Measurement of Direct Radiation Loudspeakers and Closed Box Loudspeaker Systems

Parameters Using a Laser Velocity Transducer

vorgelegt von Magister en Fisica ApJicada Jorge Nestor Moreno Ruiz

aus Lima

von der Fakultät V - Verkehrs- und Maschinensysteme der Technischen Universität Berlin

zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften

- Dr.-Ing. ­

genehm igte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Paschereit Berichter: Prof. Dr. Möser Berichter: Prof. Dr. Vorländer

Tag der wissenschaftlichen Aussprache: )O. 11.2006

Berlin 2006

D 83

CONTENTS

Measurement of Loudspeaker Parameters Using a Chapter 1 Laser Velocity Transducer and a Signal Analyzer- 1

Original Approach

1.1 Introduction 1 1.2 Loudspeaker Equivalent Circuit 2 1.3 Simplified Electric Circuit 3 1.4 Analysis 4

1.4.1 Calculation of f s and QMS 4

1.4.2 7Calculation of Q1S

1.4.3 8Calculation of Q/;s

1.4.4 Calculation of Force Factor BI 9 1.4.5 11Calculation of RE 1.4.6 12Calculation of MMS I RMS I CMS

1.4.7 13Calculation of VAS y 770

1.5 Measurement Setup 13 1.6 Measurement 14 1.7 Results 15 1.8 Some Additional Information 17 1.9 Conclusions - Chapter One 20 Appendix A 22

Chapter 2 Measurement of Loudspeaker Parameters Using 23Laser Velocity Transducer - An Improved Method

2.1 Introduction 23 2.2 Influence of The Voice Coil 24 2.3 How to Remove the Inductance 31

2.3.1 First Approximation 33 2.3.2 Second Approximation 34 2.3.3 Third Approximation 34 2.3.4 The Effect of Eddy Currents 38

2.4 Measurement setup 39 2.5 Measurements 40

Chapter 3

2.6 Results 42 2.7 Discussion 43

2.7.1 Calculation of f, and QMS 46

2.7.2 Calculation of QTS 47

2.7.3 Calculation of QES 47

2.7.4 Calculation of RE:. 47

2.7.5 Calculation of BI 47 2.7.6 Calculation of RMS I CMS ' and M MS 48

2.7.7 Calculation of VAS and 770 48

2.7.8 Calculation of Lvc 48

2.8 Conclusions - Chapter Two 48 Appendix 81 50 Appendix 82 51

Measurement of Loudspeaker Parameters vs. 52 Displacement Using a Laser Velocity Transducer

3.1 Introduction 52 3.2 Linear Parameter Measurement 53

Simplified Approach 3.2.1 54Calculation of f, and Q\1S 3.2.2 55Calculation of QJ::s and Q7S 3.2.3 Calculation of the Force Factor 56 3.2.4 Calculation of MMS' RMS and CMS

56

3.3 Measurement of Parameters vs. 57 Displacement

3.4 Measuring Setup 58 3.5 Conclusions - Chapter 3 67 Appendix C 68

Measurement of Closed Box Loudspeaker System Parameters using a Laser Velocity Transducer and

69 an Audio Analyzer

4.1 Introduction 69

Chapter 4

1\

42 43 46of .I: and Q,\.fS

of Q/s 47

of QL'i 47

of R/ 47

of BI 47

of Rus ' CMS ' and MMS 48

48of V. IS and T7" 48of Lw

- Chapler Two 48 50 51

,speaker Parameters vs. 52 Laser Velocity Transducer

52 'arameIer Measurement 53 Approach

of .1: and Q\JS 54

of Q/s and Q/s 55

of lhe Force Factor 56 56of MAIs, R'I/S and CMS

It of Parameters vs. 57 it

Setup 58 - Chapter 3 67

68

Box Loudspeaker System r Velocity Transducer and

69

69

Chapter 5

References

4.2 Equivalent Circuit of a Closed Box 70 System

4.3 Simplified Electrical Circuit 71 4.4 Theoretical Analysis 72 4.5 Behavior of the Parameters 75 4.6 Mechanicallmpedance Behavior 80 4.7 Measurement Setup 85 4.8 Measuremenl 86 4.9 Conclusions - Chapter 4 87

Measurement of Loudspeaker Parameters Using a Visco - Elastic Model for the Suspension - Final 88 Approach

5.1 Introduction 88 5.2 Visco- Elastic Loudspeaker Model - 89

Mechanical Part 5.3 Parameter Determination Procedure 91

5.3.1 Curve Fitting 92 5.3.2 Root Finding 94

5.4 Measuring Setup 96 5.4.1 Method Proposed 96 5.4.2 Validation 99

5.5 Results 103 5.5.1 Method Proposed 103 5.5.2 Validation 106

5.6 Additional comment 112 5.7 Conclusions Chapter 5 113 5.8 Acknowledgments 113

115

11 111