Continuous-Time Active Filter Design

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ISBN: 9780849325731 | 0849325730
Cover: Hardcover
Copyright: 12/16/1998

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This book presents the design of active RC filters in continuous time.Topics include:o filter fundamentalso active elementso realization of functions using opampso LC ladder filterso operational transconductance amplifier circuits (OTACs)o MOSFET-C filtersContinuous-Time Active Filter Design uses wave variables to enable the reader to better understand the introduction of more complex variables created through linear transformations of voltages and currents.Intended for undergraduate students in electrical engineering, Continuous-Time Active Filter Design provides chapters as self-contained units, including introductory material leading to active RC filters.

Chapter 1 Filter Fundamentals

(34)

1.1 Introduction

(1)

1.2 Filter Characterization

(3)

1.2.1 Lumped

(1)

1.2.2 Linear

(1)

1.2.3 Continuous-Time and Discrete-Time

(1)

1.2.4 Time-Invariant

(1)

1.2.5 Finite

(1)

1.2.6 Passive and Active

(1)

1.3 Types of Filters

(2)

1.4 Steps in Filter Design

(1)

1.5 Analysis

(12)

1.5.1 Nodal Analysis

(3)

1.5.2 Network Parameters

(1)

1.5.2.1 One-Port Network

(1)

1.5.2.2 Two-Port Network

(3)

1.5.3 Two-Port Interconnections

(1)

1.5.3.1 Series-Series Connection

(1)

1.5.3.2 Parallel-Parallel Connection

(1)

1.5.3.3 Series Input-Parallel Output Connection

(1)

1.5.3.4 Parallel Input-Series Output Connection

(1)

1.5.3.5 Cascade Connection

(1)

1.5.4 Network Transfer Functions

(2)

1.6 Continuous-Time Filter Functions

(7)

1.6.1 Pole-Zero Locations

(1)

1.6.2 Frequency Response

(1)

1.6.3 Transient Response

(1)

1.6.3.1 Impulse Response

(1)

1.6.3.2 Step Response

(1)

1.6.4 Step and Frequency Response

(2)

1.7 Stability

(3)

1.7.1 Short-Circuit and Open-Circuit Stability

(1)

1.7.2 Absolute Stability and Potential Instability.

(2)

1.8 Passivity Criterial for One-and Two-Port Networks

(3)

1.8.1 One-Ports

(1)

1.8.2 Two-Ports

(1)

1.8.3 Activity

(1)

1.8.4 Passivity and Stability

(1)

1.9 Reciprocity

(1)

1.10 Summary

(1)

References and Further Reading

(2)

Chapter 2 The Approximation problem

(40)

2.1 Introduction

(1)

2.2 Filter Specifications and Permitted Functions

(2)

2.2.1 Causality

(1)

2.2.2 Rational Functions

(1)

2.2.3 Stability

(1)

2.3 Formulation of the Approximation Problem

(1)

2.4 Approximation of the Ideal Lowpass Filter

(14)

2.4.1 Butterworth or Maximally Flat Approximation

(3)

2.4.2 Chebyshev or Equiripple Approximation

(3)

2.4.3 Inverse Chebyshev Approximation

(2)

2.4.4 Papoulis Approximation

(1)

2.4.5 Elliptic Function or Cauer Approximation

(2)

2.4.6 Selecting the Filter from Its Specifications

(3)

2.4.7 Ampulitude Equalization

(1)

2.5 Filter with Linear Phase: Delays

(7)

2.5.1 Bessel-Thomson Delay Approximation

(4)

2.5.2 Other Delay Functions

(1)

2.5.3 Delay Equalization

(1)

2.6 Frequency Transformations

(5)

2.6.1 Lowpass-to-Lowpass Transformation

(1)

2.6.2 Lowpass-to-Highpass Transformation

(1)

2.6.3 Lowpass-to-Bandpass Transformation

(1)

2.6.4 Lowpass-to-Bandstop Transformation

(1)

2.6.5 Delay Denormalization

(1)

2.7 Design Tables for Passive LC Ladder Filters

(6)

2.7.1 Transformation of Elements

(1)

2.7.1.1 LC Filters

(3)

2.7.1.2 Active RC Filters

(2)

2.8 Impedance Scaling

(1)

2.9 Predistortion

(1)

2.10 Summary

(1)

References

(2)

Chapter 3 Active Elements

(32)

3.1 Introduction

(1)

3.2 Ideal Controlled Sources

(1)

3.3 Impedance Transformation (Generalized Impedance Converters and Inverters)

(6)

3.3.1 Generalized Impedance Converters

(1)

3.3.1.1 The Ideal Active Transformer

(1)

3.3.1.2 The Ideal Negative Impedance Converter

(1)

3.3.1.3 The Positive Impedance Converter

(1)

3.3.1.4 The Frequency-Dependent Negative Resistor

(1)

3.3.2 Generalized Impedance Inverters

(1)

3.3.2.1 The Gyrator

(1)

3.3.2.2 Negative Impedance Inverter

(1)

3.4 Negative Resistance

(2)

3.5 Ideal Operational Amplifier

(16)

3.5.1 Operations Using the Ideal Opamp

(1)

3.5.1.1 Summation of Voltages

(1)

3.5.1.2 Integration

(1)

3.5.2 Realization of Some Active Elements Using Opamps

(1)

3.5.2.1 Realization of Controlled Sources

(1)

3.5.2.2 Realization of Negative-Impedance Converters

(2)

3.5.2.3 Gyrator Realizations

(1)

3.5.2.4 GIC Circuit Using Opamps

(2)

3.5.3 Characterstics of IC Opamps

(1)

3.5.3.1 Open-Loop Voltage Gain of Practical Opamps

(1)

3.5.3.2 Input and Output Impedances

(1)

3.5.3.3 Input Offset Voltage V(IO)

(1)

3.5.3.4 Input Offset Current I(IO)

(1)

3.5.3.5 Input Voltage Range V(I)

(1)

3.5.3.6 Power Supply Sensitivity Delta V(IO) / Delta V(GG)

(1)

3.5.3.7 Slew Rate SR

(1)

3.5.3.8 Short-Circuit Output Current

(1)

3.5.3.9 Maximum Peak-to-Peak Output Voltage Swing V(opp)

(1)

3.5.3.10 Input Capacitance C(i)

(1)

3.5.3.11 Common-Mode Rejection Ratio CMRR

(1)

3.5.3.12 Total Power Dissipation

(1)

3.5.3.13 Rise Time t(r)

(1)

3.5.3.14 Overshoot

(1)

3.5.4 Effect of the Single-Pole Compensation on the Finite Voltage Gain Controlled Sources

(2)

3.6 The Ideal Operational Transconductance Amplifier (OTA)

100

(6)

3.6.1 Voltage Amplification

100

(1)

3.6.2 A Voltage-Variable Resistor (VVR)

101

(1)

3.6.3 Voltage Summation

101

(1)

3.6.4 Integration

102

(1)

3.6.5 Gyrator Realization

102

(1)

3.6.6 Practical OTAs

103

(1)

3.6.7 Current Conveyor

104

(2)

3.7 Summary

106

(1)

References

106

(1)

Chapter 4 Realization of First-and Second-Order Functions Using Opamps

107

(44)

4.1 Introduction

107

(1)

4.2 Realization of First-Order Functions

107

(3)

4.2.1 Lowpass Circuits

108

(1)

4.2.2 Highpass Circuits

109

(1)

4.2.3 Allpas Circuits

110

(1)

4.3 The General Second-Order Filter Function

110

(1)

4.4 Sensitivity of Second-Order Filters

111

(3)

4.5 Realization of Biquadratic Functions Using SABs

114

(18)

4.5.1 Classification of SABs

115

(1)

4.5.2 A Lowpass SAB

116

(4)

4.5.3 A Highpass SAB

120

(1)

4.5.4 A Bandpass SAB

121

(5)

4.5.5 Lowpass-and Highpass-Notch Biquads

126

(1)

4.5.6 Lowpass Notch (R(6) = Infinity)

127

(2)

4.5.7 Highpass Notch (R(7) = Infinity)

129

(1)

4.5.8 An Allpass SAB

129

(3)

4.6 Realization of a Quadratic with a Positive Real Zero

132

(2)

4.7 Biquads Obtained Using the Twin-T RC Network

134

(2)

4.8 Two-Opamp Biquads

136

(5)

4.8.1 Biquads by Inductance Simulation

136

(2)

4.8.2 Two-Opamp Allpass Biquads

138

(1)

4.8.3 Selectivity Enhancement

139

(2)

4.9 Three-Opamp Biquads

141

(6)

4.9.1 The Tow-Thomas [25-27] Three-Opamp Biquad

144

(1)

4.9.2 Excess Phase and Its Compensation in Three-Opamp Biquads

145

(1)

4.9.3 The Akerberg-Mossberg Three-Opamp Biquad

146

(1)

4.10 Summary

147

(1)

References

148

(3)

Chapter 5 Realization of High-Order Functions

151

(32)

5.1 Introduction

151

(1)

5.2 Selection Criteria for High-Order Function Realizations

151

(2)

5.3 Multiparameter Sensitivity

153

(1)

5.4 High-Order Function Realization Methods

154

(1)

5.5 Cascade Connection of Second-Order Sections

155

(7)

5.5.1 Pole-Zero Pairing

156

(2)

5.5.2 Cascade Sequence

158

(1)

5.5.3 Gain Distribution

159

(3)

5.6 Multiple-Loop Feedback Filters

162

(9)

5.6.1 The Shifted-Companion-Form (SCF) Design Method

166

(2)

5.6.2 Follow-the-Leader Feedback Design (FLF)

168

(3)

5.7 Cascade of Biquartics

171

(9)

5.7.1 The BR Section

171

(2)

5.7.2 Effect of Eta on Omega'(i) and Q'(i)

173

(2)

5.7.3 Cascading Biquartic Sections

175

(1)

5.7.4 Realization of Biquartic Sections

175

(1)

5.7.4.1 Design Example

176

(2)

5.7.5 Sensitivity of CBR Filters

178

(2)

5.8 Summary

180

(1)

References

180

(1)

Further Reading

181

(2)

Chapter 6 Simulation of LC Ladder Filters Using Opamps

183

(22)

6.1 Introduction

183

(1)

6.2 Resistively-Terminated Lossless LC Ladder Filters

184

(1)

6.3 Methods of LC Ladder Simulation

184

(1)

6.4 The Gyrator

185

(5)

6.4.1 Gyrator Imprefections

186

(2)

6.4.2 Use of Gyrator in Filter Synthesis

188

(2)

6.5 Generalized Impedance Converter, GIC

190

(3)

6.5.1 Use of GICs in Filter Synthesis

190

(3)

6.6 FDNRs: Complex Impedance Scaling

193

(2)

6.7 Functional Simulation

195

(7)

6.7.1 Example

198

(1)

6.7.2 Bandpass Filters

199

(2)

6.7.3 Dynamic Range of LF Filters

201

(1)

6.8 Summary

202

(1)

References

202

(3)

Chapter 7 Wave Active Filters

205

(26)

7.1 Introduction

205

(1)

7.2 Wave Active Filters

205

(3)

7.3 Wave Active Equivalents (WAEs)

208

(9)

7.3.1 Wave Active Equivalent of a Series-Arm Impedance

208

(1)

7.3.2 Wave Active Equivalent of a Shunt-Arm Admittance

209

(1)

7.3.3 WAEs for Equal Port Normalization Resistances

209

(1)

7.3.4 Wave Active Equivalent of the Signal Source

210

(1)

7.3.5 Wave Active Equivalent of the Terminating Resistance

211

(1)

7.3.6 WAEs of Shunt-Arm Admittances

212

(1)

7.3.7 Interconnection Rules

212

(2)

7.3.8 WAEs of Tuned Circuits

214

(2)

7.3.9 WA Simulation Example

216

(1)

7.3.10 Comments on the Wave Active Filter Approach

216

(1)

7.4 Economical Wave Active Filters

217

(3)

7.5 Sensitivity of WAFs

220

(1)

7.6 Operation of WAFs at Higher Frequencies

221

(2)

7.7 Complementary Transfer Functions

223

(1)

7.8 Wave Simulation of Inductance

224

(1)

7.9 Linear Transformation Active Filters (LTA Filters)

224

(5)

7.9.1 Interconnection Rule

227

(2)

7.9.2 General Remarks on the Method

229

(1)

7.10 Summary

229

(1)

References

229

(2)

Chapter 8 Single Operational Transconductance Amplifier (OTA) Filters

231

(38)

8.1 Introduction

231

(1)

8.2 Single OTA Filters Derived from Three-Admittance Model

232

(9)

8.2.1 First-Order Filter Structures

232

(1)

8.2.1.1 First-Order Filters with One or Two Passive Components

233

(1)

8.2.1.2 First-Order Filters with Three Passive Components

234

(1)

8.2.2 Lowpass Second-Order Filter with Three Passive Components

235

(1)

8.2.3 Lowpass Second-Order Filters with Four Passive Components

236

(2)

8.2.4 Bandpass Second-Order Filters with Four Passive Components

238

(3)

8.3 Second-Order Filters Derived from Four-Admittance Model

241

(8)

8.3.1 Filter Structures and Design

241

(1)

8.3.1.1 Lowpass Filter

241

(2)

8.3.1.2 Bandpass Filter

243

(1)

8.3.1.3 Other Considerations on Structure Generation

244

(1)

8.3.2 Second-Order Filters with the OTA Transposed

245

(1)

8.3.2.1 Highpass Filter

245

(2)

8.3.2.2 Lowpass Filter

247

(1)

8.3.2.3 Bandpass Filter

247

(2)

8.4 Tunability of Active Filters Using Single OTA

249

(1)

8.5 OTA Nonideality Effects

249

(5)

8.5.1 Direct Analysis Using Practical OTA Macro-Model

249

(4)

8.5.2 Simple Formula Method

253

(1)

8.5.3 Reduction and Elimination of Parasitic Effects

253

(1)

8.6 OTA-C Filters Derived from Single OTA Filters

254

(4)

8.6.1 Simulated OTA Resistors and OTA-C Filters

254

(1)

8.6.2 Design Considerations of OY Structures

255

(3)

8.7 Second-Ordre Filters Derived from Five-Admittance Model

258

(6)

8.7.1 Highpass Filter

259

(1)

8.7.2 Bandpass Filters

260

(2)

8.7.3 Lowpass Filter

262

(1)

8.7.4 Comment and Comparison

263

(1)

8.8 Summary

264

(1)

References

264

(5)

Chapter 9 Two Integer Loop OTA-C Filters

269

(40)

9.1 Introduction

269

(1)

9.2 OTA-C Building Blocks and First-Order OTA-C Filters

270

(2)

9.3 Two Integrator Loop Configurations and Performance

272

(2)

9.3.1 Configurations

272

(1)

9.3.2 Pole Equations

272

(2)

9.3.3 Design

273

(1)

9.3.4 Sensitivity

273

(1)

9.3.5 Tuning

273

(1)

9.3.6 Biquadratic Specifications

273

(1)

9.4 OTA-C Realization of Distributed-Feedback (DF) Configuration

274

(6)

9.4.1 DF OTA-C Circuit and Equations

274

(2)

9.4.2 Filter Functions

276

(1)

9.4.3 Design Examples

277

(1)

9.4.4 DF OTA-C Realizations with Special Feedback Coefficients

278

(2)

9.5 OTA-C Filters Based on Summed-Feedback (SF) Configuration

280

(3)

9.5.1 SF OTA-C Realization with Arbitrary k(12) and k(11)

281

(1)

9.5.1.1 Design Example of KHN OTA-C Biquad

282

(1)

9.5.2 SF OTA-C Realization with k(12) = k(11) = k

282

(1)

9.6 Biquadratic OTA-C Filters Using Lossy Integrators

283

(2)

9.6.1 Tow-Thomas OTA-C Structure

284

(1)

9.6.2 Feedback Lossy Integrator Biquad

284

(1)

9.7 Comparison of Basic OY Filter Structures

285

(2)

9.7.1 Multifunctionality and Number of OTA

285

(1)

9.7.2 Sensitivity

286

(1)

9.7.3 Tunability

286

(1)

9.8 Versatile Filter Functions Based on Node Current Injection

287

(4)

9.8.1 DF Structures with Node Current Injection

288

(1)

9.8.2 SF Structures with Node Current Injection

289

(2)

9.9 Universal Biquads Using Output Summation Approach

291

(3)

9.9.1 DF-Type Universal Biquads

292

(1)

9.9.2 SF Type Universal Biquads

292

(1)

9.9.3 Universal Biquads Based on Node Current Injection and Output Summation

293

(1)

9.9.4 Comments on Universal Biquads

294

(1)

9.10 Universal Biquads Based on Canonical and TT Circuits

294

(1)

9.11 Effects and Compensation of OTA Nonidealities

295

(8)

9.11.1 General Model and Equations

295

(3)

9.11.2 Finite Impedance Effects and Compensation

298

(1)

9.11.3 Finite Bandwidth Effects and Compensation

299

(2)

9.11.4 Selection of OTA-C Filter Structures

301

(1)

9.11.5 Selection of Input and Output Methods

302

(1)

9.11.6 Dynamic Range Problem

302

(1)

9.12 Summary

303

(1)

References

304

(5)

Chapter 10 OTA-C Filters Based on Ladder Simulation

309

(40)

10.1 Introduction

309

(1)

10.2 Component Substitution Method

310

(10)

10.2.1 Direct Inductor Substitution

310

(1)

10.2.1.1 OTA-C Inductors

310

(1)

10.2.1.2 Tolerance Sensitivity of Filter Function

311

(1)

10.2.1.3 Parasitic Effects on Simulated Inductor

312

(1)

10.2.1.4 Parasitic Effects on Filter Function

313

(2)

10.2.2 Application Examples of Inductor Substitution

315

(1)

10.2.2.1 OTA-C Biquad Derived from RLC Resonator Circuit

315

(1)

10.2.2.2 A Lowpass OTA-C Filter

316

(1)

10.2.3 Bruton Transformation and FDNR Simulation

317

(3)

10.3 Admittance/Impedance Simulation

320

(5)

10.3.1 General Description of the Method

320

(1)

10.3.2 Application Examples and Comparison

321

(3)

10.3.3 Parial Floating Admittance Concept

324

(1)

10.4 Signal Flow Simulation and Leapfrog Structures

325

(11)

10.4.1 Leapfrog Simulation Structures of General Ladder

325

(3)

10.4.2 OTA-C Lowpass LF Filters

328

(2)

10.4.2.1 Example

330

(2)

10.4.3 OTA-C Bandpass LF Filter Design

332

(1)

10.4.4 Partial Floating Admittance Block Diagram and OTA-C Realization

332

(2)

10.4.5 Alternative Leapfrog Structures and OTA-C Realizations

334

(2)

10.5 Equivalence of Admittance and Signal Simulation Methods

336

(2)

10.6 OTA-C Simulation of LC Ladders Using Matrix Methods

338

(2)

10.7 Coupled Biquad OTA Structures

340

(2)

10.8 Some General Practical Design Considerations

342

(1)

10.8.1 Selection of Capacitors and OTAs

342

(1)

10.8.2 Tolerance Sensitivity and Parasitic Effects

343

(1)

10.8.3 OTA Finite Impedances and Frequency-Dependent Transconductance

343

(1)

10.9 Summary

343

(1)

References

344

(5)

Chapter 11 Multiple Integrator Loop Feedback OTA-C Filters

349

(38)

11.1 Introduction

349

(1)

11.2 General Design Theory of All-Pole Structures

350

(5)

11.2.1 Multiple Loop Feedback OTA-C Model

350

(1)

11.2.2 System Equations and Transfer Function

350

(3)

11.2.3 Feedback Coefficient Matrix and Systematic Structure Generation

353

(1)

11.2.4 Filter Synthesis Prcedure Based on Coefficient Matching

354

(1)

11.3 Structure Generation and Design of All-Pole Filters

355

(8)

11.3.1 First-and Second-Order Filters

355

(1)

11.3.2 Third-Order Filters

356

(1)

11.3.3 Fourth-Order Filters

357

(2)

11.3.4 Design Examples of Fourth-Order Filters

359

(1)

11.3.5 General nth-Order Architectures

360

(1)

11.3.5.1 General IFLF Configuration

360

(1)

11.3.5.2 General LF Configureation

361

(1)

11.3.6 Other Types of Realization

362

(1)

11.4 Generation and Synthesis of Transmission Zeros

363

(10)

11.4.1 Output Summation of OTA Network

364

(1)

11.4.2 Input Distribution of OTA Network

364

(2)

11.4.3 Universal and Special Third-Order OTA-C Filters

366

(1)

11.4.3.1 IFLF and Output Summation Structure in Fig. 11.10(a)

367

(1)

11.4.3.2 IFLF and Input Distribution Structure in Fig.11.10(b)

367

(1)

11.4.3.3 LF and Output Summation Structure in Fig. 11.10(c)

367

(1)

11.4.3.4 LF and Input Distribution Structure in Fig. 11.10(d)

368

(1)

11.4.3.5 Realization of Special Characteristics

368

(1)

11.4.3.6 Design of Elliptic Filters

368

(2)

11.4.4 General nth-Order OTA-C Filters

370

(2)

11.4.4.1 Universal IFLF Architectures

370

(2)

11.4.4.2 Universal LF Architectures

372

(1)

11.5 General Formulation of Sensitivity Analysis

373

(4)

11.5.1 General Sensitivity Relations

373

(2)

11.5.2 Sensitivity of Different Filter Structures

375

(2)

11.6 Determination of Maximum Signal Magnitude

377

(2)

11.7 Effects of OTA Frequency Response Nonidealities

379

(2)

11.8 Summary

381

(1)

References

382

(5)

Chapter 12 Current-Mode Filters and Other Architectures

387

(44)

12.1 Introduction

387

(1)

12.2 Current-Mode Filters Based on Single DO-OTA Model

388

(8)

12.2.1 General Model and Filter Architecture Generation

389

(1)

12.2.1.1 First-Order Filter Structures

389

(1)

12.2.1.2 Second-Order Filter Architectures

390

(1)

12.2.2 Passive Resistor and Active Resistor

390

(1)

12.2.3 Design of Second-Order Filters

391

(3)

12.2.4 Effects of DO-OTA Nonidealities

394

(2)

12.3 Current-Mode Two Integrator Loop DO-OTA-C Filters

396

(9)

12.3.1 Basic Building Blocks and First-Order Filters

396

(1)

12.3.2 Current-Mode DO-OTA-C Configurations with Arbitrary k(ij)

397

(1)

12.3.3 Current-Mode DO-OTA-C Biquadratic Architectures with k(12) = k(ij)

398

(1)

12.3.4 Current-Mode DO-OTA-C Biquadratic Architectures with k(12) = 1

399

(2)

12.3.5 DO-OTA Nonideality Effects

401

(1)

12.3.6 Universal Current-Mode DO-OTA-C Filters

401

(4)

12.4 Current-Mode DO-OTA-C Ladder Simulation Filters

405

(6)

12.4.1 Leapfrog Simulation Structures of General Ladder

405

(2)

12.4.2 Current-Mode DO-OTA-C Lowpass LF Filters

407

(2)

12.4.3 Current-Mode DO-OTA-C Bandpass LF Filter Design

409

(1)

12.4.4 Alternative Current-Mode Leapfrog DO-OTA-C Structure

410

(1)

12.5 Current-Mode Multiple Loop Feedback DO-OTA-C Filters

411

(8)

12.5.1 Design of All-Pole Filters

411

(4)

12.5.2 Realization of Transmission Zeros

415

(1)

12.5.2.1 Multiple Loop Feedback with Input Distribution

415

(1)

12.5.2.2 Multiple Loop Feedback with Output Summation

416

(1)

12.5.2.3 Filter Structures and Design Formulas

417

(2)

12.6 Other Continous-Time Filter Structures

419

(6)

12.6.1 Balanced Opamp-RC and OTA-C Structures

419

(1)

12.6.2 MOSFET-C Filters

420

(2)

12.6.3 OTA-C Opamp Filter Design

422

(1)

12.6.4 Active Filters Using Current Conveyors

423

(2)

12.6.5 Log-Domain, Current Amplifier, and Integrated-RLC Filters

425

(1)

12.7 Summary

425

(1)

References

426

(5)

Appendix A A Sample of Filter Functions

431

(6)

Index

437

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Continuous-Time Active Filter Design

Summary

Table of Contents

Supplemental Materials