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26_Lecutre

# 26_Lecutre - EE 114 Lecture 26 Lecture 26 OTA Feedback...

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EE 114 Lecture 26 R. Dutton, B. Murmann 1 EE114 (HO #30) Lecture 26 OTA Feedback Circuits (Part IV) R. Dutton, B. Murmann Stanford University R. Dutton, B. Murmann 2 (Basic) Two-Stage OTA High gain ~ 0.5(g m r o ) 2 Large output range Possible extensions Cascodes in stage 1 Gain becomes ~0.5(g m r o ) 3 (!) Current mirror in stage 1 M1a V DD V xm V o M3 V BN V BP M2 M4 V xp M1b EE114 (HO #30)

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EE 114 Lecture 26 R. Dutton, B. Murmann 3 AC Model with Capacitive Feedback R 1 C 1 R 2 v i v o (-) v x C Ltot C s C f C L C x G m1 g m2 2 1 1 m m g G = 3 1 1 2 o o r r R = 1 1 2 gd gs x C C C + = 4 2 2 o o r r R = ( ) 4 4 2 1 gd db db f L Ltot C C C C C C + + + ! " + = x s f f C C C C + + = ! (ignoring C gd2 for the time being) 3 1 3 1 2 1 gd gd db db gs C C C C C C + + + + = EE114 (HO #30) R. Dutton, B. Murmann 4 Loop Gain ( ) ( ) ( ) ( ) s a s a s a p s p s R g R G s T v v v m m ! " = ! " = # # \$ % & & ( ) ! # # \$ % & & ( ) ! " = 2 1 2 1 2 2 1 1 1 1 1 1 1 1 C R p ! = 2 2 2 1 C R p ! = R 1 C 1 R 2 v i v o (-) v x C Ltot C s C f C L C x G m1 g m2 EE114 (HO #30)
EE 114 Lecture 26 R. Dutton, B. Murmann 5 Bode Plot of Loop Gain If ω p1 and ω p2 are close to each other, the loop will have a very small phase margin ! 1 p ! ° 0 ° ! 90 ° ! 180 ! 2 p ! ( ) ! j Mag ( ) ! j Phase ( ) s a 1 ( ) s a ! " ( ) s a 2 ( ) s a ! " EE114 (HO #30) R. Dutton, B. Murmann 6 Introducing a Dominant Pole The problem is solved if we somehow manage to make ω p1 << ω p2 – Or ω p2 << ω p1 The loop then behaves close to first order system around crossover frequency Phase margin follows from expression on slide 14 of lecture 25 ! 1 p ! ° 0 ° ! 90 ° ! 180 ! 2 p ! ( ) ! j Mag ( ) [ ] ! j T Phase ( ) s a 1 ( ) s a ! " ( ) s a 2 c ! EE114 (HO #30)

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