Driver-Array Based Flat-Panel Loudspeakers

178 Pages·2017·20.9 MB·English

Driver-Array Based Flat-Panel
Loudspeakers: Theoretical Background and
Design Guidelines
by
David Allan Anderson
Submitted in Partial Ful(cid:28)llment of the
Requirements for the Degree
Doctor of Philosophy
Supervised by Professor Mark F. Bocko
Department of Electrical and Computer Engineering
Arts, Sciences and Engineering
Edmund A. Hajim School of Engineering and Applied Sciences
University of Rochester
Rochester, New York
2017
ii
Table of Contents
Biographical Sketch vii
Acknowledgments ix
Abstract x
Contributors and Funding Sources xii
List of Tables xiii
List of Figures xxii
1 A History of Bending-Wave Loudspeakers 1
1.1 Vintage Bending-Wave Loudspeakers . . . . . . . . . . . . . . . . . . 1
1.2 Bending-Wave Loudspeaker Research . . . . . . . . . . . . . . . . . . 5
1.3 Modern Speakers using Bending-Wave Principles . . . . . . . . . . . . 9
1.4 Motivation for Further Study . . . . . . . . . . . . . . . . . . . . . . 11
2 MeasurementsofSpeechIntelligibilityLossUsingSingle-DriverFlat-
Panel Loudspeakers 13
2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Impulse Response Measurements . . . . . . . . . . . . . . . . . . . . 14
TABLE OF CONTENTS iii
2.3 STI scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Speech Signal Measurements . . . . . . . . . . . . . . . . . . . . . . . 17
3 Mechanics of Point-Driven Flat Panels 21
3.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Single Mode Response . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.3 Non-ideal Driver Shape . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Resonant Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 Resonant Frequencies . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Panel Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Plate Velocity Pro(cid:28)les . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Transient Mechanical Response . . . . . . . . . . . . . . . . . . . . . 34
3.4.1 Transient velocity and acceleration . . . . . . . . . . . . . . . 38
3.4.2 Simulations of time-dependent panel motion . . . . . . . . . . 40
3.5 Equivalent Electrical Circuit for the Mechanical System . . . . . . . . 41
3.6 Solution Using Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.7 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Flat-Panel Loudspeakers with Rear Enclosures 48
4.1 Sealed Box: Modeling Air as a Spring . . . . . . . . . . . . . . . . . . 49
4.1.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.2 Equivalent Electrical Circuit . . . . . . . . . . . . . . . . . . . 51
4.1.3 Solution Using Matrices . . . . . . . . . . . . . . . . . . . . . 54
4.2 Ported Enclosures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Equivalent Electrical Circuit Model for Ported Enclosures . . . 55
TABLE OF CONTENTS iv
4.2.2 Solution Using Matrices . . . . . . . . . . . . . . . . . . . . . 58
5 Coupled Plates and Mass-Spring Oscillators 60
5.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Equivalent Electrical Circuit Model . . . . . . . . . . . . . . . . . . . 65
6 Driver Arrays 68
6.1 Single Driver Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Modal Actuation by Driver Arrays . . . . . . . . . . . . . . . . . . . 70
6.3 Modal Aliasing: ‘Spillover’ . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4 Modal Drive Experiments . . . . . . . . . . . . . . . . . . . . . . . . 73
6.5 Optimal Driver Placement . . . . . . . . . . . . . . . . . . . . . . . . 76
6.5.1 Driver Coupling E(cid:30)ciency . . . . . . . . . . . . . . . . . . . . 77
6.5.2 Point Force Driver Location Optimization Algorithm . . . . . 79
6.5.3 Point-force Optimization Results . . . . . . . . . . . . . . . . 80
6.5.4 Optimal Array Experiments . . . . . . . . . . . . . . . . . . . 82
6.6 Changing Panel Vibration Characteristics Using An Array . . . . . . 85
6.6.1 Mechanical Measurements . . . . . . . . . . . . . . . . . . . . 86
7 A Complete Matrix Solution and Equivalent Circuit Model for Panel
Loudspeakers with Ported Rear Enclosures and Driver Arrays 88
7.0.2 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.0.3 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . 91
7.1 Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2.1 Equivalent Circuit Simulation . . . . . . . . . . . . . . . . . . 95
7.2.2 Matrix Solution Simulation . . . . . . . . . . . . . . . . . . . 96
TABLE OF CONTENTS v
7.2.3 Comparisons of Simulated and Measured Flat-Panel System
Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.3 Rigidly backed drivers . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8 The Acoustics of Ba(cid:31)ed Flat Panels 101
8.1 Steady State Acoustic Response of Ba(cid:31)ed Panels . . . . . . . . . . . 101
8.2 Time-Dependent Acoustic Response . . . . . . . . . . . . . . . . . . . 104
8.3 Coincidence Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.4 Simulations vs. Measurements . . . . . . . . . . . . . . . . . . . . . . 107
8.5 Creating Piston-Like Radiation Characteristics Using a Driver Array 112
9 Modal Crossover Networks 116
9.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.2 Tuning Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.2.1 Implications of Spillover Modes . . . . . . . . . . . . . . . . . 119
9.2.2 Performance of MXN Method versus a Single Driver Con(cid:28)gu-
ration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3 Tuning Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3.1 Large Panel Prototype . . . . . . . . . . . . . . . . . . . . . . 126
10 Driver Count Based on Regions of Operation 130
10.1 Modal Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
10.1.1 Regions of Operation . . . . . . . . . . . . . . . . . . . . . . . 131
10.2 Required Number of Drivers . . . . . . . . . . . . . . . . . . . . . . . 133
10.3 A Note on High-Frequency Region Acoustics . . . . . . . . . . . . . . 135
11 Conclusion and Future Work 137
11.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
TABLE OF CONTENTS vi
Bibliography 142
Appendix A An Example of Driver Location Optimization 153
A.1 MATLAB Code for couplingplate function . . . . . . . . . . . . . . . 155
A.2 MATLAB Code for plotdrivers function . . . . . . . . . . . . . . . . . 156
vii
Biographical Sketch
The author was born in Wolf Point, MT but grew up mostly in Denver, CO. He
attended Colorado State University, and graduated with a Bachelor of Science degree
in Electrical Engineering, Cum Laude, with Discipline Honors and University Honors.
He began doctoral studies in Electrical Engineering at the University of Rochester
in 2012. He received a Master of Science degree from the University of Rochester
in 2014. He pursued his research in Electrical Engineering under the direction of
Professor Mark F. Bocko. During this time, he was awarded the Edward Peck Curtis
Award for Excellence in Teaching by a Graduate Student in 2016 for work with the
Audio Music Engineering and Early Connection Opportunity programs.
The following publications were a result of work conducted during doctoral study:
D. Anderson and M.F. Bocko, (cid:16)Modal crossover networks for (cid:29)at-panel loudspeakers,(cid:17)
J. Audio Eng. Soc., vol. 64, no. 4, pp. 229(cid:21)240, May 2016.
D. Anderson and M. F. Bocko, (cid:16)A model for the impulse response of distributed-mode
loudspeakers and multi-actuator panels,(cid:17) in 139th Convention of the AES, October
2015.
D. Anderson and M. F. Bocko, (cid:16)Measuring speech intelligibility loss in single-driver
panel loudspeakers,(cid:17) in 139th Convention of the AES, Oct 2015.
D. Anderson and M. F. Bocko, (cid:16)A model for the impulse response of distributed-mode
loudspeakers and multi-actuator panels,(cid:17) in 139th Convention of the AES, October
2015.
D. A. Anderson, M. C. Heilemann, and M. F. Bocko, (cid:16)Optimal driver placement for
array-driven (cid:29)at-panel loudspeakers,(cid:17) Archives of Acoustics, in press, 2017.
BIOGRAPHICAL SKETCH viii
M. C. Heilemann, D. A. Anderson, and M. F. Bocko, (cid:16)Sound source localization on
(cid:29)at-panel loudspeakers,(cid:17) J. Audio Eng. Soc., in press, 2017.
D. Anderson and M. F. Bocko, (cid:16)Measures of vibrational localization on point-driven
(cid:29)at-panel loudspeakers,(cid:17) in 171st Meeting of the Acoustical Society of America, May
2016.
ix
Acknowledgments
I would like to acknowledge the following people whose contributions allowed me to
completetheworkinthisthesis: ProfessorMarkF.Bocko,ProfessorZeljkoIgnjatovic,
Michael Heilemann, Stephen Roessner, Tim Dick, and Frank White.
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Abstract
This thesis relates to the simulation and design of (cid:29)at-panel loudspeakers using
moving-coil driver elements. A brief history of the industry is given, including a
collection of products and patents from 1925 until the present, an overview of re-
search papers, and a discussion of current products available. The mechanics of
bending (cid:29)at panels are developed with respect to localized driving forces, both in the
frequency domain and the time domain as an impulse response. These simulations
are compared to measurements on prototype panels. Additional resonant elements
in(cid:29)uence the behavior of the system: an optional ported rear enclosure and the res-
onant characteristics of the drivers. The governing equations for these systems are
derived and solutions are implemented using equivalent mechanical circuits and nu-
merical methods. The idea of using driver arrays to independently actuate modes of
the panel is discussed at length with respect to modal addressability, modal spillover,
and experimental validation. The numerical approach to determining the optimal
driver placement for a given set of modes is derived and experimentally validated.
An investigation of the acoustic behavior of (cid:29)at panel loudspeakers is presented, us-
ing mechanical simulation results to predict the acoustic radiation. The simulations
are compared to measurements and found to accurately predict important mechani-
cal and acoustical behaviors. It is demonstrated that a driver array, with the proper
biasing, is capable of creating a (cid:29)at panel loudspeaker which acts more like a piston