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by Douglas Self
The Design of Active Crossovers, 2nd Edition
Cover
Title
Copyright
Dedication
Contents
Acknowledgments
Preface
Chapter 1: Crossover Basics
What a Crossover Does
Why a Crossover Is Necessary
Beaming and Lobing
Passive Crossovers
Active Crossover Applications
Bi-Amping and Bi-Wiring
Loudspeaker Cables
The Advantages and Disadvantages of Active Crossovers
The Advantages of Active Crossovers
Some Illusory Advantages of Active Crossovers
The Disadvantages of Active Crossovers
The Next Step in Hi-Fi
Active Crossover Systems
Matching Crossovers and Loudspeakers
A Modest Proposal: Popularising Active Crossovers
Multi-Way Connectors
Subjectivism
Chapter 2: How Loudspeakers Work
Sealed-Box Loudspeakers
Reflex (Ported) Loudspeakers
Auxiliary Bass Radiator (ABR) Loudspeakers
Transmission Line Loudspeakers
Horn Loudspeakers
Electrostatic Loudspeakers
Ribbon Loudspeakers
Electromagnetic Planar Loudspeakers
Air-Motion Transformers
Plasma Arc Loudspeakers
The Rotary Woofer
MTM Tweeter-Mid Configurations (d’Appolito)
Vertical Line Arrays
Line Array Amplitude Tapering
Line Array Frequency Tapering
CBT Line Arrays
Diffraction
Sound Absorption in Air
Modulation Distortion
Drive Unit Distortion
Doppler Distortion
Further Reading on Loudspeaker Design
Chapter 3: Crossover Requirements
General Crossover Requirements
1 Adequate Flatness of Summed Amplitude/Frequency Response On-Axis
2 Sufficiently Steep Roll-Off Slopes Between the Filter Outputs
3 Acceptable Polar Response
4 Acceptable Phase Response
5 Acceptable Group Delay Behaviour
Further Requirements for Active Crossovers
1 Negligible Extra Noise
2 Negligible Impairment of System Headroom
3 Negligible Extra Distortion
4 Negligible Impairment of Frequency Response
5 Negligible Impairment of Reliability
Linear Phase
Minimum Phase
Absolute Phase
Phase Perception
Target Functions
Chapter 4: Crossover Types
All-Pole and Non-All-Pole Crossovers
Symmetric and Asymmetric Crossovers
Allpass and Constant-Power Crossovers
Constant-Voltage Crossovers
First-Order Crossovers
First-Order Solen Split Crossover
First-Order Crossovers: 3-Way
Second-Order Crossovers
Second-Order Butterworth Crossover
Second-Order Linkwitz-Riley Crossover
Second-Order Bessel Crossover
Second-Order 1.0 dB-Chebyshev Crossover
Third-Order Crossovers
Third-Order Butterworth Crossover
Third-Order Linkwitz-Riley Crossover
Third-Order Bessel Crossover
Third-Order 1.0 dB-Chebyshev Crossover
Fourth-Order Crossovers
Fourth-Order Butterworth Crossover
Fourth-Order Linkwitz-Riley Crossover
Fourth-Order Bessel Crossover
Fourth-Order 1.0 dB-Chebyshev Crossover
Fourth-Order Linear-Phase Crossover
Fourth-Order Gaussian Crossover
Fourth-Order Legendre Crossover
Higher-Order Crossovers
Determining Frequency Offsets
Filler-Driver Crossovers
The Duelund Crossover
Crossover Topology
Crossover Conclusions
Chapter 5: Notch Crossovers
Elliptical Filter Crossovers
Neville Thiele MethodTM (NTM) Crossovers
Chapter 6: Subtractive Crossovers
Subtractive Crossovers
First-Order Subtractive Crossovers
Second-Order Butterworth Subtractive Crossovers
Third-Order Butterworth Subtractive Crossovers
Fourth-Order Butterworth Subtractive Crossovers
Subtractive Crossovers With Time Delays
Performing the Subtraction
Chapter 7: Lowpass and Highpass Filter Characteristics
Active Filters
Lowpass Filters
Highpass Filters
Bandpass Filters
Notch Filters
Allpass Filters
All-Stop Filters
Brickwall Filters
The Order of a Filter
Filter Cutoff Frequencies and Characteristic Frequencies
First-Order Filters
Second-Order and Higher-Order Filters
Filter Characteristics
Amplitude Peaking and Q
Butterworth Filters
Linkwitz-Riley Filters
Bessel Filters
Chebyshev Filters
1 dB-Chebyshev Lowpass Filter
3 dB-Chebyshev Lowpass Filter
Higher-Order Filters
Butterworth Filters up to 8th-Order
Linkwitz-Riley Filters up to 8th-Order
Bessel Filters up to 8th-Order
Chebyshev Filters up to 8th-Order
More Complex Filters—Adding Zeros
Inverse Chebyshev Filters (Chebyshev Type II)
Elliptical Filters (Cauer Filters)
Some Lesser-Known Filter Characteristics
Transitional Filters
Linear-Phase Filters
Gaussian Filters
Legendre-Papoulis Filters
Laguerre Filters
Synchronous Filters
Other Filter Characteristics
Chapter 8: Designing Lowpass Filters: Sallen & Key
Designing Real Filters
Component Sensitivity
First-Order Lowpass Filters
Second-Order Filters
Sallen & Key 2nd-Order Lowpass Filters
Sallen & Key Lowpass Filter Components
Sallen & Key 2nd-Order Lowpass: Unity Gain
Sallen & Key 2nd-Order Lowpass Unity Gain: Component Sensitivity
Filter Frequency Scaling
Sallen & Key 2nd-Order Lowpass: Equal Capacitor
Sallen & Key 2nd-Order Lowpass Equal-C: Component Sensitivity
Sallen & Key 2nd-Order Butterworth Lowpass: Defined Gains
Sallen & Key 2nd-Order Lowpass: Non-Equal Resistors
Sallen & Key 2nd-Order Lowpass: Optimisation
Sallen & Key 3rd-Order Lowpass: Two Stages
Sallen & Key 3rd-Order Lowpass: Single Stage
Sallen & Key 3rd-Order Lowpass in a Single Stage: Non-Equal Resistors
Sallen & Key 4th-Order Lowpass: Two Stages
Sallen & Key 4th-Order Lowpass: Single-Stage Butterworth
Sallen & Key 4th-Order Lowpass: Single-Stage Linkwitz-Riley
Sallen & Key 4th-Order Lowpass: Single Stage With Non-Equal Resistors
Sallen & Key 4th-Order Lowpass: Single Stage With Other Filter Characteristics
Sallen & Key 5th-Order Lowpass: Three Stages
Sallen & Key 5th-Order Lowpass: Two Stages
Sallen & Key 5th-Order Lowpass: Single Stage
Sallen & Key 6th-Order Lowpass: Three Stages
Sallen & Key 6th-Order Lowpass: Single Stage
Sallen & Key Lowpass: Input Impedance
Linkwitz-Riley Lowpass With Sallen & Key Filters: Loading Effects
Lowpass Filters With Attenuation
Bandwidth Definition Filters
Bandwidth Definition: Butterworth Versus Bessel
Variable-Frequency Lowpass Filters: Sallen & Key
Chapter 9: Designing Highpass Filters
First-Order Highpass Filters
Sallen & Key 2nd-Order Filters
Sallen & Key 2nd-Order Highpass Filters
Sallen & Key Highpass Filter Components
Sallen & Key 2nd-Order Highpass: Unity Gain
Sallen & Key 2nd-Order Highpass: Equal Resistors
Sallen & Key 2nd-Order Butterworth Highpass: Defined Gains
Sallen & Key 2nd-Order Highpass: Non-Equal Capacitors
Sallen & Key 3rd-Order Highpass: Two Stages
Sallen & Key 3rd-Order Highpass in a Single Stage
Sallen & Key 4th-Order Highpass: Two Stages
Sallen & Key 4th-Order Highpass: Butterworth in a Single Stage
Sallen & Key 4th-Order Highpass: Linkwitz-Riley in a Single Stage
Sallen & Key 4th-Order Highpass: Single-Stage With Other Filter Characteristics
Sallen & Key 5th-Order Highpass: Three Stages
Sallen & Key 5th-Order Butterworth Filter: Two Stages
Sallen & Key 5th-Order Highpass: Single Stage
Sallen & Key 6th-Order Highpass: Three Stages
Sallen & Key 6th-Order Highpass: Single Stage
Sallen & Key Highpass: Input Impedance
Bandwidth Definition Filters
Bandwidth Definition: Subsonic Filters
Bandwidth Definition: Combined Ultrasonic and Subsonic Filters
Variable-Frequency Highpass Filters: Sallen & Key
Chapter 10: Other Lowpass and Highpass Filters
Designing Filters
Multiple-Feedback Filters
Multiple-Feedback 2nd-Order Lowpass Filters
Multiple-Feedback 2nd-Order Highpass Filters
Multiple-Feedback 3rd-Order Filters
Multiple-Feedback 3rd-Order Lowpass Filters
Multiple-Feedback 3rd-Order Highpass Filters
Biquad Filters
Akerberg-Mossberg Lowpass Filter
Akerberg-Mossberg Highpass Filters
Tow-Thomas Biquad Lowpass and Bandpass Filter
Tow-Thomas Biquad Notch and Allpass Responses
Tow-Thomas Biquad Highpass Filter
State-Variable Filters
Variable-Frequency Filters: State-Variable 2nd Order
Variable-Frequency Filters: State-Variable 4th-Order
Variable-Frequency Filters: Other Orders of State-Variable
Other Filters
Chapter 11: Lowpass and Highpass Filter Performance
Aspects of Filter Performance: Noise and Distortion
Distortion in Active Filters
Distortion in Sallen & Key Filters: The Distortion Aggravation Factor
Distortion in Sallen & Key Filters: Looking for DAF
Distortion in Sallen & Key Filters: 2nd-Order Lowpass
Distortion in Sallen & Key Filters: 2nd-Order Highpass
Mixed Capacitors in Low-Distortion 2nd-Order Sallen & Key Filters
Distortion in Sallen & Key Filters: 3rd-Order Lowpass Single Stage
Distortion in Sallen & Key Filters: 3rd-Order Highpass Single Stage
Distortion in Sallen & Key Filters: 4th-Order Lowpass Single Stage
Distortion in Sallen & Key Filters: 4th-Order Highpass Single Stage
Distortion in Sallen & Key Filters: Simulations
Distortion in Sallen & Key Filters: Capacitor Conclusions
Distortion in Multiple-Feedback Filters: The Distortion Aggravation Factor
Distortion in Multiple-Feedback Filters: 2nd-Order Lowpass
Distortion in Multiple-Feedback Filters: 2nd-Order Highpass
Distortion in Tow-Thomas Filters: 2nd-Order Lowpass
Distortion in Tow-Thomas Filters: 2nd-Order Highpass
Noise in Active Filters
Noise and Bandwidth
Noise in Sallen & Key Filters: 2nd-Order Lowpass
Noise in Sallen & Key Filters: 2nd-Order Highpass
Noise in Sallen & Key Filters: 3rd-Order Lowpass Single Stage
Noise in Sallen & Key Filters: 3rd-Order Highpass Single Stage
Noise in Sallen & Key Filters: 4th-Order Lowpass Single Stage
Noise in Sallen & Key Filters: 4th-Order Highpass Single Stage
Noise in Multiple-Feedback Filters: 2nd-Order Lowpass
Noise in Multiple-Feedback Filters: 2nd-Order Highpass
Noise in Tow-Thomas Filters
Chapter 12: Bandpass and Notch Filters
Multiple-Feedback Bandpass Filters
High-Q Bandpass Filters
Notch Filters
The Twin-T Notch Filter
The 1-Bandpass Notch Filter
The Bainter Notch Filter
Bainter Notch Filter Design
Bainter Notch Filter Example
An Elliptical Filter Using a Bainter Highpass Notch
The Bridged-Differentiator Notch Filter
Boctor Notch Filters
Other Notch Filters
Simulating Notch Filters
Chapter 13: Time-Delay Filters
The Requirement for Delay Compensation
Calculating the Required Delays
Signal Summation
Physical Methods of Delay Compensation
Delay Filter Technology
Sample Crossover and Delay Filter Specification
Allpass Filters in General
First-Order Allpass Filters
Distortion and Noise in 1st-Order Allpass Filters
Cascaded 1st-Order Allpass Filters
Second-Order Allpass Filters
Distortion and Noise in 2nd-Order Allpass Filters
Third-Order Allpass Filters
Distortion and Noise in 3rd-Order Allpass Filters
Higher-Order Allpass Filters
Delay Lines for Subtractive Crossovers
Variable Allpass Time Delays
Lowpass Filters for Time Delays
Chapter 14: Equalisation
The Need for Equalisation
What Equalisation Can and Can’t Do
Loudspeaker Equalisation
1 Drive Unit Equalisation
2 6 dB/octave Dipole Equalisation
3 Bass Response Extension
4 Diffraction Compensation Equalisation
5 Room Interaction Correction
Equalisation Circuits
HF-Boost and LF-Cut Equaliser
HF-Cut and LF-Boost Equaliser
Combined HF-Boost and HF-Cut Equaliser
Adjustable Peak/Dip Equalisers: Fixed Frequency and Low Q
Adjustable Peak/Dip Equalisers: Variable Centre Frequency and Low Q
Adjustable Peak/Dip Equalisers With High Q
Parametric Equalisers
The Bridged-T Equaliser
The Biquad Equaliser
Capacitance Multiplication for the Biquad Equaliser
Equalisers With Non-Standard Slopes
Equalisers With −3 dB/Octave Slopes
Equalisers With −3 dB/Octave Slopes Over Limited Range
Equalisers With −4.5 dB/Octave Slopes
Equalisers With Other Slopes
Equalisation by Filter Frequency Offset
Equalisation by Adjusting All Filter Parameters
Chapter 15: Passive Components for Active Crossovers
Component Values
Resistors
Through-Hole Resistors
Surface-Mount Resistors
Resistors: Values and Tolerances
Improving Accuracy With Multiple Components: Gaussian Distribution
Resistor Value Distributions
Improving Accuracy With Multiple Components: Uniform Distribution
Obtaining Arbitrary Resistance Values
Other Resistor Combinations
Resistor Noise: Johnson and Excess Noise
Resistor Non-Linearity
Capacitors: Values and Tolerances
Obtaining Arbitrary Capacitance Values
Capacitor Shortcomings
Non-Electrolytic Capacitor Non-Linearity
Electrolytic Capacitor Non-Linearity
Chapter 16: Opamps for Active Crossovers
Active Devices for Active Crossovers
Opamp Types
Opamp Properties: Noise
Opamp Properties: Slew Rate
Opamp Properties: Common-Mode Range
Opamp Properties: Input Offset Voltage
Opamp Properties: Bias Current
Opamp Properties: Cost
Opamp Properties: Internal Distortion
Opamp Properties: Slew Rate Limiting Distortion
Opamp Properties: Distortion Due to Loading
Opamp Properties: Common-Mode Distortion
Opamps Surveyed
The TL072 Opamp
The NE5532 and 5534 Opamps
The 5532 With Shunt Feedback
5532 Output Loading in Shunt-Feedback Mode
The 5532 With Series Feedback
Common-Mode Distortion in the 5532
Reducing 5532 Distortion by Output Stage Biasing
Which 5532?
The 5534 Opamp
The LM4562 Opamp
Common-Mode Distortion in the LM4562
The LME49990 Opamp
Common-Mode Distortion in the LME49990
The AD797 Opamp
Common-Mode Distortion in the AD797
The OP27 Opamp
Opamp Selection
Chapter 17: Active Crossover System Design
Crossover Features
Input Level Controls
Subsonic Filters
Ultrasonic Filters
Output Level Trims
Output Mute Switches, Output Phase-Reverse Switches
Control Protection
Features Usually Absent
Metering
Relay Output Muting
Switchable Crossover Modes
Noise, Headroom, and Internal Levels
Circuit Noise and Low-Impedance Design
Using Raised Internal Levels
Placing the Output Attenuator
The Amplitude/Frequency Distribution of Musical Signals and Internal Levels
Gain Structures
Noise Gain
Active Gain Controls
Filter Order in the Signal Path
Output Level Controls
Mute Switches
Phase-Invert Switches
Distributed Peak Detection
Power Amplifier Considerations
Chapter 18: Subwoofer Crossovers
Subwoofer Applications
Subwoofer Technologies
Sealed-Box (Infinite Baffle) Subwoofers
Reflex (Ported) Subwoofers
Auxiliary Bass Radiator (ABR) Subwoofers
Transmission Line Subwoofers
Bandpass Subwoofers
Isobaric Subwoofers
Dipole Subwoofers
Horn-Loaded Subwoofers
Subwoofer Drive Units
Hi-Fi Subwoofers
Home Entertainment Subwoofers
Low-Level Inputs (Unbalanced)
Low-Level Inputs (Balanced)
High-Level Inputs
High-Level Outputs
Mono Summing
LFE Input
Level Control
Crossover In/Out Switch
Crossover Frequency Control (Lowpass Filter)
Highpass Subsonic Filter
Phase Switch (Normal/Inverted)
Variable Phase Control
Signal Activation Out of Standby
Home Entertainment Crossovers
Fixed Frequency
Variable Frequency
Multiple Variable
Power Amplifiers for Home Entertainment Subwoofers
Subwoofer Integration
Sound-Reinforcement Subwoofers
Line or Area Arrays
Cardioid Subwoofer Arrays
Aux-Fed Subwoofers
Automotive Audio Subwoofers
Chapter 19: Motional Feedback Loudspeakers
Motional Feedback Loudspeakers
History
Feedback of Position
Feedback of Velocity
Feedback of Acceleration
Other MFB Speakers
Published Projects
Conclusions
Chapter 20: Line Inputs
External Signal Levels
Internal Signal Levels
Input Amplifier Functions
Unbalanced Inputs
Balanced Interconnections
The Advantages of Balanced Interconnections
The Disadvantages of Balanced Interconnections
Balanced Cables and Interference
Balanced Connectors
Balanced Signal Levels
Electronic vs Transformer Balanced Inputs
Common-Mode Rejection Ratio (CMRR)
The Basic Electronic Balanced Input
Common-Mode Rejection Ratio: Opamp Gain
Common-Mode Rejection Ratio: Opamp Frequency Response
Common-Mode Rejection Ratio: Opamp CMRR
Common-Mode Rejection Ratio: Amplifier Component Mismatches
A Practical Balanced Input
Variations on the Balanced Input Stage
Combined Unbalanced and Balanced Inputs
The Superbal Input
Switched-Gain Balanced Inputs
Variable-Gain Balanced Inputs
The Self Variable-Gain Balanced Input
High Input Impedance Balanced Inputs
The Instrumentation Amplifier
Instrumentation Amplifier Applications
The Instrumentation Amplifier With 4x Gain
The Instrumentation Amplifier at Unity Gain
Transformer Balanced Inputs
Input Overvoltage Protection
Noise and Balanced Inputs
Low-Noise Balanced Inputs
Low-Noise Balanced Inputs in Real Life
Ultra-Low-Noise Balanced Inputs
Chapter 21: Line Outputs
Unbalanced Outputs
Zero-Impedance Outputs
Ground-Cancelling Outputs
Balanced Outputs
Transformer Balanced Outputs
Output Transformer Frequency Response
Transformer Distortion
Reducing Transformer Distortion
Chapter 22: Power Supply Design
Opamp Supply Rail Voltages
Designing a ±15 V Supply
Designing a ±17 V Supply
Using Variable-Voltage Regulators
Improving Ripple Performance
Dual Supplies From a Single Winding
Mutual Shutdown Circuitry
Power Supplies for Discrete Circuitry
Chapter 23: An Active Crossover Design
Design Principles
Example Crossover Specification
The Gain Structure
Resistor Selection
Capacitor Selection
The Balanced Line Input Stage
The Bandwidth Definition Filter
The HF Path: 3 kHz Linkwitz-Riley Highpass Filter
The HF Path: Time-Delay Compensation
The MID Path: Topology
The MID Path: 400 Hz Linkwitz-Riley Highpass Filter
The MID Path: 3 kHz Linkwitz-Riley Lowpass Filter
The MID Path: Time-Delay Compensation
The LF Path: 400 Hz Linkwitz-Riley Lowpass Filter
The LF Path: No Time-Delay Compensation
Output Attenuators and Level Trim Controls
Balanced Outputs
Crossover Programming
Noise Analysis: Input Circuitry
Noise Analysis: HF Path
Noise Analysis: MID Path
Noise Analysis: LF Path
Improving the Noise Performance: The MID Path
Improving the Noise Performance: The Input Circuitry
The Noise Performance: Comparisons With Power Amplifier Noise
Conclusion
Appendix 1 Crossover Design References
Appendix 2 US Crossover Patents
Appendix 3 Crossover and Loudspeaker Articles in Wireless World/Electronics World
Appendix 4 Loudspeaker Design References
Appendix 5 Component Series E3 to E96
Index
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