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1 st and 2 nd stage gain with Cc=0

1 st and 2 nd stage gain with Cc=0. C C. v o1. = v i2. v o2. v id. A v1,0 =g m1 R 1. 1. w P1,0. w u1,0. 1/R 1 C 1. g m1 /C 1. g m1 v gs1. g m1 v id. R 2. R 1. C 2. C 1. g m2 v i2. g m1 v id. R 1. R 2. C 2. C 1. A v2,0 =g m2 R 2. 1. w P2,0. w u2,0. 1/R 2 C 2.

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1 st and 2 nd stage gain with Cc=0

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  1. 1st and 2nd stage gain with Cc=0 CC vo1 = vi2 vo2 vid Av1,0=gm1R1 1 wP1,0 wu1,0 1/R1C1 gm1/C1 gm1vgs1 gm1vid R2 R1 C2 C1 gm2vi2 gm1vid R1 R2 C2 C1 Av2,0=gm2R2 1 wP2,0 wu2,0 1/R2C2 gm2/C2

  2. Overall gain with Cc=0 1/w Av0 = Av1,0Av2,0=gm1R1gm2R2 Av1,0 1/w2 Av2,0 1 wP1,0 wP2,0 wu1,0 wu2,0 • Things to think about: • What is the equation for gain between the first two poles? • What is the equation for gain after the second pole? • What is the gain at the first-stage unity gain frequency? • What is the gain at the second-stage unity gain frequency? • What is the unity gain frequency?

  3. Example with Cc=0 Av0 = 1000 gm1= 1mS R1=100k C1=10pF gm2= 10mS R2=1k C2=10pF Av1,0= 100 wp1=1M wu1=100M Av2,0= 10 wp2=100M wu2=1G Av1,0=100 Av2,0=10 1 What’s the phase margin? What’s the phase margin if I use this amplifier with f=0.1? 100M 1M 1G 0 -90 Phase margin for unity gain (f=1) feedback -180

  4. Zo1 with Av2,0Cc > C1 > Cc CC vo1 = vi2 vo2 vid 1/(w Av2,0CC) wu2 R1 gm1vid gm1vgs1 R1 R2 C2 C1 1/wCC wp1 wp2,0 wp2 1/wC1 wp1,0

  5. Av1 = gm1Zo1 with Av2,0Cc > C1 > Cc gm1/(w Av2,0CC) wu2 gm1R1 gm1/wCC wp2,0 wp1,0 gm1/wC1 wp1 wp2 • Things to think about: • What’s the equation for the gain in the various sections? • What does the curve look like if Cc > C1? • What does the curve look like if wp2,0 > wp1,0 • What is the frequency ratio of the old and new first pole? • What is the frequency ratio of the old and new second pole? • Answer questions 4 & 5 assuming 2 and/or 3.

  6. Overall gain with wp2 > wu Original gain w/ Cc=0 1/w Compensated gain w/ Cc>0 Av1,0 1/w2 Av2,0 1 wP1,0 wP2,0 wu1,0 wu2,0 wP1 wP2 Overall gain with C1 > Cc > 0 Av1,0 Av2,0 wu2,0 1 wP1,0 wP2,0 wu1,0 wP1 wP2

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