Technical Documentation Microphone Handbook Vol. 1: Theory Brüel&Kjær B K WORLD HEADQUARTERS: DK-2850 Nærum • Denmark • Telephone: +4542800500 •Telex: 37316 bruka dk • Fax: +4542801405 • e-mail: [email protected] • Internet: http://www.bk.dk BE 1447 –12 Microphone Handbook Volume 1 March 2019 Brüel & Kjær Microphone Handbook BE 1447 –12 Vol.1 Copyright © 2019, Brüel & Kjær A/S All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without prior consent in writing from Brüel & Kjær Sound & Vibration Measurement A/S, Nærum, Denmark. 0 − 0 Microphone Handbook Brüel & Kjær Vol.1 Preface This volume provides background information on the Brüel & Kjær microphone product range. It gives an insight into the theory behind the development of microphones and pream- plifiers and explains the terminology used to describe these products. The aim of this volume is to promote a full understanding of measurement microphones and to provide sufficient background information for customers to get the best out of these prod- ucts. It also gives adequate information for customers to be able to make informed and qualified decisions about the microphone products which are most suitable for their meas- urement requirements. These products are described in detail in more specific literature, such as Volume 2 of this handbook and in product data sheets. Chapter 1 gives a brief history of microphone development at Brüel & Kjær and provides an insight into the research and development invested in microphone products. An overview of the production of microphones is also given. Chapter 2 gives a general introduction to microphone theory and explains the decisions that are made about the design and construction of microphones. Chapter 3 provides more detailed information about the characteristics of microphones with the aim of allowing an informed view on the specifications applied to microphone products. Chapter 4 introduces the main characteristics of preamplifiers and explains the categories of information given in Volume 2. Chapter 5 provides information on the selection criteria commonly used to identify the most suitable microphone for different applications and also the most applicable accessories that should be used. Chapter 6 discusses the requirement for the calibration of microphones and offers an over- view of calibration methods. BE 1447 –12 Microphone Handbook 0 − i Vol.1 0 − ii Microphone Handbook Brüel & Kjær Vol.1 Contents 1. Introduction....................................................................................................................... 1 – 1 1.1 Historical Background to Microphone Development at Brüel & Kjær ..................... 1 – 2 1.2 Development of Microphone Products........................................................................ 1 – 5 1.3 Production of Microphones at Brüel & Kjær .............................................................. 1 – 9 1.4 Product Support ........................................................................................................ 1 – 11 2. Microphone Theory ..................................................................................................... 2 – 1 2.1 Sound Levels and Sound Fields.................................................................................. 2 – 2 Sound Field Parameters......................................................................................... 2 – 2 Sound Pressure and Pressure Level...................................................................... 2 – 2 Particle Velocity and Particle Velocity Level........................................................ 2 – 3 Sound Intensity and Sound Intensity Level ......................................................... 2 – 3 Pressure-field.......................................................................................................... 2 – 4 Free-field................................................................................................................. 2 – 4 Diffuse-field............................................................................................................. 2 – 5 2.2 Measurement Microphone Requirement.................................................................... 2 – 5 2.3 Measurement Microphone Design.............................................................................. 2 – 7 Introduction ............................................................................................................ 2 – 7 Design Description ................................................................................................. 2 – 7 Material and Process Requirements ..................................................................... 2 – 9 Transduction Principles ....................................................................................... 2 – 11 Diaphragm and Air Stiffness............................................................................... 2 – 15 Static Pressure Equalization ............................................................................... 2 – 16 Low Frequency Response and Vent Position ...................................................... 2 – 17 High Frequency Response.................................................................................... 2 – 20 Microphone Sensitivity ........................................................................................ 2 – 24 Microphone Modelling by Equivalent Electric Circuits ..................................... 2 – 25 Acoustic Impedance of Diaphragm System......................................................... 2 – 27 Equivalent Volume of the Diaphragm System ................................................... 2 – 28 2.4 Combination of Microphone and Preamplifier......................................................... 2 – 31 Microphone Capacitance ...................................................................................... 2 – 31 Electrical Frequency Response of Microphone and Preamplifier ...................... 2 – 32 Inherent Noise of Microphone Systems............................................................... 2 – 35 Distortion .............................................................................................................. 2 – 39 2.5 Microphone Types Dedicated to Different Sound Fields......................................... 2 – 43 Influence of the Microphone on the Pressure-Field............................................ 2 – 43 BE 1447 –12 Microphone Handbook 0 − 1 Vol.1 Contents Pressure Field Microphone and Sensitivity........................................................ 2 – 45 Influence of Microphone on the Measured Sound Pressure in a Free-Field..... 2 – 45 Free-Field Microphone and Sensitivity............................................................... 2 – 48 Influence of the Microphone on the Measured Sound Pressure in a Diffuse Field ......................................................................................................... 2 – 49 Diffuse Field Microphone and Sensitivity........................................................... 2 – 50 2.6 Long Term Microphone Stability ............................................................................. 2 – 51 2.7 Electrostatic Actuator Calibration ........................................................................... 2 – 54 Introduction .......................................................................................................... 2 – 54 Electrostatic Actuator .......................................................................................... 2 – 55 Electrostatic Calibration Pressure ...................................................................... 2 – 55 Electrostatic Actuator Operation ........................................................................ 2 – 57 Actuator and Pressure-field Responses............................................................... 2 – 58 General Note on Actuator Calibration ................................................................ 2 – 58 2.8 Conclusion ................................................................................................................. 2 – 59 3. Characteristics of Microphones........................................................................ 3 – 1 3.1 Introduction to Characteristics .................................................................................. 3 – 2 The Calibration Chart and Diskette ..................................................................... 3 – 2 3.2 Sensitivity.................................................................................................................... 3 – 3 Open-circuit Sensitivity (So) .................................................................................. 3 – 3 Loaded Sensitivity (Sc)........................................................................................... 3 – 4 Correction-factors K and Ko................................................................................... 3 – 5 3.3 Frequency Response.................................................................................................... 3 – 5 Introduction and Optimised response ................................................................... 3 – 5 Low Frequency Response....................................................................................... 3 – 6 High Frequency Response...................................................................................... 3 – 7 Electrostatic Actuator Response...........................................................................