1 st and 2 nd stage gain with Cc=0 g m1 v id R1R1 C1C1 R1R1 C1C1 g m1 v gs1 R2R2 C2C2C v id v o1 = v i2 v o2  u2,0  P2,0 1/R 2 C 2 g m2 /C 2 A v2,0 =g m2 R 2 1  u1,0  P1,0 1/R 1 C 1 g m1 /C 1 A v1,0 =g m1 R 1 1 g m2 v i2 R2R2 C2C2

Overall gain with Cc=0  u2,0  P2,0 A v2,0 1  u1,0  P1,0 A v0 = A v1,0 A v2,0 =g m1 R 1 g m2 R 2 1/  1/  2 A v1,0 Things to think about: 1.What is the equation for gain between the first two poles? 2.What is the equation for gain after the second pole? 3.What is the gain at the first-stage unity gain frequency? 4.What is the gain at the second-stage unity gain frequency? 5.What is the unity gain frequency?

Example with C c =0 A v2,0 =10 1 1M A v0 = 1000 A v1,0 =100 g m1 = 1mS R 1 =100k C1=10pF g m2 = 10mS R 2 =1k C2=10pF A v1,0 = 100  p1 =1M  u1 =100M A v2,0 = 10  p2 =100M  u2 =1G 100M 1G Phase margin for unity gain (f=1) feedback What’s the phase margin? What’s the phase margin if I use this amplifier with f=0.1?

Z o1 with A v2,0 C c > C 1 > C c g m1 v id R1R1 C1C1 g m1 v gs1 R2R2 C2C2C v id v o1 = v i2 v o2 1/(  A v2,0 C C)  p2,0  p1 1/  C C 1/  C 1 R1R1  p2  u2  p1,0

A v1 = g m1 Z o1 with A v2,0 C c > C 1 > C c g m1 /(  A v2,0 C C)  p2,0  p1 g m1 /  C C g m1 /  C 1 g m1 R 1  p2  u2  p1,0 Things to think about: 1.What’s the equation for the gain in the various sections? 2.What does the curve look like if C c > C 1 ? 3.What does the curve look like if  p2,0 >  p1,0 4.What is the frequency ratio of the old and new first pole? 5.What is the frequency ratio of the old and new second pole? 6.Answer questions 4 & 5 assuming 2 and/or 3.

Overall gain with  p2 >  u  u2,0  P2,0 A v2,0 1  u1,0  P1,0 1/  1/  2 A v1,0 Original gain w/ C c =0  P1  P2 Compensated gain w/ C c >0  u2,0  P2,0 A v2,0 1  u1,0  P1,0 A v1,0  P1  P2 Overall gain with C 1 > C c > 0