The Design of Active Crossovers

699 Pages·2018·57.68 MB·English

by  Douglas Self

The Design of
Active Crossovers
The use of active crossovers is increasing. They are used by almost every sound reinforcement system,
and by almost every recording studio monitoring set-up. There is also a big usage of active crossovers
in car audio, with the emphasis on routing the bass to enormous low-frequency loudspeakers. Active
crossovers are used to a small but rapidly growing extent in domestic hifi, and I argue that their
widespread introduction may be the next big step in this field.
The Design of Active Crossovers has now been updated and extended for the Second Edition, taking
in developments in loudspeaker technology and crossover design. Many more pre-designed filters are
included so that crossover development can be faster and more certain, and the result will have a high
performance. The Second Edition continues the tradition of the first in avoiding complicated algebra
and complex numbers, with the mathematics reduced to the bare minimum; there is nothing more
complicated to grapple with than a square root.
New features of the Second Edition include:
• More on loudspeaker configurations and their crossover requirements:
MTM Mid-Tweeter-Mid configurations (The d’Appolito arrangement)
Line arrays (J arrays) for sound reinforcement
Frequency tapering
Band zoning
Power tapering
Constant-Beamwidth Transducer (CBT) loudspeaker arrays
• More on specific sound-reinforcement issues like the loss of high frequencies due to the
absorption of sound in air and how it varies.
• Lowpass filters now have their own separate chapter.
Much more on third, fourth, fifth, and sixth-order lowpass filters.
Many more examples are given with component values ready-calculated
• Highpass filters now have their own separate chapter, complementary to the chapter on lowpass
filters.
Much more on third, fourth, fifth, and sixth-order highpass filters.
Many more examples are given with component values ready-calculated
• A new chapter dealing with filters other than the famous Sallen & Key type. New filter types are
introduced such as the third-order multiple feedback filter.
There is new information on controlling the Q and gain of state-variable filters.
• More on the performance of crossover filters, covering noise, distortion, and the internal overload
problems of filters.
• The chapter on bandpass and notch filters is much extended, with in-depth coverage of the Bainter
filter, which can produce beautifully deep notches without precision components or adjustment.
• Much more information on the best ways to combine standard components to get very accurate
non-standard values. Not only can you get a very accurate nominal value, but also the effective
tolerance of the combination can be significantly better than that of the individual components
used. There is no need to keep huge numbers of resistor and capacitor values in stock.
• More on low-noise high-performance balanced line inputs for active crossovers, including
versions that give extraordinarily high common-mode rejection. (noise rejection)
• Two new appendices giving extensive lists of crossover patents, and crossover-based articles in
journals.
This book is packed full of valuable information, with virtually every page revealing nuggets of
specialized knowledge never before published. Essential points of theory bearing on practical
performance are lucidly and thoroughly explained, with the mathematics kept to an essential minimum.
Douglas’ background in design for manufacture ensures he keeps a very close eye on the cost of things.
Douglas Self studied engineering at Cambridge University, then psychoacoustics at Sussex University.
He has spent many years working at the top level of design in both the professional audio and hi-fi
industries and has taken out a number of patents in the field of audio technology. He currently acts as a
consultant engineer in the field of audio design.
Douglas Self maintains a website at douglas-self.com
The Design of
Active Crossovers
Second Edition
Douglas Self
Second edition published 2018
by Routledge
711 Third Avenue, New York, NY 10017
and by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2018 Taylor & Francis
The right of Douglas Self to be identified as author of this work has been
asserted by him in accordance with sections 77 and 78 of the Copyright,
Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced or
utilised in any form or by any electronic, mechanical, or other means, now
known or hereafter invented, including photocopying and recording, or in
any information storage or retrieval system, without permission in writing
from the publishers.
Trademark notice: Product or corporate names may be trademarks or
registered trademarks, and are used only for identification and explanation
without intent to infringe.
First edition published by Focal Press 2011
Library of Congress Cataloging-in-Publication Data
Names: Self, Douglas, author.
Title: The design of active crossovers / Douglas Self.
Description: Second edition. | New York, NY : Routledge, 2018.
Identifiers: LCCN 2017048835 | ISBN 9781138733022
(hardback : alk. paper) | ISBN 9781138733039 (pbk. : alk. paper) |
ISBN 9781315187891 (ebook)
Subjects: LCSH: Electric filters, Active—Design and construction. |
Bridge circuits—Design and construction.
Classification: LCC TK7872.F5 S447 2018 | DDC 621.3815/324—dc23
LC record available at https://lccn.loc.gov/2017048835
ISBN: 978-1-138-73302-2 (hbk)
ISBN: 978-1-138-73303-9 (pbk)
ISBN: 978-1-315-18789-1 (ebk)
Typeset in Times New Roman
by Apex CoVantage, LLC
To Julie, with all my love

Contents
Acknowledgments ��������������������������������������������������������������������������������������������� xxi
Preface �����������������������������������������������������������������������������������������������������������xxiii
Chapter 1: Crossover Basics ���������������������������������������������������������������������������������1
What a Crossover Does ................................................................................................1
Why a Crossover Is Necessary .....................................................................................1
Beaming and Lobing.....................................................................................................2
Passive Crossovers .......................................................................................................4
Active Crossover Applications .....................................................................................5
Bi-Amping and Bi-Wiring ............................................................................................6
Loudspeaker Cables ......................................................................................................8
The Advantages and Disadvantages of Active Crossovers ...........................................9
The Advantages of Active Crossovers .......................................................................9
Some Illusory Advantages of Active Crossovers .....................................................13
The Disadvantages of Active Crossovers .................................................................14
The Next Step in Hi-Fi ...............................................................................................16
Active Crossover Systems ..........................................................................................16
Matching Crossovers and Loudspeakers ....................................................................20
A Modest Proposal: Popularising Active Crossovers .................................................21
Multi-Way Connectors ................................................................................................22
Subjectivism ...............................................................................................................23
Chapter 2: How Loudspeakers Work ������������������������������������������������������������������25
Sealed-Box Loudspeakers ..........................................................................................26
Reflex (Ported) Loudspeakers.....................................................................................27
Auxiliary Bass Radiator (ABR) Loudspeakers...........................................................28
Transmission Line Loudspeakers ...............................................................................28
Horn Loudspeakers .....................................................................................................29
Electrostatic Loudspeakers .........................................................................................29
Ribbon Loudspeakers .................................................................................................30
Electromagnetic Planar Loudspeakers ........................................................................30
Air-Motion Transformers ............................................................................................31
Plasma Arc Loudspeakers ...........................................................................................31
The Rotary Woofer .....................................................................................................32
MTM Tweeter-Mid Configurations (d’Appolito) .......................................................33
vii
Contents
Vertical Line Arrays ....................................................................................................34
Line Array Amplitude Tapering ...............................................................................37
Line Array Frequency Tapering ...............................................................................37
CBT Line Arrays .........................................................................................................39
Diffraction ...................................................................................................................39
Sound Absorption in Air .............................................................................................44
Modulation Distortion ................................................................................................46
Drive Unit Distortion ..................................................................................................47
Doppler Distortion ......................................................................................................48
Further Reading on Loudspeaker Design ...................................................................49
Chapter 3: Crossover Requirements ��������������������������������������������������������������������51
General Crossover Requirements ...............................................................................51
1 Adequate Flatness of Summed Amplitude/Frequency Response On-Axis ..........51
2 Sufficiently Steep Roll-Off Slopes Between the Filter Outputs ...........................51
3 Acceptable Polar Response ..................................................................................52
4 Acceptable Phase Response .................................................................................53
5 Acceptable Group Delay Behaviour .....................................................................53
Further Requirements for Active Crossovers .............................................................54
1 Negligible Extra Noise .........................................................................................54
2 Negligible Impairment of System Headroom ......................................................55
3 Negligible Extra Distortion ..................................................................................55
4 Negligible Impairment of Frequency Response ...................................................56
5 Negligible Impairment of Reliability ...................................................................56
Linear Phase................................................................................................................56
Minimum Phase ..........................................................................................................57
Absolute Phase ...........................................................................................................57
Phase Perception .........................................................................................................58
Target Functions .........................................................................................................59
Chapter 4: Crossover Types �������������������������������������������������������������������������������61
All-Pole and Non-All-Pole Crossovers ......................................................................61
Symmetric and Asymmetric Crossovers .....................................................................62
Allpass and Constant-Power Crossovers ....................................................................62
Constant-Voltage Crossovers ......................................................................................63
First-Order Crossovers................................................................................................63
First-Order Solen Split Crossover ..............................................................................69
First-Order Crossovers: 3-Way ...................................................................................70
Second-Order Crossovers ...........................................................................................70
Second-Order Butterworth Crossover ......................................................................71
Second-Order Linkwitz-Riley Crossover .................................................................78
Second-Order Bessel Crossover ...............................................................................79
Second-Order 1.0 dB-Chebyshev Crossover ...........................................................80
viii
Contents
Third-Order Crossovers ..............................................................................................83
Third-Order Butterworth Crossover .........................................................................84
Third-Order Linkwitz-Riley Crossover ....................................................................86
Third-Order Bessel Crossover ..................................................................................89
Third-Order 1.0 dB-Chebyshev Crossover ..............................................................89
Fourth-Order Crossovers ............................................................................................92
Fourth-Order Butterworth Crossover .......................................................................93
Fourth-Order Linkwitz-Riley Crossover ..................................................................95
Fourth-Order Bessel Crossover ................................................................................99
Fourth-Order 1.0 dB-Chebyshev Crossover .............................................................99
Fourth-Order Linear-Phase Crossover ...................................................................101
Fourth-Order Gaussian Crossover ..........................................................................103
Fourth-Order Legendre Crossover .........................................................................106
Higher-Order Crossovers ..........................................................................................108
Determining Frequency Offsets ................................................................................109
Filler-Driver Crossovers ............................................................................................111
The Duelund Crossover ............................................................................................113
Crossover Topology ..................................................................................................113
Crossover Conclusions .............................................................................................118
Chapter 5: Notch Crossovers ����������������������������������������������������������������������������121
Elliptical Filter Crossovers .......................................................................................121
Neville Thiele MethodTM (NTM) Crossovers ...........................................................125
Chapter 6: Subtractive Crossovers ��������������������������������������������������������������������131
Subtractive Crossovers .............................................................................................131
First-Order Subtractive Crossovers ..........................................................................132
Second-Order Butterworth Subtractive Crossovers..................................................133
Third-Order Butterworth Subtractive Crossovers ....................................................135
Fourth-Order Butterworth Subtractive Crossovers ...................................................135
Subtractive Crossovers With Time Delays ...............................................................137
Performing the Subtraction .......................................................................................141
Chapter 7: Lowpass and Highpass Filter Characteristics ��������������������������������������145
Active Filters ............................................................................................................145
Lowpass Filters .........................................................................................................146
Highpass Filters ........................................................................................................146
Bandpass Filters ........................................................................................................146
Notch Filters .............................................................................................................146
Allpass Filters ...........................................................................................................147
All-Stop Filters .........................................................................................................147
Brickwall Filters .......................................................................................................147
The Order of a Filter .................................................................................................147
ix