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IIT-Bombay Lecture 27 M. Shojaei Baghini
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Slides Figures
- Unless it’s mentioned figures and contents of
Frequency Compensation Part I Chapters 9 from Gray and Meyers book - - PowerPoint PPT Presentation
Frequency Compensation Part I Chapters 9 from Gray and Meyers book - - PowerPoint PPT Presentation
2 Frequency Compensation Part I Chapters 9 from Gray and Meyers book Chapter 10 from Razavis book IIT-Bombay Lecture 27 M. Shojaei Baghini 3 Slides
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Example – Effect of “gm” mismatch
mV v Induced r R g g H LF
amp diff
- ut
- D
avg m m CM DM
60 _ 10 3 2 _
) ( _ 4 3 , _
= ⇒ × = ∆ − =
−
1 2 1 2
If Vout=Vout1-Vout2 then ADM-CM=0 for a matched differential pair.
If gm-avg=2mA/V , RD=3kΩ , ro3=100kΩ , Amplitude of Vin,CM=200mV Mismatch between gm1 and gm1 =2% Low frequency ADM-CM=? Location of poles and zero?
- What about CMRR of
diff-amp with active load?
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Stability of Feedback Systems
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IIT-Bombay Lecture 27 M. Shojaei Baghini
( )
2 2 2 1 2 2 2 1 2 1 2 1 2 1 2 2 1 2 1
2 ) ( 1 ) ( ) ( , 1 1 ) (
n n n n f
s Q s P P H s s P P H P P T P P s P P s P P H s H s H s H H T P s P s H s H ω ω ω ςω β β + + = + + = + + + + = + = ⇒ = + + =
Location of closed loop poles:
( ) ( ) ( )
2 1 4 1 1
2 2 1 2 1 2 1
P P P P T P P Poles + + − ± + − =
Stability, Feedback and Pole Locations – Example: A Circuit with the Second Order H(s) with Real Poles
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Example: A Circuit with the Second Order H(s) with Real Poles (cont’d)
( ) ( ) ( ) ( ) ( ) ( )
= = + − = ⇒ + + − = + + − ± − + = 2 1 1 2 4 1 2 4 1 1 1
2 1 2 1 2 2 1 2 2 1 2 1 2 1
Q
- r
P P Poles P P P P T P P P P T P P Poles ς
Location of closed loop poles:
P1 P2
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Example: Phase margin = 5° ⇒ Φ = -175°⇒|H(jωu)|=11.5/β
Φ Φ
+ = + =
j j u u u f
e e j H j H j H 1 1 ) ( 1 ) ( ) ( β ω β ω ω
Phase Margin
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Frequency Response and Time Response
- Is phase margin enough to predict transient
behavior of the circuit? Designed for fu=150 MHz and phase margin of 65º
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IIT-Bombay Lecture 27 M. Shojaei Baghini
Normalized frequency (ω/ ω n) Normalized frequency (ω/ ω n) Normalized closed loop gain Normalized phase
Normalized time response
Normalized time (ωt)
Frequency and Time Domain Behavior
2
2 1 1 Q
n peak
− = ω ω
For a second order TF:
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IIT-Bombay Lecture 28 M. Shojaei Baghini
Example: Telescopic Op-Amp
- CA » CN , CX (or CY)
- CN > CX (or CY)