Frequency Compensation Part I Chapters 9 from Gray and Meyers book - PowerPoint PPT Presentation

2 Frequency Compensation – Part I Chapters 9 from Gray and Meyer’s book Chapter 10 from Razavi’s book IIT-Bombay Lecture 27 M. Shojaei Baghini

3 Slides Figures • Unless it’s mentioned figures and contents of slides are taken from: ‘Design of Analog CMOS Integrated Circuits’ by Behzad Razavi IIT-Bombay Lecture 27 M. Shojaei Baghini

4 Example – Effect of “g m ” mismatch If V out =V out1 -V out2 then A DM-CM =0 1 2 1 2 for a matched differential pair. If g m-avg =2mA/V , R D =3k Ω , r o3 =100k Ω , Amplitude of V in,CM =200mV Mismatch between g m1 and g m1 =2% Low frequency A DM-CM =? Location of poles and zero? ∆ g R − = − = × 4 m D LF _ H 3 10 • What about CMRR of DM _ CM g r 2 m , avg o 3 diff-amp with active ⇒ = Induced _ v 60 mV load? out _ diff ( amp ) IIT-Bombay Lecture 27 M. Shojaei Baghini

5 Stability of Feedback Systems IIT-Bombay Lecture 27 M. Shojaei Baghini

6 Stability, Feedback and Pole Locations – Example: A Circuit with the Second Order H(s) with Real Poles H = = β ⇒ 0 H ( s ) , T H  +   +  0 0 s s     1 1         P P 1 2 H ( s ) H P P = = 0 1 2 H s ( ) ( ) + β + + + + f 2 1 H ( s ) s P P s P P T P P 1 2 1 2 0 1 2 H P P H P P = = 0 1 2 0 1 2 ω + + ςω ω 2 2 s 2 s + + ω 2 2 n s s n n n Q ( ) + T P P 4 1 ± − 0 1 2 1 1 ( ) Location of closed + 2 P P ( ) = − + 1 2 Poles P P loop poles: 1 2 2 IIT-Bombay Lecture 27 M. Shojaei Baghini

Example: A Circuit with the Second Order H(s) with 7 Real Poles (cont’d) ( ) + T 1 4 P P − ± − 0 1 2 1 1 ( ) + 2 P P ( ) Location of closed = + 1 2 Poles P P 1 2 2 loop poles: ( ) ( ) + + 2 P P P P = − + ⇒ = − 1 2 1 2 T 1 Poles 0 4 P P 2 1 2   ( ) 1 ς = =   1 or Q   2 P 2 P 1 IIT-Bombay Lecture 27 M. Shojaei Baghini

8 Phase Margin 1 Φ j e ω β H ( j ) ω = = u H ( j ) Φ + β ω + f u j 1 H ( j ) 1 e u Example: Phase margin = 5 ° ⇒ Φ = -175 °⇒ |H(j ω u )|=11.5/ β IIT-Bombay Lecture 27 M. Shojaei Baghini

9 Frequency Response and Time Response • Is phase margin enough to predict transient behavior of the circuit? Designed for f u =150 MHz and phase margin of 65 º IIT-Bombay Lecture 27 M. Shojaei Baghini

Frequency and Time Domain Behavior 10 Normalized closed loop gain Normalized phase Normalized frequency ( ω / ω n ) Normalized frequency ( ω / ω n ) Normalized time response For a second order TF: 1 ω = ω − 1 peak n 2 2 Q Normalized time ( ω t) IIT-Bombay Lecture 27 M. Shojaei Baghini

4 Example: Telescopic Op-Amp C A » C N , C X (or C Y ) • C N > C X (or C Y ) • Zero (2 × mirror pole) Dominant pole Mirror pole IIT-Bombay Lecture 28 M. Shojaei Baghini