ErrorCorrectionofLoudspeakers:
AstudyofLoudspeakerDesignsupported
byDigitalSignalProcessing
AalborgUniversity
BoRohdePedersen
PhDthesis,May2008
Introduction
Error Correction of Loudspeakers,
2
Published by: The department of Software, Medialogy, and Electronics. Esbjerg Tekniske
Institut. Aalborg University, DK6700 Esbjerg, Denmark, 2008. ISBN: 987-87-7606-024-4
Introduction
by Bo Rohde Pedersen
3
Preface
From my experience in the sales and support of digital amplifiers in Japan, 2001, I learned
about the marketplace and the drivers for home audio applications. In the marketplace of
music sound systems there is a considerable technical and marketing advantage to be gained
by focusing on improving the efficiency and thereby achieving smaller designs. Currently,
overheating tends to be the primary cause of loudspeaker breakdowns, a factor that constrains
both design freedom and innovation in music system technology. From a marketing
perspective, it makes good sense to work towards increasing the efficiency of loudspeakers, as
this would inevitably lead to the need for smaller power amplifiers, making music systems
more compact overall and less expensive to manufacture. The size of audio equipment is a
main market driver today.
In 2002, through Jens Arnspang, Aalborg Univeristy Esbjerg, I met Knud Bank Christensen
who had a proposal for a PhD project in loudspeaker modelling. This led to 5 years
employment by Aalborg University of ½ lecturing position and ½ PhD position, and this is
the final Thesis.
Finn T. Agerkvist from Ørsted, Acoustic Technology, Technical University of Denmark
(DTU) was included in the supervisory committee at the beginning of 2003. He has,
throughout the project, been very supportive with comments, ideas and has always been a
helpful reviewer. Many of the experiments in this project have been carried out at the acoustic
lab at DTU. In 2005, Per Rubak, from Aalborg University, became a member of the
supervisory committee. Per has been very inspiring and has been very helpful with digital
signal processing.
At the end of the project, I visited John Mourjopoulos and his Audio Group at the University
of Patras in Greece. During my three month stay, there was studied digital loudspeakers,
which has been a great supplement to the objective of this project; namely, loudspeaker
design supported by digital signal processing.
_______________________________
Bo Rohde Pedersen
Introduction
Error Correction of Loudspeakers,
4
Summary
Throughout this thesis, the topic of electrodynamic loudspeaker unit design and modelling are
reviewed. The research behind this project has been to study loudspeaker design, based on
new possibilities introduced by including digital signal processing, and thereby achieving
more freedom in loudspeaker unit design.
This freedom can be used for efficiency improvements where different loudspeaker design
cases show design opportunities. Optimization by size and efficiency, instead of flat
frequency response and linearity, is the basis of the loudspeaker efficiency designs studied.
In the project, a nonlinear loudspeaker model has been used for both power consumption and
distortion simulations. The nonlinear model has been improved by adding time varying
suspension behaviour. The basic improvement is a heating phenomenon of the suspension.
The addition to the model improves the loudspeaker model performance at low frequencies.
A model based controller has been constructed, where a simulation study including a
measurement series of parameter drift in the loudspeaker units has been included. This led to
the conclusion that a parameter update of the loudspeaker parameters is needed during
operation of a nonlinear feed forward controller.
System identification is used for tracking the loudspeaker parameters. Different system
identification methods are reviewed, and the investigations ends with a simple FIR based
algorithm. Finally, the parameter tracking system is tested with music signals on a 6½ inch
bass-mid range loudspeaker unit.
The knowledge of loudspeaker construction and efficiency is used for the analysis of Digital
Loudspeaker Arrays (DLA). This work is made in cooperation with the University of Patras,
where DLA is a focus area. This project focuses on efficiency and transducer limitations of
the DLA. Performance analysis of DLA is the name of the joint research project. Parts from
this project are presented in this thesis.
Introduction
by Bo Rohde Pedersen
5
Table of Contents:
0. INTRODUCTION 7
0.1 Reading Guide 7
0.2 Notations and Abbreviations 8
0.3 Introduction 10
0.4 Research Objectives 13
1. LINEAR LOUDSPEAKER MODELLING 15
1.1 The Electrodynamic Loudspeaker 15
1.2 Modelling of Loudspeakers 18
1.3 Conclusion of the Linear Loudspeaker 25
2. NONLINEAR LOUDSPEAKER MODELLING 27
2.1 One Dimensional Nonlinearities 27
2.2 Force Factor 28
2.3. Suspension 34
2.4. Voice Coil Induction 48
2.5 Diaphragm Area and Mass 50
2.6 Air in the Loudspeaker Enclosure 51
2.7 Simulation of major Nonlinearities 52
2.8 Discussion of Nonlinearities in Loudspeakers 62
2.9 Conclusion of Nonlinearities in Loudspeakers 64
3. LOUDSPEAKER PARAMETER DRIFT 65
3.1. Basis of Investigation 65
3.2 Temperature Drift of Parameters 66
3.3 Production Spread of Parameters 68
3.4. Summary of Loudspeaker Parameter Drift 71
3.5. Conclusion of Loudspeaker Parameter Drift 71
4. LOUDSPEAKER EFFICIENCY 73
4.1 Definition of Loudspeaker’s Efficiency 73
4.2 Improving Efficiency 75
4.3 Electrical Power Consumption 85
4.4 Nonlinear Loudspeaker Efficiency 86
4.5 Nonlinear Efficiency Design 87
4.6. Discussion of Loudspeaker Efficiency 99
4.7 Conclusion of Loudspeaker Efficiency 100
