NONLINEARITY AND NOISE MODELING OF OTA for CT filters

hi_china59

NONLINEARITY AND NOISE MODELING OF OPERATIONAL
TRANSCONDUCTANCE AMPLIFIERS FOR CONTINUOUS TIME
ANALOG FILTERS
A Thesis
by
ARUN RAMACHANDRAN
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
May 2005

TABLE OF CONTENTS
Page
ABSTRACT……………………………………………………………………………..iii
ACKNOWLEDGMENTS...……………………………………………………………...v
TABLE OF CONTENTS……………………………………………………………….vii
LIST OF FIGURES…………….………………………………………………………...x
LIST OF TABLES…………………......…………………………………………....….xvi
CHAPTER
I INTRODUCTION ..........................................................................................1
1.1. Motivation and Background.....................................................................1
1.1.1. Digital Filters……………………………………………………..2
1.1.2. Sampled-Data Filters……………………………………………..3
1.1.3. Continuous Time Filters………………………………………….5
1.2. Continuous Time Analog Filters..............................................................5
1.2.1. Passive Filters ................................................................................7
1.2.1.1. RLC Filters ........................................................................7
1.2.1.2. Surface Acoustic Filters ....................................................8
1.2.1.3. MEMS Filters ....................................................................9
1.2.2. Active Filters................................................................................10
1.2.2.1. Active-RC Filters ............................................................11
1.2.2.2. OTA-C Filters .................................................................12
1.2.2.3. MOSFET-C Filters ..........................................................13
1.2.2.4. Current Mode Filters .......................................................14
1.3. Filter Design Procedure .........................................................................17
1.3.1. Filter Specifications .....................................................................19
1.3.2. The Approximation Problem.......................................................20
1.3.3. Filter Class ...................................................................................20
1.3.4. Filter Topology ............................................................................21
1.3.4.1. Cascade Topology ...........................................................21
1.3.4.2. Leapfrog Topology..........................................................23
1.3.4.3. Summed-feedback Topology ..........................................23
1.3.4.4. LC Ladder Simulation.....................................................25
1.4. Active Blocks Design Considerations....................................................25
1.4.1. Noise ............................................................................................26
1.4.2. Non-Linearity...............................................................................27
1.5. Organization...........................................................................................31
viii
CHAPTER Page
II NONLINEARITY AND NOISE MODELING OF OTA-C FILTERS ........34
2.1. Motivation and Background...................................................................34
2.1.1. Transconductor Amplifier............................................................35
2.1.2. Differential Input Operational Transconductor Amplifiers .........39
2.1.2.1. Macromodel of the OTA.................................................43
2.1.3. Simple Applications of OTA.......................................................45
2.1.3.1. Voltage Amplifier / Integrator.........................................45
2.1.3.2. Voltage Variable Resistor ...............................................46
2.1.3.3. Voltage Summation.........................................................47
2.1.3.4. Integrator .........................................................................48
2.1.4. Non Idealities of OTA .................................................................51
2.1.4.1. Non-Linearity of the OTA...............................................51
2.1.4.2. Capacitor Non-Linearity..................................................51
2.2. Proposed Generalized Non-Linearity and Noise Modeling Approach .53
2.2.1. A General Structure of a Gm-C (OTA-C) Filter..........................53
2.2.2. Dynamics of Nonlinear OTA-C Filters........................................58
2.2.3. Noise Analysis in General OTA-C Filters ...................................64
2.2.4. Verification of the Nonlinearity and Noise Analysis Tool ..........70
2.2.5. Performance Optimization of OTA-C Filters ..............................86
2.3. Conclusion .............................................................................................95
III A LINEARIZED CMOS OTA USING ACTIVE ERROR
FEED-FORWARD TECHNIQUE................................................................96
3.1. Motivation and Background...................................................................96
3.1.1 Linearization Techniques..............................................................97
3.1.1.1 Source Degeneration ......................................................100
3.1.1.2 Attenuation .....................................................................100
3.1.1.3 Combination of Techniques ...........................................103
3.1.1.4 Linearization Using Complimentary Differential Pairs .106
3.2. A Highly Linear OTA-C Based Filter for VDSL Applications ...........107
3.2.1 Biquad Section............................................................................110
3.2.2 Simulation Results ......................................................................111
3.2.3 Summary.....................................................................................115
3.3. Proposed Highly Linear OTA..............................................................116
3.3.1 Feed-Forward Linearization........................................................116
3.3.2 Analysis of Linearity Performance .............................................118
3.3.3 Second Order Effects ..................................................................120
3.3.4 Linearized OTA Circuit Architecture .........................................121
3.3.5 Common Mode Feedback Circuits .............................................122
3.3.6 Tuning of the OTA......................................................................123
ix
CHAPTER Page
3.3.7 Measurement Results ..................................................................126
3.4. Conclusion ...........................................................................................135
IV CONCLUSION...........................................................................................138
REFERENCES...............................................................................................................140
APPENDIX A ................................................................................................................153
APPENDIX B ................................................................................................................165
VITA ..............................................................................................................................170

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