ELECTRONIC FILTER DESIGN HANDBOOK Arthur B. Williams Fred J.Taylor Fourth Edition McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto CONTENTS Preface xiii Chapter 1. Introduction to Modern Network Theory 1 1.1. Modern Network Theory / / The Pole-Zero Concept / 1 Synthesis of Filters from Polynomials / 2 Active vs. Passive Filters / 7 Bibliography / 8 Chapter 2. Sefecting the Response Characteristic 9 2.1. Frequency-Response Normalization / 9 Frequency and Impedance Scaling / 9 Low-Pass Normalization / 12 High-Pass Normalization / 14 Bandpass Normalization / 16 Band-Reject Normalization / 24 2.2. Transient Response / 29 The Effect of Nonuniform Time Delay / 29 Step Response of Networks / 32 Impulse Response / 34 Estimating Transient Characteristies / 34 2.3. Butterworth Maximally Fiat Amplitude / 42 2.4. Chebyshev Response / 47 2.5. Bessel Maximally Fiat Delay / 52 2.6. Linear Phase with Equiripple Error / 64 2.7. Transitional Filters / 64 2.8. Syncbronously Tuned Filters / 70 2.9. Elliptic-Function Filters / 79 Using the Filter Solutions (Book Version) Software for Design of Elliptic Function Low- Pass Filters / 86 Using the ELI 1.0 Program for the Design of Odd-Order Elliptic-Function Low-Pass Filters upto the 3Ist Order / 87 2.10. Maximally Fiat Delay with Chebyshev Stopband / 88 Bibliography / 88 Chapter 3. Low-Pass Filter Design 89 3.1. LCLow-Pass Filters / 89 All-Pole Filters / 89 v VI CONTENTS Elliptic-Function Filters / 90 Duality and Reciprocity / 93 Designing for Unequal Terminadons / 93 Effects of Dissipation / 97 Using Predistorted Designs / 99 3.2. Active Low-Pass Filters / 103 All-Pole Filters / 103 VCVS Uniform Capacitor Structure / /13 The Low-Sensitivity Second-Order Section / 114 Elliptic-Function VCVS Filters / 116 State-Variable Low-Pass Filters / 120 Generalized Impcdance Converters / 128 Bibliography / 135 Chapter 4. High-Pass Filter Design 137 4.1. LC High-Pass Filters / 137 The Lüw-Pass to High-Pass Transformation / 137 The T-to-Pi Capacitance Conversion / 142 4.2. Active High-Pass Filters / 143 The Low-Pass to High-Pass Transformation / 143 All-Pole High-Pass Filters / 144 Elliptic-Function High-Pass Filters / 145 State-Variable High-Pass Filters / 151 High-Pass Filters Using the GIC / 159 Active Elliptic-Function High-Pass Filters Using theGIC / 161 Bibliography / 164 Chapter 5. Bandpass Filters 165 5.1. LC Bandpass Filters / 165 Wideband Filters / 165 Narrowband Filters / 167 Narrowband Coupied Resonators / 183 Predistorted Bandpass Filters / 189 Elliptic-Function Bandpass Filers / 192 5.2. Active Bandpass Filters / 199 Wideband Filters / 199 The Bandpass Transformation of Low-Pass Poles and Zeros / 202 Sensitivity in Active Bandpass Circuits / 207 All-Pole Bandpass Configuraüons / 207 Elliptic-Function Bandpass Filters / 224 State-Variabie (Biquad) Circuit / 230 Bibliography / 237 Chapter 6. Band-Reject Filters 239 6.1. LC Band-Reject Filters / 239 The Band-Reject Circuit Transformation / 239 All-Pole Band-Reject Filters / 240 Elliptic-Function Band-Reject Filters / 245 Null Networks / 252 6.2. Active Band-Reject Filters / 257 Wideband Active Band-Reject Filters / 257 CONTENTS VII Band-Reject Transformation of Low-Pass Poles / 261 Narrowband Active Band-Reject Filters / 265 Active Null Networks / 271 Bibliography / 277 Chapter 7. Networks for the Time Domain 7.1. All-Pass Transfer Functions / 279 First-Order All-Pass Transfer Functions / 279 Second-Order All-Pass Transfer- Functions / 281 7.2. Delay Equalizer Sections / 283 LC All-Pass Structurcs / 283 Active All-Pass Structures / 287 7.3. Design of Delay Lines / 292 The Low-Pass to All-Pass Transformation / 292 LC Delay Lines / 293 Active Delay Lines / 297 7.4. Delay Equalizationof Filters / 299 Firsl-Order Equalizers / 300 Second-Order Equalizers / 303 7.5. Wideband 90° Phase-Shift Networks / 307 7.6. Adjustable Delay and Amplitude Equalizers / 313 LC Delay Equalizers / 314 LC Delay and Amplitude Equalizers / 3/6 Active Delay and Amplitude Equalizers / 319 Bibliography / 323 Chapter 8. Refinements in LC Filter Design and the Use of Resistive Networks 8.1. Introduction / 325 8.2. Tapped Inductors / 325 8.3. Circuit Transformations / 327 Norton'sCapacitance Transformer / 328 Narrowband Approximations / 330 8.4. Designing with Parasitic Capacitance / 333 8.5. Amplitude Equalization for Inadequate Q ! 336 8.6. Coil-Saving Elliptic-Function Bandpass Filters / 340 8.7. Filter Tuning Methods / 343 8.8. Measurement Methods / 345 Insertion Loss and Frequency Response / 345 iaput Impedance of Filter Networks / 346 Time-Domain Characteristics / 347 Measuring the Q of inductors / 351 8.9. Designing for Unequal Impedances / 351 Impedance Matching / 351 Exponentially Tapered Impedance Sealing / 351 Minimum Loss Resistive Päd for Impedance Matching / 352 8.10. Symmetrica] Attenuators / 355 Bridged T Attenuator / 356 8.11. Puwer Splitters / 357 Resistive Power Splitters / 357 A Magic-T Splitter / 357 Bibliography / 360 CONTENTS Chapter 9. Design and Selection of Inductors for LC Filters 361^ 9.1. Basic Principlesof Magnefic-Circuil Design / 361 Units of Measurement / 361 Saturation and DC Polarization / 362 Inductor Losses / 363 Effect of an Air Gap / 363 The Design of Coil Windings / 364 9.2. MPP Toroidal Coils / 367 Charactcristics of Gores / 367 Winding Methods for Q Optimizaüon / 371 Designing MPP Toroids from Q Curvcs / 372 9.3. Ferrite Pot Gores / 376 The Pol Gore Structure / 376 Hlectrical Properties of Ferrite Pot Cores / 377 Winding of Bobbins / 380 RMCorcs / 382 9.4. High-Frequency Coil Design / 383 Powdered-lron Toroids / 383 Winding Methods / 384 Air-Core Inductors / 387 Surface Mount RF Inductors / 387 Bibliography / 392 Chapter 10. Component Selection for LC and Active Filters 393 10.1. Capacitor Selection / 393 Properlies ofDielcctri es / 393 Capacitor Conslruction / 394 Selecling Capacitors for Filier Applications / 398 10.2. Resistors / 403 Fixed Resistors / 403 Variable Resistors / 408 Resistor Johnson (Thermal) Noise / 409 10.3. Operational Amplifiers / 410 A Review of Basic Üperationai-Amplifier Theory / 410 An Analysis ofNon-ldeal Amplifiers / 413 Practical Amplifier Considerations / 415 Operational Amplifier Selection / 417 A Survey of Populär Amplifier Types / 419 10.4. General Manufacturing Considerations / 422 Bibliography / 423 Chapter 11. Normalized Filter Design Tables *25 Chapter 12. Introduction to Digital Filters 497 12.1. Introduction to Signal Processing / 497 12.2. Introduction to Digital Signal Processing (DSP) / 497 12.3. The Relation to Analog Filters / 498 Digital Advantages / 498 Analog Advantages / 499 12.4. Signal Representation / 500 CONTENTS IX 12.5. Digital Data Representation / 500 12.6. Sampling Theorem / 505 12.7. Signal Reconstruction / 506 12.8. Practica] Interpolators / 506 12.9. Sampling Modalities / 507 12.10. AHasing / 507 12.11. Data Conversion / 509 12.12. Finite Wordlength Effects / 510 12.13. Mathematical Signaland System Representation / 512 12.14. Spectral Representation / 514 Bibliography / 515 Chapter 13. Finite Impuise-Response Fiiters 517 1.3.1. Digital Pikers / 517 13.2. FIR Digital Filters / 517 13.3. Stability / 519 13.4. Linear-Phase Behavior / 520 13.5. Non-Linear-Phase Behavior / 522 13.6. Minimum Phase Behavior / 523 13.7. Fir Design Methods / 524 13.8. Window Design Melhod / 524 13.9. Non-Reetangular Window Design Method / 526 13.10. Least Squares FIR Design / 530 13.11. Equiripple FIR Design / 532 13.12. Equiripple Hubert FIR Design / 53S 13.13. Equiripple Differentiator FIR Design / 538 13.14. Special Case FIR Digital Filters / 539 13.15. Multiplier-Free FIR Filters / 541 13.! 6. L-Band FIR Filters / 542 13.17. Mirror and Complement FIR Filters / 544 13.18. Frequency Sampling FIR Filters / 547 13.19. Savitzky-Golay FIR Filters / 550 13.20. Raised FIR Filters / 551 13.21. Matlab FIR Support / 553 13.22. FirArchitectures / 553 13.23. Direct Form FIR / 553 13.24. Transpose Form FIR / 557 13.25. Symmetrie Form FIR / 558 13.26. Lattice Form FIR / 558 13.27. DistributedArithmetic / 561 13.28. Canonic Signed Digit (CSD) / 564 13.29. Finite Wordlength Effect / 566 13.30. CoefficientRounding / 567 13.31. Arithmetic Error / 568 13.32. Scaling / 569 13.33. Multiple Mac Architecture / 569 Bibliography / 571 Chapter 14. infinite Impuise-Response Filters 573 14.1. lntroduction / 573 14.2. Classic Analog Filters / 576 14.3. Matlab Analog Filter Production / 579 14.4. Impulse Invariant HR / 580 X CONTENTS 14.5. Bilinear z-TransformllR / 583 14.6. Matlab Classic HR Support / 588 14.7. Other HR Models / 590 14.8. Comparison of FTR and HR Filters / 592 14.9. State Variable Filter Model / 593 14.10. Architecture / 595 14.11. Direel II Architecture / 596 14.12. Matlab Direct II Architecture / 598 14.13. Cascade Architecture / 600 14.14. The Matlab Cascade Architecture / 602 14.15. Parallel Architecture / 604 14.16. Lattice/Ladder Architecture / 605 14.17. Matlab Ladder/Lattice Support / 608 14.18. Normal Architecture / 609 14.19. Stability / 611 14.20. Finite Wordlength Effects / 612 14.21. Overflow Arithmetic / 613 14.22. Register Overflow / 614 14.23. Arithmetic Enrors / 617 14.24. Coefficient Rounding Errors / 622 14.25. Scaling / 623 14.26. Zero Input Limit Cycling / 624 Bibliography / 626 Chapter 15. Multirate Digital Filters 627 15.1. IntroductiontoMulti-Rate Signal Processing / 627 15.2. Decimation / 628 15.3. Interpolation / 633 15.4. Sample Rate Conversion / 636 15.5. Polyphase Representation / 637 15.6. Filter Banks