Continuous- Time Active Filter Design

Transcription

1 Continuous- Time Active Filter Design T. Deliyannis Yichuang Sun J.K. Fidler CRC Press Boca Raton London New York Washington, D.C.

2 Contents Chapter 1 Filter Fundamentals 1.1 Introduction Filter Characterization Lumped Linear Continuous-Time and Discrete-Time Time-Invariant Finite Passive and Active Types of Filters Steps in Filter Design Analysis Nodal Analysis Network Parameters One-Port Network Two-Port Network Two-Port Interconnections Series-Series Connection Parallel-Parallel Connection Series Input-Parallel Output Connection Parallel Input-Series Output Connection Cascade Connection Network Transfer Functions Continuous-Time Filter Functions Pole-Zero Locations Frequency Response Transient Response Impulse Response Step Response Step and Frequency Response Stability Short-Circuit and Open-Circuit Stability Absolute Stability and Potential Instability Passivity Criteria for One- and Two-Port Networks One-Ports Two-Ports Activity Passivity and Stability Reciprocity Summary 33 References and Further Reading 33 Chapter 2 The Approximation Problem 2.1 Introduction 35

3 2.2 Filter Specifications and Permitted Functions Causality Rational Functions Stability Formulation of the Approximation Problem Approximation of the Ideal Lowpass Filter Butterworth or Maximally Flat Approximation Chebyshev or Equiripple Approximation Inverse Chebyshev Approximation Papoulis Approximation Elliptic Function or Cauer Approximation Selecting the Filter from Its Specifications Amplitude Equalization Filters with Linear Phase: Delays Bessel-Thomson Delay Approximation Other Delay Functions Delay Equalization Frequency Transformations Lowpass-to-Lowpass Transformation Lowpass-to-Highpass Transformation Lowpass-to-Bandpass Transformation Lowpass-to-Bandstop Transformation Delay Denormalization Design Tables for Passive LC Ladder Filters Transformation of Elements LC Filters Active RC Filters Impedance Scaling Predistortion Summary 72 References 73 Chapter 3 Active Elements 3.1 Introduction Ideal Controlled Sources Impedance Transformation (Generalized Impedance Converters and Inverters) Generalized Impedance Converters The Ideal Active Transformer The Ideal Negative Impedance Converter The Positive Impedance Converter The Frequency-Dependent Negative Resistor Generalized Impedance Inverters TheGyrator Negative Impedance Inverter Negative Resistance Ideal Operational Amplifier Operations Using the Ideal Opamp Summation of Voltages Integration Realization of Some Active Elements Using Opamps 87

4 Realization of Controlled Sources Realization of Negative-Impedance Converters Gyrator Realizations GIC Circuit Using Opamps Characteristics of IC Opamps Open-Loop Voltage Gain of Practical Opamps Input and Output Impedances Input Offset Voltage V ro Input Offset Current I IO Input Voltage Range V t Power Supply Sensitivity AV IO /AVGG Slew Rate SR Short-Circuit Output Current Maximum Peak-to-Peak Output Voltage Swing V opp Input Capacitance Q Common-Mode Rejection Ratio CMRR Total Power Dissipation Rise Time t r Overshoot Effect of the Single-Pole Compensation on the Finite Voltage Gain Controlled Sources The Ideal Operational Transconductance Amplifier (OTA) Voltage Amplification A Voltage-Variable Resistor (WR) Voltage Summation Integration Gyrator Realization Practical OTAs Current Conveyor Summary 106 References 106 Chapter 4 Realization of First- and Second-Order Functions Using Opamps 4.1 Introduction Realization of First-Order Functions Lowpass Circuits Highpass Circuits Allpass Circuits The General Second-Order Filter Function Sensitivity of Second-Order Filters Ill 4.5 Realization of Biquadratic Functions Using SABs Classification of SABs A Lowpass SAB A Highpass SAB A Bandpass SAB Lowpass- and Highpass-Notch Biquads Lowpass Notch (R 6 = <») Highpass Notch (R 7 = <*>) An Allpass SAB Realization of a Quadratic with a Positive Real Zero Biquads Obtained Using the Twin-T RC Network 134

5 4.8 Two-Opamp Biquads Biquads by Inductance Simulation Two-Opamp Allpass Biquads Selectivity Enhancement Three-Opamp Biquads The Tow-Thomas [25-27] Three-Opamp Biquad Excess Phase and Its Compensation in Three-Opamp Biquads The Akerberg-Mossberg Three-Opamp Biquad Summary 147 References 148 Chapter 5 Realization of High-Order Functions 5.1 Introduction Selection Criteria for High-Order Function Realizations Multiparameter Sensitivity High-Order Function Realization Methods Cascade Connection of Second-Order Sections Pole-Zero Pairing Cascade Sequence Gain Distribution Multiple-Loop Feedback Filters The Shifted-Companion-Form (SCF) Design Method Follow-the-Leader Feedback Design (FLF) Cascade of Biquartics..., The BR Section Effect of r on co'j and Q'j Cascading Biquartic Sections Realization of Biquartic Sections Design Example Sensitivity of CBR Filters Summary 180 References 180 Further Reading 181 Chapter 6 Simulation of LC Ladder Filters Using Opamps 6.1 Introduction Resistively-Terminated Lossless LC Ladder Filters Methods of LC Ladder Simulation The Gyrator Gyrator Imperfections Use of Gyrators in Filter Synthesis Generalized Impedance Converter, GIC Use of GICs in Filter Synthesis FDNRs: Complex Impedance Scaling 193 6:7 Functional Simulation Example Bandpass Filters Dynamic Range of LF Filters Summary 202 References 202

6 Chapter 7 Wave Active Filters 7.1 Introduction Wave Active Filters Wave Active Equivalents (WAEs) Wave Active Equivalent of a Series-Arm Impedance Wave Active Equivalent of a Shunt-Arm Admittance WAEs for Equal Port Normalization Resistances Wave Active Equivalent of the Signal Source Wave Active Equivalent of the Terminating Resistance WAEs of Shunt-Arm Admittances Interconnection Rules WAEs of Tuned Circuits WA Simulation Example Comments on the Wave Active Filter Approach Economical Wave Active Filters Sensitivity of WAFs Operation of WAFs at Higher Frequencies Complementary Transfer Functions Wave Simulation of Inductance Linear Transformation Active Filters (LTA Filters) Interconnection Rule General Remarks on the Method Summary 229 References 229 Chapter 8 Single Operational Transconductance Amplifier (OTA) Filters 8.1 Introduction Single OTA Filters Derived from Three-Admittance Model First-Order Filter Structures First-Order Filters with One or Two Passive Components First-Order Filters with Three Passive Components Lowpass Second-Order Filter with Three Passive Components Lowpass Second-Order Filters with Four Passive Components Bandpass Second-Order Filters with Four Passive Components Second-Order Filters Derived from Four-Admittance Model Filter Structures and Design Lowpass Filter Bandpass Filter Other Considerations on Structure Generation Second-Order Filters with the OTA Transposed Highpass Filter Lowpass Filter Bandpass Filter Tunability of Active Filters Using Single OTA OTA Nonideality Effects Direct Analysis Using Practical OTA Macro-Model Simple Formula Method Reduction and Elimination of Parasitic Effects OTA-C Filters Derived from Single OTA Filters Simulated OTA Resistors and OTA-C Filters 254

7 8.6.2 Design Considerations of OY Structures Second-Ordre Filters Derived from Five-Admittance Model Highpass Filter Bandpass Filter...,, Lowpass Filter Comments and Comparison Summary. 264 References 264 Chapter 9 Two Integer Loop OTA-C Filters 9.1 Introduction OTA-C Building Blocks and First-Order OTA-C Filters Two Integrator Loop Configurations and Performance Configurations Pole Equations Design Sensitivity Tuning Biquadratic Specifications.' OTA-C Realizations of Distributed-Feedback (DF) Configuration DF OTA-C Circuit and Equations Filter Functions Design Examples DF OTA-C Realizations with Special Feedback Coefficients OTA-C Filters Based on Summed-Feedback (SF) Configuration SF OTA-C Realization with Arbitrary k u and k n Design Example of KHN OTA-C Biquad SF OTA-C Realization with k u = k n = k Biquadratic OTA-C Filters Using Lossy Integrators Tow-Thomas OTA-C Structure Feedback Lossy Integrator Biquad Comparison of Basic OY Filter Structures Multifunctionality and Number of OTA Sensitivity Tunability Versatile Filter Functions Based on Node Current Injection DF Structures with Node Current Injection SF Structures with Node Current Injection Universal Biquads Using Output Summation Approach DF-Type Universal Biquads SF Type Universal Biquads Universal Biquads Based on Node Current Injection and Output Summation Comments on Universal Biquads Universal Biquads Based on Canonical and TT Circuits Effects and Compensation of OTA Nonidealities General Model and Equations Finite Impedance Effects and Compensation Finite Bandwidth Effects and Compensation Selection of OTA-C Filter Structures Selection of Input and Output Methods 302

8 Dynamic Range Problem Summary : 303 References 304 Chapter 10 OTA-C Filters Based on Ladder Simulation 10.1 Introduction Component Substitution Method Direct Inductor Substitution OTA-C Inductors Tolerance Sensitivity of Filter Function Parasitic Effects on Simulated Inductor Parasitic Effects on Filter Function Application Examples of Inductor Substitution OTA-C Biquad Derived from RLC Resonator Circuit A Lowpass OTA-C Filter Bruton Transformation and FDNR Simulation Admittance/Impedance Simulation General Description of the Method Application Examples and Comparison Parial Floating Admittance Concept Signal Flow Simulation and Leapfrog Structures Leapfrog Simulation Structures of General Ladder OTA-C Lowpass LF Filters Example OTA-C Bandpass LF Filter Design Partial Floating Admittance Block Diagram and OTA-C Realization Alternative Leapfrog Structures and OTA-C Realizations Equivalence of Admittance and Signal Simulation Methods OTA-C Simulation of LC Ladders Using Matrix Methods Coupled Biquad OTA Structures Some General Practical Design Considerations Selection of Capacitors and OTAs Tolerance Sensitivity and Parasitic Effects OTA Finite Impedances and Frequency-Dependent Transconductance Summary 343 References 344 Chapter 11 Multiple Integrator Loop Feedback OTA-C Filters 11.1 Introduction General Design Theory of All-Pole Structures Multiple Loop Feedback OTA-C Model System Equations and Transfer Function, Feedback Coefficient Matrix and Systematic Structure Generation Filter Synthesis Prcedure Based on Coefficient Matching Structure Generation and Design of All-Pole Filters First- and Second-Order Filters Third-Order Filters Fourth-Order Filters Design Examples of Fourth-Order Filters General nth-order Architectures 360

9 General IFLF Configuration General LF Configureation Other Types of Realization Generation and Synthesis of Transmission Zeros Output Summation of OTA Network Input Distribution of OTA Network Universal and Special Third-Order OTA-C Filters IFLF and Output Summation Structure in Fig (a) IFLF and Input Distribution Structure in Fig (b) LF and Output Summation Structure in Fig (c) LF and Input Distribution Structure in Fig (d) Realization of Special Characteristics Design of Elliptic Filters General nth-order OTA-C Filters Universal IFLF Architectures Universal LF Architectures General Formulation of Sensitivity Analysis General Sensitivity Relations Sensitivities of Different Filter Structures Determination of Maximum Signal Magnitude Effects of OTA Frequency Response Nonidealities Summary 381 References 382 Chapter 12 Current-Mode Filters and Other Architectures 12.1 Introduction Current-Mode Filters Based on Single DO-OTA Model General Model and Filter Architecture Generation First-Order Filter Structures Second-Order Filter Architectures Passive Resistor and Active Resistor Design of Second-Order Filters Effects of DO-OTA Nonidealities Current-Mode Two Integrator Loop DO-OTA-C Filters Basic Building Blocks and First-Order Filters Current-Mode DO-OTA-C Configurations with Arbitrary fy Current-Mode DO-OTA-C Biquadratic Architectures with k u = k tj Current-Mode DO-OTA-C Biquadratic Architectures with k u = DO-OTA Nonideality Effects Universal Current-Mode DO-OTA-C Filters Current-Mode DO-OTA-C Ladder Simulation Filters Leapfrog Simulation Structures of General Ladder Current-Mode DO-OTA-C Lowpass LF Filters Current-Mode DO-OTA-C Bandpass LF Filter Design Alternative Current-Mode Leapfrog DO-OTA-C Structure Current-Mode Multiple Loop Feedback DO-OTA-C Filters Design of All-Pole Filters Realization of Transmission Zeros Multiple Loop Feedback with Input Distribution Multiple Loop Feedback with Output Summation Filter Structures and Design Formulas 417

10 12.6 Other Continuous-Time Filter Structures Balanced Opamp-RC and OTA-C Structures MOSFET-C Filters OTA-C Opamp Filter Design Active Filters Using Current Conveyors Log-Domain, Current Amplifier, and Integrated-RLC Filters Summary 425 References 426 Appendix A A Sample of Filter Functions 431 Index 437