The Design of Active Crossovers

605 Pages·2011·10.92 MB·English

by  Douglas Self

The Design of
Active Crossovers
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The Design of
Active Crossovers
Douglas Self
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Self,Douglas.
Thedesignofactivecrossovers/DouglasSelf.
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Includesbibliographicalreferences.
ISBN978-0-240-81738-5
1.Electric filters, Active–Designandconstruction. I. Title.
TK7872.F5S4472011
621.3815'324–dc22 2011013096
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To Julie with all my love
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Contents
Preface................................................................................................ xix
Acknowledgments.................................................................................. xxiii
Chapter 1: Crossover Basics....................................................................... 1
1.1 What a Crossover Does...........................................................................1
1.2 Why a Crossover Is Necessary..................................................................2
1.3 Beaming and Lobing...............................................................................2
1.4 Active Crossover Applications..................................................................4
1.5 Bi-Amping and Bi-Wiring........................................................................5
1.6 Loudspeaker Cables................................................................................8
1.7 The Advantages and Disadvantages of Active Crossovers.............................8
1.7.1 The Advantages of Active Crossovers...................................................9
1.7.2 The Disadvantages of Active Crossovers.............................................15
1.8 The Next Step in Hi-Fi..........................................................................17
1.9 Active Crossover Systems......................................................................17
1.10 Matching Crossovers and Loudspeakers..................................................22
1.11 A Modest Proposal: Popularising Active Crossovers.................................23
1.12 Multi-Way Connectors.........................................................................24
1.13 Subjectivism.......................................................................................25
References..................................................................................................26
Chapter 2: How Loudspeakers Work.......................................................... 27
2.1 Sealed Box Loudspeakers.......................................................................27
2.2 Reflex (Ported) Loudspeakers.................................................................29
2.3 Auxiliary Bass Radiator (ABR) Loudspeakers...........................................30
2.4 Transmission Line Loudspeakers.............................................................31
2.5 Horn Loudspeakers................................................................................31
2.6 Diffraction............................................................................................32
2.7 Modulation Distortion............................................................................37
Further Reading..........................................................................................37
References..................................................................................................37
vii
Contents
Chapter 3: Crossover Requirements............................................................ 39
3.1 General Crossover Requirements............................................................. 39
3.1.1 Adequate Flatness of Summed Amplitude/Frequency
Response On-Axis...........................................................................39
3.1.2 Sufficiently Steep Rolloff Slopes between the Filter Outputs..................40
3.1.3 Acceptable Polar Response................................................................40
3.1.4 Acceptable Phase Response...............................................................41
3.1.5 Acceptable Group Delay Behaviour....................................................41
3.2 Further Requirements for Active Crossovers............................................. 42
3.2.1 Negligible Extra Noise......................................................................42
3.2.2 Negligible Impairment of System Headroom........................................43
3.2.3 Negligible Extra Distortion................................................................44
3.2.4 Negligible Impairment of Frequency Response.....................................44
3.2.5 Negligible Impairment of Reliability...................................................45
3.3 Linear Phase......................................................................................... 45
3.4 Minimum Phase.................................................................................... 45
3.5 Absolute Phase..................................................................................... 46
3.6 Phase Perception................................................................................... 47
3.7 Target Functions................................................................................... 49
References.................................................................................................. 49
Chapter 4: Crossover Types...................................................................... 51
4.1 All-Pole and Non-All-Pole Crossovers..................................................... 51
4.2 Symmetric and Asymmetric Crossovers.................................................... 52
4.3 All-Pass and Constant-Power Crossovers.................................................. 52
4.4 Constant-Voltage Crossovers................................................................... 53
4.5 First-Order Crossovers........................................................................... 54
4.5.1 First-Order Solen Split Crossover.......................................................60
4.5.2 First-Order Crossovers: 3-Way...........................................................60
4.6 Second-Order Crossovers....................................................................... 62
4.6.1 Second-Order Butterworth Crossover..................................................62
4.6.2 Second-Order Linkwitz–Riley Crossover.............................................69
4.6.3 Second-Order Bessel Crossover..........................................................70
4.6.4 Second-Order 1.0dB-Chebyshev Crossover.........................................73
4.7 Third-Order Crossovers.......................................................................... 75
4.7.1 Third-Order Butterworth Crossover.....................................................76
4.7.2 Third-Order Linkwitz–Riley Crossover................................................79
4.7.3 Third-Order Bessel Crossover............................................................81
4.7.4 Third-Order 1.0dB-Chebyshev Crossover............................................83
4.8 Fourth-Order Crossovers........................................................................ 85
4.8.1 Fourth-Order Butterworth Crossover...................................................86
4.8.2 Fourth-Order Linkwitz–Riley Crossover..............................................88
4.8.3 Fourth-Order Bessel Crossover...........................................................91
4.8.4 Fourth-Order 1.0dB-Chebyshev Crossover..........................................93
viii
Contents
4.8.5 Fourth-Order Linear-Phase Crossover..................................................95
4.8.6 Fourth-Order Gaussian Crossover.......................................................97
4.8.7 Fourth-Order Legendre Crossover.......................................................99
4.9 Higher-Order Crossovers......................................................................102
4.10 Determining Frequency Offsets............................................................102
4.11 Summary of Crossover Properties........................................................104
4.12 Filler-Driver Crossovers......................................................................104
4.13 The Duelund Crossover......................................................................106
4.14 Crossover Topology...........................................................................107
4.15 Crossover Conclusions........................................................................ 112
References................................................................................................112
Chapter 5: Notch Crossovers................................................................... 115
5.1 Elliptical Filter Crossovers....................................................................115
5.2 Neville Thiele MethodTM (NTM) Crossovers...........................................120
References................................................................................................125
Chapter 6: Subtractive Crossovers............................................................ 127
6.1 Subtractive Crossovers.........................................................................127
6.1.1 First-Order Subtractive Crossovers....................................................129
6.1.2 Second-Order Butterworth Subtractive Crossovers...............................130
6.1.3 Third-Order Butterworth Subtractive Crossovers.................................131
6.1.4 Fourth-Order Butterworth Subtractive Crossovers................................132
6.2 Subtractive Crossovers with Time Delays...............................................134
6.3 Performing the Subtraction....................................................................138
References................................................................................................140
Chapter 7: Lowpass & Highpass Filter Characteristics.................................. 141
7.1 Active Filters......................................................................................142
7.2 Lowpass Filters................................................................................... 142
7.3 Highpass Filters...................................................................................142
7.4 Bandpass Filters.................................................................................. 142
7.5 Notch Filters.......................................................................................143
7.6 Allpass Filters.....................................................................................143
7.7 The Order of a Filter............................................................................143
7.8 Filter Cutoff Frequencies and Characteristic Frequencies...........................144
7.9 First-Order Filters................................................................................144
7.10 Second-Order and Higher-Order Filters.................................................145
7.11 Filter Characteristics...........................................................................146
7.11.1 Butterworth Filters........................................................................148
7.11.2 Linkwitz–Riley Filters...................................................................150
7.11.3 Bessel Filters...............................................................................153
7.11.4 Chebyshev Filters.........................................................................153
7.11.5 1dB-Chebyshev Lowpass Filter......................................................158
7.11.6 3dB-Chebyshev Lowpass Filter......................................................158
ix