple i p G G G G Al, if 0, then p / ( G Anal-ircuit e 6- h-uan an / EE, NHU

7 urce fllwer (cnt d nput ipedance G i red, we have G Anal-ircuit e G b G G b At relative lw frequencie, b >> and G b b b b G b dicat that the equivalent put capacitance i equal t G b / ( b By Miller apprxiatin: The lw-frequency a A v / ( b Thu, eq G ( A v G b / ( b, and, ttal At hih-frequencie, b << and G 6- h-uan an / EE, NHU G G G b b Neative reitr urce fllwer (cnt d Output ipedance G i nelected, G G G G At lw frequencie, / At very hih frequencie,, becaue G hrt the ate and urce > < Anal-ircuit e 6-3 h-uan an / EE, NHU

8 6-4 h-uan an / EE, NHU Anal-ircuit e urce fllwer (cnt d Equivalent put ipedance f a urce fllwer f, fd, and : Take /, /, then That i, the dependence f upn iplie that if a urce fllwer i driven by a lare reitance, then it exhibit ubtantial ductive behavir G G G G 6-5 h-uan an / EE, NHU Anal-ircuit e n-ate tae G tae at hih frequencie nput ipedance, where ce nw depend n, it i difficult t aciate a ple with the put nde b, where G B (, where G B At lw frequency, Thu, An iprtant prperty f G tae i that it exhibit n Miller ultiplicatin f capacitance, ptentially achiev a wide band ( ( b b v A ( ( ( ( A b b b v ( b b r

9 n-ate tae (cnt d G tae Tranfer functin: ( r ( ( The a at lw frequencie i equal t r nput ipedance: r b A r creae, apprache /( b and hence the put ple can be defed a p, b r [ r ( r ] ( b r Anal-ircuit e 6-6 h-uan an / EE, NHU acde tae Hih-frequency del f a cacde tae acde tae tae (put ipedance G tae (uppre the iller effect Ga: A Nde A: Nde : Nde : p, A p, p, b G b b G b G B B G ( B G n actual de, p, i typically chen t be farther fr the ri than the ther tw Thi chice play an iprtant rle the tability f p ap Anal-ircuit e 6-7 h-uan an / EE, NHU

10 6-8 h-uan an / EE, NHU Anal-ircuit e acde tae (cnt d iplified del f a cacde tae with a current urce ( / ( G ( / ( fr r >> and r / >> (ie, >, hence We can fd that the ple at nde i iven by / Nelect G and, we have ( r r, where r ( ( ( ( r r r r / 6-9 h-uan an / EE, NHU Anal-ircuit e ifferential pair ifferential pair Equivalent circuit fr cn-de put f the put ple i uch farther fr the ri than i the ple at nde P, the cn-de rejectin f the circuit derade cniderably at hih frequencie ( 3, r A P M v Half-circuit equivalent

11 ifferential pair (cnt d Effect f hih-frequency upply nie differential pair f the upply vltae cnta hih-frequency nie and the circuit exhibit iatche, the reult cn-de ditance at nde P lead t a differential nie cpnent at the put A trade-ff between vltae headr and M: T iize the headr cnued by M 3, it width i axiized, trduc ubtantial capacitance at the urce f M and M and derad the hih-frequency M The iue bece re eriu at lw upply vltae Anal-ircuit e 6-0 h-uan an / EE, NHU ifferential pair (cnt d ifferential pair with current-urce lad Nde G i an ac rund The put ple i iven by ( r r 3, the dant ple Anal-ircuit e 6- h-uan an / EE, NHU

12 ifferential pair (cnt d Hih-frequency behavir f differential pair with active current irrr Mirrr ple: 3 p, E E, where E dente the ttal capacitance at E t rund E : G3, G4, B3, B, and the iller effect f G and G4 Anal-ircuit e 6- h-uan an / EE, NHU ifferential pair (cnt d Hih-frequency del f differential pair with active current irrr Theven equivalent: N r N, r N Aued / P << r P, E P E ( and 4 E r r P N E E P ( r, we have NrN ( P E [( r r r ( r ] ( r r N P P E P P N ce the iller ple i typical quite hiher anitude than the put ple, we et P N P p P ( rn rp ( r N r P E r P ( P r N P and p E ( r N r P fr P r N >> Anal-ircuit e 6-3 h-uan an / EE, NHU

13 ifferential pair (cnt d n additin, there i a zer with a P anitude f the left half E plane The appearance f uch a zer i that the circuit cnit f a lw path (M, M 3 and M 4 parallel with a fat path (M and M epreent the tw path, we have A ( / p( / p A0( / p ( / ( / p 0 p A0 / That i, the yte exhibit a zer at p p Anal-ircuit e 6-4 h-uan an / EE, NHU ifferential pair (cnt d etere the zer (ethd Fr zer frequency, 0 and 4 We have 4 P E 4 E ( P E Thu, P E E ( P E z P E Anal-ircuit e 6-5 h-uan an / EE, NHU