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The Design of Active Crossovers

Name: The Design of Active Crossovers
Author: Douglas Self
ISBN: 9781136111891

by Douglas Self

August 2012

Intermediate to advanced

608 pages

17h 15m

English

Focal Press

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Cover
Halftitle
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
Chapter 1: Crossover Basics
1.1 What a Crossover Does1.2 Why a Crossover Is Necessary1.3 Beaming and Lobing1.4 Active Crossover Applications1.5 Bi-Amping and Bi-Wiring1.6 Loudspeaker Cables1.7 The Advantages and Disadvantages of Active Crossovers1.7.1 The Advantages of Active Crossovers1.7.2 The Disadvantages of Active Crossovers1.8 The Next Step in Hi-Fi1.9 Active Crossover Systems1.10 Matching Crossovers and Loudspeakers1.11 A Modest Proposal: Popularising Active Crossovers1.12 Multi-Way Connectors1.13 SubjectivismReferences
Chapter 2: How Loudspeakers Work
2.1 Sealed Box Loudspeakers2.2 Reflex (Ported) Loudspeakers2.3 Auxiliary Bass Radiator (ABR) Loudspeakers2.4 Transmission Line Loudspeakers2.5 Horn Loudspeakers2.6 Diffraction2.7 Modulation DistortionFurther ReadingReferences

Chapter 3: Crossover Requirements
3.1 General Crossover Requirements3.1.1 Adequate Flatness of Summed Amplitude/Frequency Response On-Axis3.1.2 Sufficiently Steep Rolloff Slopes between the Filter Outputs3.1.3 Acceptable Polar Response3.1.4 Acceptable Phase Response3.1.5 Acceptable Group Delay Behaviour3.2 Further Requirements for Active Crossovers3.2.1 Negligible Extra Noise3.2.2 Negligible Impairment of System Headroom3.2.3 Negligible Extra Distortion3.2.4 Negligible Impairment of Frequency Response3.2.5 Negligible Impairment of Reliability3.3 Linear Phase3.4 Minimum Phase3.5 Absolute Phase3.6 Phase Perception3.7 Target FunctionsReferences
Chapter 4: Crossover Types
4.1 All-Pole and Non-All-Pole Crossovers4.2 Symmetric and Asymmetric Crossovers4.3 All-Pass and Constant-Power Crossovers4.4 Constant-Voltage Crossovers4.5 First-Order Crossovers4.5.1 First-Order Solen Split Crossover4.5.2 First-Order Crossovers: 3-Way4.6 Second-Order Crossovers4.6.1 Second-Order Butterworth Crossover4.6.2 Second-Order Linkwitz–Riley Crossover4.6.3 Second-Order Bessel Crossover4.6.4 Second-Order 1.0 dB-Chebyshev Crossover4.7 Third-Order Crossovers4.7.1 Third-Order Butterworth Crossover4.7.2 Third-Order Linkwitz–Riley Crossover4.7.3 Third-Order Bessel Crossover4.7.4 Third-Order 1.0 dB-Chebyshev Crossover4.8 Fourth-Order Crossovers4.8.1 Fourth-Order Butterworth Crossover4.8.2 Fourth-Order Linkwitz–Riley Crossover4.8.3 Fourth-Order Bessel Crossover4.8.4 Fourth-Order 1.0 dB-Chebyshev Crossover4.8.5 Fourth-Order Linear-Phase Crossover4.8.6 Fourth-Order Gaussian Crossover4.8.7 Fourth-Order Legendre Crossover4.9 Higher-Order Crossovers4.10 Determining Frequency Offsets4.11 Summary of Crossover Properties4.12 Filler-Driver Crossovers4.13 The Duelund Crossover4.14 Crossover Topology4.15 Crossover ConclusionsReferences
Chapter 5: Notch Crossovers
5.1 Elliptical Filter Crossovers5.2 Neville Thiele MethodTM (NTM) CrossoversReferences
Chapter 6: Subtractive Crossovers
6.1 Subtractive Crossovers6.1.1 First-Order Subtractive Crossovers6.1.2 Second-Order Butterworth Subtractive Crossovers6.1.3 Third-Order Butterworth Subtractive Crossovers6.1.4 Fourth-Order Butterworth Subtractive Crossovers6.2 Subtractive Crossovers with Time Delays6.3 Performing the SubtractionReferences
Chapter 7: Lowpass & Highpass Filter Characteristics
7.1 Active Filters7.2 Lowpass Filters7.3 Highpass Filters7.4 Bandpass Filters7.5 Notch Filters7.6 Allpass Filters7.7 The Order of a Filter7.8 Filter Cutoff Frequencies and Characteristic Frequencies7.9 First-Order Filters7.10 Second-Order and Higher-Order Filters7.11 Filter Characteristics7.11.1 Butterworth Filters7.11.2 Linkwitz–Riley Filters7.11.3 Bessel Filters7.11.4 Chebyshev Filters7.11.5 1 dB-Chebyshev Lowpass Filter7.11.6 3 dB-Chebyshev Lowpass Filter7.12 Higher-Order Filters7.12.1 Butterworth Filters Up to Eighth-Order7.12.2 Linkwitz–Riley Filters Up to Eighth-Order7.12.3 Bessel Filters Up to Eighth-Order7.12.4 Chebyshev Filters Up to Eighth-Order7.13 More Complex Filters—Adding Zeros7.13.1 Inverse Chebyshev Filters (Chebyshev Type II)7.13.2 Elliptical Filters (Cauer Filters)7.14 Some Lesser-Known Filter Characteristics7.14.1 Transitional Filters7.14.2 Linear-Phase Filters7.14.3 Gaussian Filters7.14.4 Legendre–Papoulis Filters7.14.5 Synchronous Filters7.15 Other Filter CharacteristicsReferences
Chapter 8: Designing Lowpass and Highpass Filters
8.1 Designing Real Filters8.2 Component Sensitivity8.3 First-Order Lowpass and Highpass Filters8.4 Second-Order Filters8.5 Sallen & Key Second-Order Filters8.6 Sallen & Key Lowpass Filter Components8.7 Sallen & Key Second-Order Lowpass: Unity Gain8.8 Sallen & Key Second-Order Lowpass Unity-Gain: Component Sensitivity8.9 Sallen & Key Second-Order Lowpass: Equal-Capacitor8.10 Sallen & Key Second-Order Lowpass Equal-C: Component Sensitivity8.11 Sallen & Key Second-Order Butterworth Lowpass: Defined Gains8.12 Sallen & Key Second-Order Lowpass: Non-Equal Resistors8.13 Sallen & Key Third-Order Lowpass in a Single Stage8.14 Sallen & Key Third-Order Lowpass in a Single Stage: Non-Equal Resistors8.15 Sallen & Key Fourth-Order Lowpass in a Single Stage8.16 Sallen & Key Fourth-Order Lowpass in a Single Stage: Non-Equal Resistors8.17 Sallen & Key Fifth- and Sixth-Order Lowpass in a Single Stage8.18 Sallen & Key Highpass Filters8.19 Sallen & Key Second-Order Highpass: Unity Gain8.20 Sallen & Key Second-Order Highpass: Equal-Resistors8.21 Sallen & Key Second-Order Butterworth Highpass: Defined Gains8.22 Sallen & Key Second-Order Highpass: Non-Equal Capacitors8.23 Sallen & Key Third-Order Highpass in a Single Stage8.24 Sallen & Key Fourth-Order Highpass in a Single Stage8.25 Implementing Linkwitz–Riley with Sallen & Key Filters: Loading Effects8.26 Lowpass Filters with Attenuation8.27 Bandwidth Definition Filters8.27.1 Bandwidth Definition: Butterworth versus Bessel Ultrasonic Filters8.27.2 Bandwidth Definition: Subsonic Filters8.27.3 Bandwidth Definition: Combined Ultrasonic and Subsonic Filters8.28 Distortion in Sallen & Key Filters: Highpass8.29 Distortion in Sallen & Key Filters: Lowpass8.30 Mixed Capacitors in Low-Distortion Sallen & Key Filters8.31 Noise in Sallen & Key Filters: Lowpass8.32 Noise in Sallen & Key Filters: Highpass8.33 Multiple-Feedback Filters8.34 Multiple-Feedback Lowpass Filters8.35 Multiple-Feedback Highpass Filters8.36 Distortion in Multiple-Feedback Filters: Highpass8.37 Distortion in Multiple-Feedback Filters: Lowpass8.38 Noise in Multiple-Feedback Filters: Highpass8.39 Noise in Multiple-Feedback Filters: Lowpass8.40 State-Variable Filters8.41 Variable-Frequency Filters: Sallen and Key8.42 Variable-Frequency Filters: State-Variable Second Order8.43 Variable-Frequency Filters: State-Variable Fourth Order8.44 Variable-Frequency Filters: Other OrdersReferences
Chapter 9: Bandpass & Notch Filters
9.1 Multiple-Feedback Bandpass Filters9.2 High-Q Bandpass Filters9.3 Notch Filters9.4 The Twin-T Notch Filter9.4.1 The 1-Bandpass Notch Filter9.4.2 The Bainter Notch Filter9.4.3 The Bridged-Differentiator Notch Filter9.4.4 Boctor Notch Filters9.4.5 Other Notch Filters9.4.6 Simulating Notch FiltersReferences
Chapter 10: Time Domain Filters
10.1 The Requirement for Delay Compensation10.2 Calculating the Required Delays10.3 Signal Summation10.4 Physical Methods of Delay Compensation10.5 Delay Filter Technology10.6 Sample Crossover and Delay Filter Specification10.7 Allpass Filters in General10.7.1 First-Order Allpass Filters10.7.2 Second-Order Allpass Filters10.7.3 Third-Order Allpass Filters10.7.4 Higher-Order Filters10.8 Delay Lines for Subtractive Crossovers10.9 Variable Allpass Time Delays10.10 Lowpass Filters for Time DelaysReferences
Chapter 11: Equalisation
11.1 The Need for Equalisation11.2 What Equalisation Can and Can’t Do11.3 Loudspeaker Equalisation11.3.1 Drive Unit Equalisation11.3.2 6 dB/oct Dipole Equalisation11.3.3 Bass Response Extension11.3.4 Diffraction Compensation Equalisation11.3.5 Room Interaction Correction11.4 Equalisation Circuits11.5 HF-Boost and LF-Cut Equaliser11.6 HF-Cut and LF-Boost Equaliser11.7 Combined HF-Boost and HF-Cut Equaliser11.8 Adjustable Peak/Dip Equalisers: Fixed Frequency and Low Q11.9 Adjustable Peak/Dip Equalisers: Variable Centre Frequency and Low Q11.10 Adjustable Peak/Dip Equalisers with High Q11.11 The Bridged-T Equaliser11.12 The Biquad Equaliser11.13 Capacitance Multiplication for the Biquad Equaliser11.14 Equalisers with Non-6 dB Slopes11.15 Equalisation by Filter Frequency Offset11.16 Equalisation by Adjusting All Filter ParametersReferences
Chapter 12: Passive Components for Active Crossovers
12.1 Resistors: Values and Tolerances12.2 Improving Accuracy with Multiple Components: Gaussian Distribution12.3 Resistor Value Distributions12.4 Improving Accuracy with Multiple Components: Uniform Distribution12.5 Obtaining Arbitrary Resistance Values12.6 Resistor Noise: Johnson and Excess Noise12.7 Resistor Non-Linearity12.8 Capacitors: Values and Tolerances12.9 Capacitor Shortcomings12.10 Non-Electrolytic Capacitor Non-Linearity12.11 Electrolytic Capacitor Non-LinearityReferences
Chapter 13: Opamps for Active Crossovers
13.1 Active Devices for Active Crossovers13.2 Opamp Types13.2.1 Opamp Properties: Noise13.2.2 Opamp Properties: Slew Rate13.2.3 Opamp Properties: Common-Mode Range13.2.4 Opamp Properties: Input Offset Voltage13.2.5 Opamp Properties: Bias Current13.2.6 Opamp Properties: Cost13.2.7 Opamp Properties: Internal Distortion13.2.8 Opamp Properties: Slew-Rate Limiting Distortion13.2.9 Opamp Properties: Distortion Due to Loading13.2.10 Opamp Properties: Common-Mode Distortion13.3 Opamps Surveyed13.4 The TL072 Opamp13.5 The NE5532 and NE5534 Opamps13.6 The 5532 with Shunt Feedback13.7 5532 Output Loading in Shunt-Feedback Mode13.8 The 5532 with Series Feedback13.9 Common-Mode Distortion in the 553213.10 Reducing 5532 Distortion by Output Biasing13.11 Which 5532?13.12 The 5534 Opamp13.13 The LM4562 Opamp13.14 Common-Mode Distortion in the LM456213.15 The LME49990 Opamp13.16 Common-Mode Distortion in the LME4999013.17 The AD797 Opamp13.18 Common-Mode Distortion in the AD79713.19 The OP27 Opamp13.20 Opamp SelectionReferences
Chapter 14: Active Crossover System Design
14.1 Crossover Features14.1.1 Input Level Controls14.1.2 Subsonic Filters14.1.3 Ultrasonic Filters14.1.4 Output Level Trims14.1.5 Output Mute Switches, Output Phase-Reverse Switches14.1.6 Control Protection14.2 Features Usually Absent14.2.1 Metering14.2.2 Relay Output Muting14.2.3 Switchable Crossover Modes14.3 Noise, Headroom, and Internal Levels14.4 Circuit Noise and Low-Impedance Design14.5 Using Raised Internal Levels14.6 Placing the Output Attenuator14.7 The Amplitude/Frequency Distribution of Musical Signals and Internal Levels14.8 Gain Structures14.9 Noise Gain14.10 Active Gain-Controls14.11 Filter Order in the Signal Path14.12 Output Level Controls14.13 Mute Switches14.14 Phase-Invert Switches14.15 Distributed Peak Detection14.16 Power Amplifier ConsiderationsReferences
Chapter 15: Subwoofer Crossovers
15.1 Subwoofer Applications15.2 Subwoofer Technologies15.2.1 Sealed-Box (Infinite Baffle) Subwoofers15.2.2 Reflex (Ported) Subwoofers15.2.3 Auxiliary Bass Radiator (ABR) Subwoofers15.2.4 Transmission Line Subwoofers15.2.5 Bandpass Subwoofers15.2.6 Isobaric Subwoofers15.2.7 Dipole Subwoofers15.2.8 Horn-Loaded Subwoofers15.3 Subwoofer Drive Units15.4 Hi-fi Subwoofers15.5 Home Entertainment Subwoofers15.5.1 Low-Level Inputs (Unbalanced)15.5.2 Low-Level Inputs (Balanced)15.5.3 High-Level Inputs15.5.4 High-Level Outputs15.5.5 Mono Summing15.5.6 LFE Input15.5.7 Level Control15.5.8 Crossover In/Out Switch15.5.9 Crossover Frequency Control (Lowpass Filter)15.5.10 Highpass Subsonic Filter15.5.11 Phase Switch (Normal/Inverted)15.5.12 Variable Phase Control15.5.13 Signal Activation Out of Standby15.6 Home Entertainment Crossovers15.6.1 Fixed Frequency15.6.2 Variable Frequency15.6.3 Multiple Variable15.7 Power Amplifiers for Home Entertainment Subwoofers15.8 Subwoofer Integration15.9 Sound Reinforcement Subwoofers15.9.1 Line or Area Arrays15.9.2 Cardioid Subwoofer Arrays15.9.3 Aux-Fed Subwoofers15.10 Automotive Audio SubwoofersReferences
Chapter 16: Line Inputs and Outputs
16.1 External Signal Levels16.2 Internal Signal Levels16.3 Input Amplifier Functions16.4 Unbalanced Inputs16.5 Balanced Interconnections16.6 The Advantages of Balanced Interconnections16.7 The Disadvantages of Balanced Interconnections16.8 Balanced Cables and Interference16.8.1 Electrostatic Coupling16.8.2 Magnetic Coupling16.8.3 Ground Voltages16.9 Balanced Connectors16.10 Balanced Signal Levels16.11 Electronic versus Transformer Balanced Inputs16.12 Common Mode Rejection Ratio (CMRR)16.13 The Basic Electronic Balanced Input16.13.1 Case 116.13.2 Case 216.13.3 Case 316.13.4 Case 416.13.5 Case 516.14 Common-Mode Rejection Ratio: Opamp Gain16.15 Common-Mode Rejection Ratio: Opamp Frequency Response16.16 Common-Mode Rejection Ratio: Opamp CMRR16.17 Common-Mode Rejection Ratio: Amplifier Component Mismatches16.18 A Practical Balanced Input16.19 Variations on the Balanced Input Stage16.20 Combined Unbalanced and Balanced Inputs16.21 The Superbal Input16.22 Switched Gain Balanced Inputs16.23 Variable-Gain Balanced Inputs16.24 High Input Impedance Balanced Inputs16.25 The Instrumentation Amplifier16.26 Transformer Balanced Inputs16.27 Input Overvoltage Protection16.28 Noise and Balanced Inputs16.29 Low-Noise Balanced Inputs16.30 Low-Noise Balanced Inputs in Real Life16.31 Ultra-Low-Noise Balanced InputsReferences
Chapter 17: Line Outputs
17.1 Unbalanced Outputs17.2 Zero-Impedance Outputs17.3 Ground-Cancelling Outputs17.4 Balanced Outputs17.5 Transformer Balanced Outputs17.6 Output Transformer Frequency Response17.7 Transformer Distortion17.8 Reducing Transformer DistortionReferences
Chapter 18: Power Supply Design
18.1 Opamp Supply Rail Voltages18.2 Designing a ±15 V Supply18.3 Designing a ±17 V Supply18.4 Using Variable-Voltage Regulators18.5 Improving Ripple Performance18.6 Dual Supplies from a Single Winding18.7 Mutual Shutdown Circuitry18.8 Power Supplies for Discrete CircuitryReference
Chapter 19: An Active Crossover Design
19.1 Design Principles19.2 Example Crossover Specification19.3 The Gain Structure19.4 Resistor Selection19.5 Capacitor Selection19.6 The Balanced Line Input Stage19.7 The Bandwidth Definition Filter19.8 The HF Path: 3 kHz Linkwitz–Riley Highpass Filter19.9 The HF Path: Time Delay Compensation19.10 The MID Path: Topology19.11 The MID Path: 400 Hz Linkwitz–Riley Highpass Filter19.12 The MID Path: 3 kHz Linkwitz–Riley Lowpass Filter19.13 The MID Path: Time Delay Compensation19.14 The LF Path: 400 Hz Linkwitz–Riley Lowpass Filter19.15 The LF Path: No Time Delay Compensation19.16 Output Attenuators and Level Trim Controls19.17 Balanced Outputs19.18 Crossover Programming19.19 Noise Analysis: Input Circuitry19.20 Noise Analysis: HF Path19.21 Noise Analysis: MID Path19.22 Noise Analysis: LF Path19.23 Improving the Noise Performance: The MID Path19.24 Improving the Noise Performance: The Input Circuitry19.25 The Noise Performance: Comparisons with Power Amplifier Noise19.26 ConclusionReference
Appendix 1 Crossover Design References
Appendix 2 Loudspeaker Design References
Index

Content preview from The Design of Active Crossovers

Acknowledgments

Thanks to Julie for her patience and very practical support as I spent long hours slaving over a hot simulator.

Thanks to Gareth Connor for practical help, unfailing encouragement, and providing the facilities with which some of the experiments in this book were done.

Thanks to Don Morrison for generously providing sample components.

Thanks to Rod Elliot for many useful discussions on notched crossovers.

Thanks to all those on the diyAudio forum who made constructive suggestions on the topics to include in this book.

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The Design of Active Crossovers

by Douglas Self

Acknowledgments

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