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Brüel&Kjær B K

BE1447–11

TechnicalDocumentation

WORLD HEADQUARTERS: DK-2850 Nærum • Denmark •Telephone: +4542800500 •Telex: 37316 bruka dk • Fax: +4542801405 •

e-mail: [email protected] • Internet: http://www.bk.dk

Microphone Handbook

Vol.1: Theory

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J uly 1996

BE1447–11B rüel & Kjær Microphone HandbookVol.1

Microphone Handbook

Volume 1

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0 − 0 Brüel & KjærMicrophone HandbookVol.1

Copyright © 1996, B rüel &Kjær A/S

All rights reserved. No part of this publication may be reproduced or distributed in any formor by a ny mea ns w ithout prior consent in w riting from Brüel &Kjær A/S, Nær um, Denma rk.

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BE1447–11 0 − iMicrophone HandbookVol.1

PrefaceThis volume provides background informa tion on the B rüel &Kjæ r microphone product

ran ge. It gives a n insight into the t heory behind t he development of microphones an d 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.

Cha pter 1 gives a brief history of microphone development a t Br üel &Kjær a nd provides a n

insight into the research and development invested in microphone products. An overview of

the production of m icrophones is a lso given.

Cha pter 2 gives a general introduction t o microphone theory a nd explains the decisions t ha t

a re ma de a bout the d esign a nd 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.

Cha pter 4 introduces t he ma in chara cteristics of preamplif iers a nd explains the cat egories of

informa tion 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.

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Contents

1. Introduction ......................................... ........................................................ ...................... 1 – 1

1. 1 H i st or ica l B a ckg r ou n d t o M icr oph on e D e velop m en t a t B r ü e l & K jæ r ... . . .. . . . .. . . . . . . . .. 1 – 2

1.2 D evelopm en t of Micr oph on e P r od uct s .. . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . 1 – 5

1.3 P r od uct ion of M icr oph on es a t B r üel & Kjæ r ... . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 1 – 9

1.4 P rod uct Suppor t ............................................... ........................................................ . 1 – 11

2. Microphone Theory ................................................ ..................................................... 2 – 1

2.1 S oun d Levels an d S oun d F ields ................................................ .................................. 2 – 2

Sound Field Pa ram eters ................................................. ........................................ 2 – 2

Sound P ressure a nd P ressure Level .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . . . 2 – 2

P a rt icle Velocity a nd P a rt icle Velocity Level .. . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . .. . 2 – 3

Sound In tensi ty an d Sound In tensi ty Level .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . .. . 2 – 3

Pressure-field ............................................... ........................................................ ... 2 – 4

Free-field ................................................ ................................................. ................ 2 – 4

Diffuse-field .................................................. ........................................................ ... 2 – 5

2.2 M ea s ur em en t M icr oph on e R eq uir em en t .. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . 2 – 5

2.3 Mea s ur em en t Micr oph on e D esign .................................................. ............................ 2 – 7

Introduction ................................................. ........................................................ ... 2 – 7

Design Description ...................................... ........................................................ ... 2 – 7

Ma ter ia l an d P rocess Requirements .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . 2 – 9

Transduction Principles ................................................. ...................................... 2 – 11

Diaphra gm a nd Air St i f fness ............................................... ................................ 2 – 15

St at ic P ressure Equa l iza t ion ............................................... ................................ 2 – 16

Low F requency Response an d Vent P osit ion .. . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . . 2 – 17

High Frequency Response .............................................. ...................................... 2 – 20

Microphone Sensitivity .................................................. ...................................... 2 – 24

Microphone M odelling by Eq uivalent Electric Circuits .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . 2 – 25

Acoustic Im pedance of Dia phra gm S ystem ... . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 2 – 27

Eq uivalent Volume of the Dia phra gm Syst em ... . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 2 – 28

2.4 C om b in a t ion of M icr oph on e a n d P r e a m pli fi er .. . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 2 – 31

Microphone C apa cita nce ................................................ ...................................... 2 – 31

Electrical Frequency Response of Microphone and Preamplifier .. . . . . .. . . . . . .. . . . . . . . 2 – 32

Inherent Noise of Microphone Systems... . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . 2 – 35

Distort ion ............................................... ................................................. .............. 2 – 39

2. 5 M icr op hon e Ty pes D ed ica t e d t o D i ff er en t S ou n d Fi el ds .. . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . . 2 – 43

In fluence of th e Microphone on th e P ressur e-Field .. . . .. . . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . 2 – 43

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Contents

P ressure Field Microphone and Sensit ivity .. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . 2 – 45

Influ ence of Microphone on th e Mea sur ed Sound P ressur e in a F ree-F ield . .. .. 2 – 45

Free-Field Microphone and Sensitivity .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 2 – 48

Influence of th e Microphone on the Mea sured S ound P ressure in a

Diffuse Field ............................................... ................................................. ......... 2 – 49

Diffuse Field Microphone a nd Sensit ivity .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 2 – 50

2.6 L on g Ter m Micr ophon e S t a bilit y .. . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 2 – 51

2.7 E lect rost a tic Act ua t or C a libr a tion ... . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . . 2 – 54

Introduction ......................................... ........................................................ ......... 2 – 54

Electrosta t ic Actua tor ...................................... .................................................. .. 2 – 55

Elect rosta t ic Ca l ibra t ion P ressure .. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . 2 – 55

Electrosta t ic Actua tor Operat ion ... . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 2 – 57

Actuator and Pressure-field Responses .. . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . 2 – 58

G eneral Note on Actua tor Ca librat ion ... . .. . . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 2 – 58

2.8 Conclusion ....................................................... ................................................. ......... 2 – 59

3. Characteristics of Microphones . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . .. . 3 – 1

3.1 I nt rod uct ion to C ha r a ct er is tics .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . 3 – 2

The Ca l ibra t ion Cha r t a nd Disket te .. . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . . 3 – 2

3.2 S ensit ivit y ........................................................ ................................................. ........... 3 – 3

Open-circuit S ensitivit y (S o) .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . 3 – 3

Loaded S ensit ivity (S c) ........................................................ ................................... 3 – 4

Correct ion-factors K a nd K o................................................ ................................... 3 – 5

3.3 Freq uency Response........................................ ................................................. ........... 3 – 5

Int roduction a nd Optimised response ... . .. . . . . . .. . . . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 3 – 5

Low F requency Response ....................................... ................................................ 3 – 6

High Frequency Response................................................... ................................... 3 – 7

Electrosta t ic Actua tor R esponse... . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . . 3 – 7

Free-field Response ................................................ ................................................ 3 – 9Random Incidence Response... . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . 3 – 9

P ressur e-field R esponse ......................................... ................................................ 3 – 9

3.4 D irect ion al Cha ra ct er ist ics ......................................... .............................................. 3 – 10

3.5 D yn a m ic Ra nge ............................................... ................................................. ......... 3 – 11

Inherent Noise .................................................. .................................................... 3 – 11

Ma ximum Sound P ressure Level.. . . . .. . . . . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . 3 – 12

3.6 E quiva lent D ia phra gm Volum e............................................... ................................. 3 – 13

3.7 C alibra t or Loa d Volum e ...................................... .................................................. .. 3 – 13

3.8 Ca pa cit a nce ........................................ ........................................................ ............... 3 – 13

3.9 P ola risa t ion Volt a ge ........................................ ................................................. ......... 3 – 14

Externa lly P ola rized Microphones .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 3 – 14

Prepolarized Microphones...................................... .............................................. 3 – 153.10 Lea ka ge Resist a nce ............................................... .................................................... 3 – 16

3.11 S t a bilit y ........................................ ........................................................ ..................... 3 – 17

3.12 I rreversible C ha nges ................................ ........................................................ ......... 3 – 17

Long-term sta bility ................................................. .............................................. 3 – 17

Handl ing ........................................ ........................................................ ............... 3 – 17

Short- term Stabili ty ............................................... .............................................. 3 – 17

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Contents

3.13 Reversible C ha nges ................................................ ................................................... 3 – 18

Effect of Temperature ....................................... ................................................... 3 – 18

E ffect of Ambient P ressure .................................................. ................................ 3 – 19

Effect of Humidit y ....................................... ........................................................ . 3 – 21

E ffect of Vibra tion ....................................... ........................................................ . 3 – 21

Effect of Magnetic Field ................................................. ...................................... 3 – 21

E lectromagnetic Compatibili ty .................................................. .......................... 3 – 21

4. Ch a ra cterist ics of P ream plifiers . . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . . . 4 – 1

4.1 I n tr od uct ion t o C h a r a ct er is tics of P r ea m p lif ier s .. . . . .. . . . . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 4 – 2

Definition of a Microphone Preamplifier .. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . .. . 4 – 2

S election of a Microphone P rea mplifier .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . .. . . . . . . .. . 4 – 2

Contents of this Chapter ................................................ ........................................ 4 – 2

4.2 F req uency Response ......................................... .................................................. ......... 4 – 2

Low F requency Response ............................................... ........................................ 4 – 2

High Frequency Response .............................................. ........................................ 4 – 3

4.3 D yna mic Ra nge ................................................ ........................................................ ... 4 – 5U pper l imit o f Dyna mic Range .................................................. ............................ 4 – 5

Maximum Voltage ....................................... .................................................. ......... 4 – 6

Maximum Current ....................................... .................................................. ......... 4 – 6

Max imum S lew Ra t e ......................................... ..................................................... 4 – 7

Lower Limit of Dyna mic Range ................................................. ............................ 4 – 8

4.4 P ha se Response ................................................ ........................................................ . 4 – 11

4.5 E ffect of Tem pera tur e ...................................... .................................................. ....... 4 – 11

4.6 E ffect of Ma gn et ic F ield s ....................................... ................................................... 4 – 13

4.7 E lect rom a gnet ic C om pa t ibilit y ................................................. ................................ 4 – 13

The E uropean EMC Direct ive.............................................. ................................ 4 – 13

The CE label ................................................ ........................................................ . 4 – 13

EMC Test Fa ci l it ies a t B rüel&K jæ r ... . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . 4 – 144.8 M on it or in g a n d C a libr a t ion Tech niq ues .. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . 4 – 15

Insert Voltage Calibrat ion ............................................. ...................................... 4 – 16

Cha rge Inject ion Calibra t ion ............................................... ................................ 4 – 17

CIC Input Signa l Requirements ................................................ .......................... 4 – 19

5. S elect ing a Microphone ...................................... ..................................................... 5 – 1

5.1 G u id elin es on S elect in g Micr oph on es .. . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . 5 – 2

5.2 Wha t t o C onsider ........................................ ................................................. ................ 5 – 4

Frequ ency Response .......................................... ..................................................... 5 – 4

Type of Sound Field ........................................................ ........................................ 5 – 4Limits of Dyna mic Ra nge ............................................... ........................................ 5 – 4

Microphone Ventin g .......................................... ..................................................... 5 – 5

Phase Response ................................................. ..................................................... 5 – 5

Polar isa t ion .................................................. ........................................................ ... 5 – 5

St an dards Compliance ...................................... ..................................................... 5 – 6

Environment ................................................ ........................................................ ... 5 – 7

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Microphone Arra y Applicat ions .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . 5 – 8

5.3 S elect in g Th e R igh t Accessor ies .. . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . 5 – 8

Low Wind S peed, Ra ndom D irect ion... . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 5 – 9

High Wind Speed, Known Direction ... . . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 5 – 9

Turbulent P ressure Fluctua t ions .. . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . .. 5 – 10

Humidi ty ........................................ ........................................................ ............... 5 – 10

6. Calibrat ion ................................................ ........................................................ ................. 6 – 1

6.1 I nt r oduct ion ........................................ ........................................................ ................. 6 – 2

6.2 C a libr at ion of Microph on es......................................... ................................................ 6 – 4

6.3 Field Ca libra t ion ............................................. ................................................. ........... 6 – 4

6.4 La bora tory Ca libra t ion ......................................... ...................................................... 6 – 5

P r ima ry Ca l ibra t ion Labora tor ies .. . . .. . . . . . .. . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . 6 – 6

Accredited Ca libra t ion La bora tories .. . . . . .. . . . . . .. . . . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . 6 – 6

Ca l ibra t ion a t the B rüel &Kjær Fa ctory.. . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . 6 – 7

6.5 C a l ib ra t i on H i er a r ch y , Tr a cea b ilit y a n d U n cer t a in t y .. . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . 6 – 8

6.6 C a libra tion Met hods ....................................... ................................................. ........... 6 – 9Reciprocity Ca librat ion Meth od... . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . 6 – 10

Subst itut ion method........................................ .................................................... 6 – 11

Compar ison Meth od ......................................... .................................................... 6 – 11

Sound P ressure Ca l ibra tor Method ... . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 6 – 12

Actuat or method ............................................... .................................................... 6 – 12

Insert Volta ge Ca librat ion Method ... . . .. . . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . 6 – 13

Cha rge Inject ion Ca librat ion Method ... . .. . . . . . .. . . . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . 6 – 14

Index

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Chapter 1

Introduction

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Ch a pter 1 — Int roductionHistorical Background to Microphone Development at Brüel&Kjær



1.1 His tor ica l Ba ckground to Microphone Development a tBrüe l&K jær

B rüel &Kjæ r began producing microphones in 1945. By the lat e 1950s they w ere

established as a leading supplier of measurement microphones, due largely to the

inspira t ional leadership and enthu siasm of Dr. P.V. B rüel in the field of microphone

development. In pa ra llel, Br üel &K jær a lso conceived, designed an d developed com-plete acoust ic measurement systems. Measurement microphones formed an impor-

tant par t o f these sys tems, in combinat ion wi th ins t ruments such as analysers ,

recorders and sound level meters.

From this beginning, Brüel &Kjæ r gained a n increasingly good reputa t ion amongst

users of microphones, both in the acoust ics industry and in the f ield of academic

research. This was achieved as a result of providing a high standard of service and

reliable, well built products. The product range was also enhanced by a programme

of research a nd development t ha t ensured continuous improvements in the a ccuracy

a nd performa nce of new inst rum ents. Today, th is approa ch continues t o deliver in-

novat ive measurement instrumentat ion, including a comprehensive range of meas-

urement microphones in sizes from 1/8″ t o 1″. Togeth er th ese microphones cover a llaspects of measur ement m icrophone usa ge.

B y t he early 1970s, B rüel &Kjær ’s strong presence in the mea surement m icrophone

field had become firmly established with the development of high sensit ivity 1/2″microphones. These microphones benefited from new techniques allowing less ten-

sion in the diaphragm, leading to an increase in sensit ivity of approximately 12dB.

During th is period B rüel &Kjær a lso improved techniques to accura tely measure

and document the performance parameters of their measurement microphones and

supplied this information in the form of calibration charts. Microphones could sub-

sequently be relied upon according to certain stated parameters.

Fi g.1 .1Range of cond enser m easur ement m i crophones

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BE1447–11 1 − 3

Calibrat ion equipment was also made, such as reciprocity equipment for laboratory

calibration and the pioneering hand-held pistonphone. This convenient calibration

device effectively improved the accuracy of everyday microphone usage by allowing

users to check m easurement a ccura cy in th e f ield.

In 1973 Brüel &Kjær consolida ted t heir posit ion a s t he leading microphone produc-

er by meeting a requ est from Western E lectr ic to supply 1″ microphones to replace

their su ccessful but a geing WE 640AA microphone. The B rüel &K jær solution took

the form of the classic Type 4160 microphone. The 4160 together with the 4180 (the1/2″ version) were quickly esta blished a s reference microphones for la bora tory st a nd-

ard use, due mainly to their stabili ty and accurately documented performance pa-

rameters.

Further innovat ions ensued, notably in improvements to electret processes duringthe 1970s, resulting in the production of stable prepolarised microphones which

beca me sta nda rd for use w ith s ound level meters. The 1980s brought furt her devel-

opments, in part icular in the f ield of sound intensity measurement . The mid 1980s

also saw the development of specialised types of probe microphone. This microphone

made use of a revolut ionary and now patented tube system which gives a f lat

F i g.1 .2 M i crophone Types 4180 1/2″ and 4160 1 ″ are used by DPL A as hi ghly stable r eference m i cr ophones for labor a- tory cal i brat ions

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frequency response and allows for measurements in places where access for stand-

ar d m easur ement m icrophones is d if f icult .

Improvements have continued into the 1990s with the introduction of highly accu-

rate yet robust microphones ( the Falcon RangeTM) and a microphone unit specially

designed for permanent outdoor use. These microphones have proven their ability to

perform effect ively in h a rsh m easurement environments.

Throughout t he history of Brü el &Kjær, a collaborat ive approa ch wit h customers

has led to improvements in the design, performance and reliabili ty of measurement

microphones. In a ddit ion, B rüel &Kjær ’s response to customer requirement s ha s

created several innovat ions in the related acoust ic measurement f ield, including:

— Sound intensity microphones, phase-ma tched for accurate, low frequ ency meas-

urements see Section 2.3.7.

— Sound intensity calibrat or, s imula t ing a free-field environment for calibrat ion of

sound intensity equipment .

— Cha rge inject ion calibra t ion (pa tented) for verif ica t ion of complete measurement

systems see, Section 4.8.

— Feedback ca librat ion (Mult itone calibra tor) a llow ing calibrat ion of microphones,

up to 16kH z.

— New intensity m easurement microphones wi th pa tented pressure equa l isa t ion

vent system giving much improved low frequency response.

Fig .1.3 Sound I n tensi ty probe using a phase-matched pai r of mi - crophones

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Ch a pter 1 — Int roductionDevelopment of Microphone Products



simulate everyday use, while shock tests reproduce the possible effect of impacts

received in tr a nsport (typically up t o the equiva lent of 1000 m/s2). Additionally, mi-

crophones are tested for severe impacts by a drop test from a height of one metre

onto a wooden block. The tested microphone must show less than 0.1dB variat ion

in sensit ivity after the fall .

As temperature and humidity are both factors which pose the greatest threat to the

performance of condenser microphones, pre-production microphones are thoroughly

tested for resistance to these influences, typically in temperatures from −20° t o

+ 70°C a nd in humidity o f up to 90% at 40°C. Finally, microphones are also tested

for resistance to corrosion, as proven by the most recent range of condenser micro-

phones which have been found to be very robust in harsh measurement environ-ments.

It is these skills, knowledge and experience acquired over more than 50 years of

development work, that a l lows the B rüel &Kjær t o handle a l l the t a sks necessary to

develop new products, from first specification to final calibration.

Fig.1.4 An echoic cham ber used for m easur ement of free-f ield r e- sponse

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Cha pter 1 — IntroductionDevelopment of Microphone Products


BE1447–11 1 − 7

Fig .1.5 M icrophone undergoing shock tests

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Ch a pter 1 — Int roductionDevelopment of Microphone Products



Fig.1.6 Aeri a l Photo of the Br üel & Kjær H eadquar ters, Næru m , Denm ark

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Cha pter 1 — IntroductionProduction of Microphones at Brüel&Kjær


BE1447–11 1 − 9

1.3 P rod uct ion of Microphones a t B rüel &K jæ r

Microphones are precision instruments and while the design of a conventional

measurement microphone may appear to be quite simple, i ts production must be

very precisely controlled to meet specified tolerances. Such tolerances impose great

demands on the materials and construct ion methods used, yet the products created

must be extremely reliable and robust. Many of the closely controlled productionprocesses stem from this requirement . At B rüel &Kjær the empha sis is therefore on

quality rather than mass-production. Some examples from the different stages of

production il lustrate this approach.

Two components which receive a lot of attention during production are the micro-

phone diaphragm and backplate . During production the surfaces of these compo-

nents are made extremely smooth as a very high electrical f ield strength must exist

across the diaphragm to backplate gap. Any unevenness in the surfaces can lead to

a rcing. All surfa ces mu st a lso be thoroughly clean to av oid conta mina t ion from du st

and dir t that would accentuate the de t r imenta l e f fec t o f humidi ty and in turn the

performance of the microphone. A very precise and clean construction environment

as well as rigorous quality control are therefore employed. This includes assemblyin a clean-room environment where potentially harmful part icles of dust in the air

are kept t o a minimum.

Fi g.1.7 Pr epolar ized m icrophones near in g th e end of produ cti on

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Ch a pter 1 — Int roductionProduction of Microphones at Brüel&Kjær



Another crit ical area of production is the distance between the microphone dia-

phragm and backplate which must be constructed to very small mechanical toler-

ances. Typically this is set to 20 µ, w ith a tolera nce of 0.5 µ. The required distance is

monitored and then implemented precisely, once the correct tolerances have been

ad justed. S imilarly, the t ension of the dia phrag m is closely monitored a nd computer

controlled.

Forced ageing using temperature and humidity is employed to ensure stabili ty. I t

does this in tw o wa ys. Tempera ture releases tension inherent in t he ma terials a f ter

manufacture. This achieves the required diaphragm tension which will then remain

highly stable. High temperature in combinat ion with high humidity also stabilises

the polarisation charge applied to pre-polarised microphones. The stability of the

microphones is such tha t B rüel &Kjær can s ta t e an a ccura cy va r ia t ion f rom th e

recorded va lues of just 0.1 dB over a period of 50 years for a t ypical 1/2″ condenser

measur ement microphone.

Fi g.1.8Diaph ragm pr ess in u se dur in g product i on

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Cha pter 1 — IntroductionProduct Support


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All such measures play an important part in achieving the renowned reliabili ty and

a ccuracy of B rüel &Kjær microphones. This reliabili ty is ba sed on t he known per-

formance parameters of the microphone. These parameters are measured at the end

of production using highly accurate calibration equipment. The results are recorded

on individual calibrat ion charts and data diskettes which are supplied with micro-

phone products.

1.4 P r oduct S upport

B rüel &Kjæ r microphone products a re supported by a w ealth of informat ion an d

services. In addition to this handbook, information about microphones is provided in

technical journals , product data sheets and applicat ion notes. Training in dif ferent

a spects of acoust ics ca n be provided. Br üel &Kjær a lso offers a ra nge of accredited

ca librat ion services for calibra t ion of microphones a nd ass ociat ed equipment .

Fig.1 .9 M icrophone ca l ib ra t ion, at the end of product ion, using an electr ostati c actuat or

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BE1447–11 2 − 1

Chapter 2

Microphone Theory

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Ch a pter 2 — Microphone TheorySound Levels and Sound Fields



2.1 S ou nd L evels a n d S ou n d F ield s

This chapter provides the background required to understand the properties, speci-

fications and use of condenser measurement microphones. The main subjects are:

— the pr inciple of operat ion

— t h e m a i n d es ig n pa r a m e t er s— how th e design para meters influence the propert ies of microphones

— the principle of how microphones intera ct wit h dif ferent t ypes of sound field

— the need for dif ferent m icrophones t ha t ar e designed for free-field, pressure-field

an d diffuse-field m easurements

— related subjects including microphone modelling, diaphra gm impedance and

electrostat ic actuator calibrat ion

2.1.1 S ou nd Field Pa r amet er s

Sound pressure has always been the sound field parameter of the greatest interest

because sound pressure is what the human ear detects . Measurement microphones

have therefore been widely used for analysis and recording of sound pressure. This

still applies today, even though modern technology has made it possible for sound

intensity and part icle velocity measurements to be quite easily and commonly per-

formed.

Sound pressure as well as part icle velocity, sound intensity and their respect ive

levels relat ive to defined references are thus the sound field parameters which are

measured and stated in most measurement reports today. The levels are expressed

in decibels (dB).

2.1.2 Sound P ressure and P ressure Level

The sound pressure at a certain point is the dif ference between the instantaneous

pressure and the ambient mean pressure. The unit of Sound Pressure (p) is Pascal

(Pa ) w hich is equa l to Newt on per Squ a re Meter (N/m 2). The reference value for

Sound Pressure Level (SPL) is twenty micro-Pascal (20 µPa) . The Sound Pressure

Level (L p ) is defined by the formula below:

where

Sound Pressure and Sound Pressure Level generally refer to the Root Mean Square

(RMS) value of the pressure. The RMS value is considered if no specific reference is

stated. A pressure equal to the reference value is thus equal to zero dB while 1Pa

Lp

10p 2

p r ef 2----------log⋅ 20

p

p r ef ----------d B log⋅= = p

r ef 20µPa=

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equa ls 94 dB (93.98dB ). The zero dB va lue corresponds to the t hreshold of hear ing

at 1000Hz for a young person with normal hearing abili ty. The pressure has no

direct ion and is thus a scalar .

2.1.3 Pa rt icle Veloci ty a nd P a rt icle Veloci ty Level

The Air P a rt icle Velocit y, or just P a rt icle Velocit y (v ) is the velocity of a smallvolume of air (particle). The dimensions of the volume regarded should be very

small in comparison with the wave-length. The unit of particle velocity is metres

per second (m/s). The pa rticle velocity d epends on th e sound pr essure a nd on th e

sound field condit ions. Toda y, the recomm ended (IS O1683) referen ce for Pa rt icle

Velocit y L evel is one na no-met re per second (1 nm /s or 10–9 m/s). How ever, fift y

na no-met res per second (50 nm/s) is a lso used, as t his nu mber w a s the commonly

a pplied reference in t he pas t . To prevent a ny misundersta nding, th e reference value

should therefore be stated together with velocity measurement results . The Part icle

Velocity Level (L v ) is defined by the formula below:

where v r ef is 1 nm/s (alt erna tiv ely 50 nm /s).

Particle Velocity and Particle Velocity Level generally refer to the Root Mean

Square (RMS) value of the velocity. This is considered if no reference is stated

specificly. In the propagation direction of a plane progressive sound wave, the veloc-

ity level is pra ct ica lly 34 dB above the pressure level w hen t he reference velocity is

1 nm /s, wh ile it is a pproxima tely equa l to the pressur e level, if 50 nm/s is a pplied.

This is valid for normal ambient conditions i.e. for a static pressure of 101.325kPa,

a temperature of 23°C and for 50%Relat ive Humidity.

2.1.4 Sound Intens ity a nd Sound In tens ity Level

Sound Intensity is acoust ic power per unit of area. I t is the power which f lows

through a certain area divided by the area. Like the part icle velocity, the sound

intensity is a funct ion of the direct ion of the sound w ave propaga t ion. The intensity

is t herefore a vector. The un it of sound int ensity is Wa tt s per squ a re-metr e (W/m 2).

The reference va lue for sound int ensit y is one pico-Wa tt per sq ua re-met re (10–12 W/m2).

The Sound Intensity Level is specified by the following formula:

where I r ef = 10–12 W/m 2

In the propagat ion direct ion of a plane progressive sound wave, the sound intensitylevel is pract ically equal to the pressure level. This is valid for normal ambient

condit ions, i .e . for a sta t ic pressure of 101.325 kPa , a tempera ture of 23 °C and for

50% Rela tiv e Hu mi dit y.

L v 10 log v

2

v r ef 2----------⋅ 20 v v r ef

----------d B log⋅= =

L I 10 logI

I r ef --------- dB⋅=

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2.1.5 P ressure-f ield

A pressure-field is characterized by a sound pressure which has the same magni-

tude and phase at any posit ion within the f ield. Microphone Pressure Sensit ivity

refers to this type of field.

Pressure f ields may be found in enclosures or cavit ies which are small compared to

the wave-length. Such fields occur in couplers applied for testing of earphones or

calibration of microphones. They also occur in most types of sound level calibrator

an d in pistonphones.

The pressure-field conditions of small cylindrical couplers have been carefully ana-

lyzed because such couplers are specificly used for primary calibration of micro-

phones by the reciprocity technique. This technique, which can be used to achieve

very high calibrat ion accuracy, is applied by most nat ional calibrat ion laboratories.

Microphone calibrations performed in small couplers are pressure-field calibrations,

but under certain circumstances they may be applied for microphones which are to

be used in other types of f ield. Pressure-field calibrat ions are widely applied, aswell-defined pressure-fields are rather easily produced.

2.1.6 F ree-field

A free sound field, or just a free-field may be created where sound waves can

propagate freely i .e . in a continuous medium without any disturbing objects . In this

document i t is considered that a free-field is made up by a plane wave which propa-

gates in one defined direction. Microphone Free-field Sensitivity refers to this type

of field.

Ideal free-fields are difficult , if not impossible, to realise. However, in practice, free-

fields which are applicable for instrument verif icat ion and calibrat ion may be creat-

ed either in anechoic rooms, or outdoors away from reflecting surfaces. A small

sound source (point source) may create a sat isfactory plane wave at the measure-

ment posit ion, provided that i t is placed sufficient ly far away.

The distance between the source and the measurement site should be at least f ive

to ten times the largest dimension of the source and of the microphone or object

which is to be placed in the field.

In pra ct ice, sound fields w hich ca n be rega rded a s being free-fields ma y be found a t

a distance of approximately one to two metres from a sound source. This is provid-

ed that no other sources contribute signif icant ly to the sound pressure and that

there are no reflecting surfaces nearby.

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Ch a pter 2 — Microphone TheoryMeasurement Microphone Requirement


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2.1.7 Di ffuse-f ield

A diffuse sound field exists at a given location if the field is created by sound waves

arriving more or less simultaneously from all direct ions with equal probabili ty and

level.

The diffuse-field or “Random Incidence” sensitivity of a microphone refers to this

type of f ield, even if, in most ca ses, the sensit ivity is calculated from m easurement s

performed under free-field conditions. The calculation method is described in the

internat ional s t andard Random-incidence and Diffuse-field cal ibration of Sound L evel M eters IEC 1183.

A diffuse sound field may be created within a room with hard sound reflect ing walls

and which essentially contains no sound absorbing materials .

Diffuse-field spectra created in such rooms may deviate from that of an ideal f ield

due to resonances in the room and due the sound absorbt ion of the air . In cases

where diffuse-fields are to be used for technical purposes, the influence of these

effects may be reduced by applying more than one sound source and by mountingreflect ing panels which are moved continuously in order to vary the dominat ing

room resonances.

Sound fields with a close resemblance to a diffuse-field may be found in environ-

ments such as factories where many simultaneous sound or noise sources exist or

in buildings with hard walls , for example, in halls or churches.

2.2 Measurement Microphone Req u irement

Today, th ere ar e ma ny d ifferent a rea s of applica tion for m icrophones, including t ele-

communications, broadcasting, recording of music, consumer electronics and acous-t ic measurements. For each f ield and applicat ion a certain set of microphone

properties is required.

To meet t he needs of a specific microphone a pplica tion, t he designer can choose

between a number of dif ferent acoust ic operat ion and transduction principles. A

microphone may either sense the pressure, the pressure gradient or the part icle

velocity. These may then be converted to electrical signals in several different ways.

Pract ically all precision measurement microphones are pressure sensing condenser

microphones that use a constant electrical charge for convert ion of the diaphragm

displacement into an analog electrical signal.

Pressure sensing condenser microphones are used because they detect what the

human ear detects , namely pressure. Furthermore, they can be realized with the

high quality and the predictable performance that is necessary for any type of

mea surement device.

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Ch a pter 2 — Microphone TheoryMeasurement Microphone Requirement



Even if part icle velocity or sound intensity are the parameters to be determined,

pressure sensing m icrophones can be used. Sound int ensity a nd velocity a re w orked

out from pressures measured simultaneously at two points . These are typically

spaced 6 to 50mm from each other, depending on the frequency range of interest .

The in ternat ional s t andard In strum ent s for M easur ement of Sound In tensi ty IEC1043 defines the requirements for pressure sensing microphones and specifies

microphone and system requirements.

As with any other type of measurement , the sound pressure that is to be measured

should not be influenced by the microphone applied or, if this is not possible, then it

should be influenced in a controlled and known way that makes it possible to cor-

rect for the influence.

Measurement microphones influence the sound pressure, especially at higher fre-

quencies, where the wave-length and microphone dimensions are of same order of

magnitude. However, the influence, which depends on the type of sound field (pres-

sure-field, free-field or diffuse-field) is thoroughly analysed for condenser measure-

ment microphones. This is done by laboratory measurements and confirmed by

calculations which are possible due to the simple cylindrical shapes of the condens-

er microphone.

The simple diaphragm system and the simple geometry of a condenser microphone

ease accurate measurement , calculat ion and descript ion of the microphone proper-

ties under various sound field and environmental conditions. These are very impor-

tant features of microphones which are to be used for accurate measurements

under the many different measurement condit ions which may occur.

Corrections for the influence of the microphone on the sound field may be incorpo-

rated in the microphone design. Alternatively, it may be made by post-processing of

the r esults .

A list of general measurement microphone requirements is given below:

good acoustic and electric performance:

— wide f requency ra nge and f la t f requency response

— wide l inear dyn am ic ra nge, low inherent noise an d low dis tor t ion

— low influence on the sound field to be mea sured

minor influence from environment:

— low influence f rom a mbient pressure, temperat ure and h umidi ty

— low influence from vibra t ion, magnetic and electroma gnetic f ields, etc.

— good mecha nical robustness, good bump and shock resista nce

— good chemical resista nce, good corrosion r esista nce

high stabili ty of sensit ivity and frequency response

— sma ll shor t term f luctua t ion (ra ndom cha nges)

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Ch a pter 2 — Microphone TheoryMeasurement Microphone Design


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— sma ll long term dr if t (sys temat ic cha nge)

— sma ll h igh tempera ture dri f t (sys temat ic cha nge)

high suitabili ty for measurement and calculat ion of propert ies

— suitable for ca l ibra t ion us ing pract ica l and a ccura te methods

— simple shapes and easy-to-descr ibe dynamic sys tem para meters

comprehensive specifications and performance descriptions

— ava i labi li ty of measured and ca lcula ted microphone type dat a

— performa nce documenta t ion by individual ca l ibra t ion char t

— a va ilabili ty of service for periodic recalibra t ion

The Internat ional Electrotechnical Commission (IEC) has worked out two standards

which prescribe performance requirements for types of Laboratory Standard and

Working S ta nda rd m icrophones respectively. These a re IE C 1094-1 (La bora tory

St a nda rds) a nd IE C 1094-4 (Working S ta nda rds) . The sta nda rds a re ava ilable

through na t iona l s t an dard orga nisa t ions .

2.3 Mea surement Microphone Des ign

2.3.1 I n tr od uct ion

The pressure-sensing microphone (as introduced in the previous section) can be

designed for use in d ifferent t ypes of sound field i.e. in a P ressur e-field, Free-field

and Diffuse-field. The influence of the different design parameters is discussed in

this section. The classic design of a pressure-sensing measurement microphone is

shown in Fig.2.1.

The microphone shown in Fig.2.1 is a 1/2″ m icrophone (12.7 mm ), but microphones of

a similar design exist with housing diameters from 1/8″ (3.16 mm ) to a bout 1″(23.77 mm ). A newer int erna l design, invented a nd pat ented by B rüel &Kjæ r, is also

described. For both designs, the microphone properties, such as sensitivity, frequen-

cy response and inherent noise, depend mainly on the diameter and on the dynamic

propert ies of th e microphone dia phra gm system. The B rüel &Kjæ r m icrophone pro-

gram is composed of a number of microphone types with properties optimised for

many different applicat ions.

2.3.2 Design Descr ipt ion

A condenser microphone consists of a metal housing inside which an electrical insu-

lator with a back-plate is mounted behind a delicate and highly tensioned dia-

phragm, see Fig.2.2, (a). The flat front surface of the back-plate is positioned close

to the front open section of the housing. The diaphragm rests across the housing in

a way which makes the diaphragm parallel to the backplate . A controlled mechani-

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which is mainly assembled by screwing the parts together, the integrated back-plate

and insulator version is assembled by pressing the parts into each other. This de-

sign also deviates from the conventional design by applying a backplate consist ing

of a metal thin-film placed directly on the surface of the insulator.

In practice, the first mentioned type implies more freedom for the designer to opti-

mise the frequency response, while the second is advantageous during production.

The main choice which must be made in respect to the two different design types is

one of more narrow frequency response tolerances offered by the conventional de-

sign, as opposed to reduced production costs for the alternative design.

2.3.3 Materia l a nd Process Requ irements

A microphone which is to be used for measurements must be stable over t ime and

its propert ies should preferably not vary with variat ions in ambient temperature,

pressure a nd h umidity. Therefore, carefully selected, high qua lity ma terials must be

used, even if they a re relat ively dif f icult t o ma chine.

The sensitivity of the microphone is inversely proportional to the diaphragm ten-

sion. The tension must therefore be kept stable. Normally i t is a requirement that a

measurement microphone has a broad frequency range and a high sensit ivity. This

creates a requirement for l ight-weight diaphragms with high internal tension and

thus a very high loading of the diaphragm material . This is achieved by applying a

tension of u p to 600 N/mm 2 (which would break most materials) to the diaphragms

Fi g.2.2 Cr oss-Sectional v iew of m icrophone types. The cla ssic type (left) is assembled by screwi ng th e par ts togeth er. The new t ype (r igh t) i s assembl ed by pr essin g component s togeth er. The design is patent ed by Br üel & K jær

950573/1e

Diaphragm

Backplate

Housing

Insulator

Diaphragm

Backplate

Housing

(b)(a)

Insulator

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made from very fine-grained nickel foil or special stainless steel alloy. These differ-

ent d iaphragm mater ia ls are used for the t radi t ional and for the newer

B rüel &Kjær microphones, respect ively. As a result , only slight a nd insignif icant

sagging occurs in the Brü el &Kjær dia phra gm foils.

Carefully controlled heat treatments during the manufacturing process also contrib-

ute to the high stability of the microphones. For most types of microphone the

systema tic sensit ivity cha nge over t ime is thus predicted to be less tha n 1 dB in 500

years at room temperature. For information about the stabili ty characterist ics of

microphones s ee also 2.6 a n d 3.11.

Dia phrag m t ension should a lso be una ffected by temperat ure changes. To ensure

this the thermal expansion of the housing and the diaphragm foil should balance

each other by being essentially equal. This puts strong ties on the selection of these

materials . In part icular , Monel (a high Nickel alloy) is the most frequently em-

ployed housing mater ia l as i t matches the diaphragm mater ia ls and has a h igh

resistance to corrosion.

The distance between the diaphragm and the back-plate is another crit ical parame-

ter. In order to keep this distance constant within the operat ion temperature range,

the thermal expansion of the back-plate must match that of the housing. Strong

restrict ions a re thu s a lso relat ed to the choice of ba ck-plat e ma teria l .

The insulator must also be mechanically stable and its electrical leakage resistance

should be as high as 1017 Ω at normal ambient condit ions. In order to match these

requirements, the insulator is normally made of either sapphire, ruby or mono-

crystall ine quartz . All insulators are machined to a high degree of f latness across

the two plane surfaces ( typically to within 0.5 µm). All surfaces are also highly

polished to achieve the high electrical resista nce tha t chara cterises Brüel &Kjær

microphones. Finally, a thin and invisible layer of silicone is applied to the insulator

by a high temperature process. This ensures proper operat ion in tropical and other

hot and humid environments.

Further requirements are imposed on the microphone design and construct ion by

the polarizat ion voltage that is applied across the diaphragm to backplate gap. As

the distance across the gap is 20 µm a nd t he volta ge is typically 200 V, the field

stren gth becomes 10 kV/mm . This exceeds t he norm a lly considered brea k-down

field strength for air by a factor of 3 to 4. However, the microphone operates be-

cause the distance between electrodes is small enough to prevent the normally

occurring electric ion multiplication from reaching a significant level. The ion multi-

plicat ion that does occur does not escalate and lead to any signif icant discharge or

detectable noise.

Due to the high f ield strength, the diaphragm and the back-plate must have f lat ,

high quality surfaces which are clean and free from part icles. This is necessary to

avoid noise due to arcing within the gap. Therefore, special grinding, polishing,

cleaning and test procedures are applied to the key components. Assembly is per-

formed in a clean-room environment.

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From this brief description of microphone construction, it can be seen that although

the design of the condenser microphone may appear to be very simple, the materi-

als that must be used, the mechanical tolerances and the required propert ies make

production of high quality microphones a task which requires signif icant knowledge

and experience.

2.3.4 Tra nsduct ion P r inciples

The condenser microphone cartridge converts sound pressure to capacitance varia-

t ions. These variat ions in capacitance may be converted to an electrical voltage in

two ways. The most simple conversion method makes use of a constant electrical

charge, which is either permanently built into the microphone cartr idge or applied

to it via the pream plif ier. Toda y t his met hod is used for pra ct ically a ll sound meas-

urements.

However, i t should be mentioned that the capacitance variat ions may also be con-

verted to voltage by using high-frequency circuits. high frequency conversion may

imply frequency or phase modulat ion and may use various types of bridge cou-

plings. In principle, such methods may work to very low frequencies (even to DC)and may therefore be used for infra sound measurements. However, in pract ice the

use of the methods is rare due to their complexity, lack of stabili ty and the relat ive-

ly high inherent noise levels that these methods imply.

Only the constant charge principle will be discussed in the following.

External Polar izat ion Source

The constant charge of the capacitance between the diaphragm and the backplate

may be applied, either from an external voltage source as employed for externally

polarized microphones or from a permanently charged polymer known as electret ,a s employed for prepolarized condenser microphones. Today, t he new er pre-pola riza -

tion principle is widely used, especially for microphones used with hand-held instru-

ments, such a s sound level meters.

The transduction principle of a condenser microphone using external polarization is

il lustrated in Fig.2.3. The capacitor of a condenser microphone is formed by two

plates: the diaphragm and the back-plate . These plates are polarized by an external

volta ge source w hich su pplies a charge via a resistor. The resistan ce of this must be

so high that i t ensures an essentially constant charge on the microphone, even

when its capacitance changes due to the sound pressure on its diaphragm. The

charge must be constant , even at the lowest operat ional frequencies. The value of

the resistor is typically in the range 109 to 10

10

Ω or 1 to 10 G Ω. One of the plates(the diaphragm) may be displaced by the sound pressure while the other plate ( the

back-plate) is stat ionary. Movements lead to distance and capacitance changes and

to a corresponding AC-voltage across the plates. The AC voltage produced is sepa-

ra ted from t he polariza t ion volta ge by a ca pacitor conta ined in the pream plifier. The

instantaneous value of the output voltage may be derived from the formula below:

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where:

A = Area of capa citor plate

C = Ins ta nta neous ca pacita nce betw een pla tes

D o = D ista nce between plates at rest posit ion

d = D ispla cement of moveable pla te (diaphra gm) from rest posit ion

E = Ins ta nta neous vol tage be tween pla tes

E o = Po lar iza t ion vol tage

e = Volta ge change ca used by plate displacement

Q o = Constant charge on pla te capa citor

ε = D ielectr ic constan t of air

Note that the output voltage of the system is proport ional to the displacement of

the moveable plate . This is also the case for large displacements. In other words,

there is a l inear relat ionship between output voltage and displacement , even if the

corresponding capacitance changes are non-linear.

The change in distance is negative for a positive pressure. Therefore, for a positive

polarizat ion voltage which is most commonly used, the phase of the output voltage

is opposite to that of the sound pressure. A positive pressure creates a negative

output voltage and vice versa.

Fig.2 .3 Capaci t i ve Transduct ion Pr in cip le. The constant elect r i - cal char ge used for polar izati on i s suppl ied fr om an ex- ter nal sour ce

950604e

Capacitor

Polarization

Resistor

Microphone Preamplifier

Polarization

VoltageSupply

Amplifier

Back-plate

Pressure

Diaphragm

E C ⋅ Q 0= E ( 0 e )+ ε A⋅D 0

d +-----------------⋅ E 0

ε A⋅D 0

-----------⋅= e E 0

d D 0-------⋅=

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BE1447–11 2 − 13

Electret Polar izat ion

Prepolarized microphones contain an electret. The electret consists of a specially

selected and stabilised, high temperature polymer material which is applied to the

top of the backplate, see Fig.2.4. The electret contains trapped or “frozen” electrical

charges which produce the necessary electrical field in the air gap. The frozen

charge remains inside the electret and stays stable for thousands of years.

The frozen charge is located near to the surface of the polymer which faces the airgap behind the diaphragm. The frozen charge a t t rac ts an equal ly large image

charge of opposite polarity which is moveable. A certain fraction of this lies on the

conducting part of the backplate , while the other part is on the inner surface of the

diaphragm. The relat ive distr ibution between the posit ions is determined by the

rat io between the capacitance of the electret and the capacitance of the air gap.

Fig.2.4 El ectr et polar i zat ion. Th e electret consists of a polymer wh ich contai ns a perm anent or 'f r ozen' electr ical char ge. Th is an d a n i mage cha r ge creat e th e necessar y fi el d betw een t he diap hr agm and th e back-plate

950601e

Frozen charge

Air-gap

Image charge

Diaphragm

Diaphragm

Image charge

Backplate

Backplate

+

– – – – – – – – –

+ + +

++ +

+ +

Electret Layer

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BE1447–11 2 − 15

To ensure a ccura te calibrat ions a nd m easurement s a fter lengthy exposure to an

externa l volta ge (+ 200 V), th e microphone should be st ored w ith zero volts betw een

its terminals for at least 24 hours. This will minimize the risk of errors due to

intermit tent charge displacements and shifts in sensit ivity which might otherwise

be up to a tenth of a decibel

B rüel &Kjæ r introduced prepolar ized mea surement m icrophones in the la te seven-

t ies and showed by experiments and by extrapolat ion of measurement results , that

such microphones could be made very stable and that they could meet all the re-

quirements s et for most a pplica t ions.

Electret microphones intended for consumer applicat ions were well-known at that

time. They used polymer foil diaphragms. The polymer foil served as both a dia-

phragm a nd a s a n e lect re t . B rüel &Kjær found th at th is solut ion w ould not w ork

for a high quality measurement microphone and decided to separate the two func-

t ions of the foil in t he new B rüel &Kjæ r design. Thus, the electret wa s placed on

the top of the back-plate . In this way the electret material could then be selected

for optimal charge stabili ty, while the highly stable metal diaphragm, used for the

existing microphones, could be maintained.

Informa tion about the sta bility char a cterist ics of B rüel &Kjæ r P repolar ized Micro-

phones may be found in Section 3.11 of this ha ndbook.

2. 3.5 D iap hr ag m an d Air S t i ffn es s

The microphone sensitivity is inversely proportional to the stiffness of the dia-

phragm system which, therefore, must be carefully controlled. The dominat ing part

of the st if fness is due to the mechanical tension of the diaphragm which is

stretched like the skin of a drum. The higher the tension, the higher the st if fness

and the lower the microphone sensitivity.

A pressure sensing microphone has an internal air- fi l led cavity which is generally

formed by the housing, the insulator and by the diaphragm. Ideally, there is no

sound pressure in this cavity, therefore, an external pressure will displace the dia-

phragm and produce an electric output signal. However, due to the diaphragm dis-

placement, a minor sound pressure is, in practice, produced in the cavity. This

pressure reacts against the external pressure and reduces the diaphragm displace-

ment by t ypically 10 %. This effect m a y be expressed in term of air-stiffn ess by

s ta t ing tha t th is ma kes 10 % of the t ota l s t i f fness o f the diaphra gm sys tem.

The cavity st i f fness depends part ly on cavity volume and part ly on stat ic pressure.

Therefore, the total stiffness and the sensitivity of the microphone become a func-

tion of sta tic pressure. To minimise t he influence of sta tic pressure on the sensit ivi-

ty of the microphone, the st if fness of the cavity must be small compared to that of

the diaphragm, as defined by the following formula. A microphone with a low dia-

phragm s t i f fness requires a larger cavi ty vo lume than one wi th a h igh diaphragm

stiffness.

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BE1447–11 2 − 17

2.3.7 Low Frequency Response a nd Vent Posit ion

The time constant of the microphone’s pressure equalisation system is typically

0.1 s. This is a good pra ct ica l compromise, a s the equa lisat ion is generally fa st

enough to eliminate any disturbance from changing stat ic pressure. I t also gives the

microphone a f lat ma gnitude response down to less tha n 5 Hz, w hich is sufficient

for most applications.

B elow 10 Hz the frequency response of the microphone is grea t ly influenced by the

pressure equalisat ion t ime constant and by the posit ion of the external vent open-

ing. The vent opening might either be exposed to, or be outside the sound field, see

Fig.2.6. The response is very different in the two cases.

Fi g.2.5 Si de and Rear Vent ed M icr ophones

Fig.2 .6 Pressure Equal i sa t ion Vent posi t i oned in side (B) and outside (A) th e soun d f ield. Th e di ffer ent si tu ati ons lead to di fferent m icr ophone r esponses at low f r equencies

960291e

PressureEqualisation

(a) (b)PressureEqualisation

800114/1e

SoundField

Vent

SoundField

A BVent

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Under general field measurement conditions the vent is exposed to the sound field.

When this is the case the vent will tend to equalise the sound pressure at low

frequencies. This reduces the pressure difference between the front and the rear of

the diaphragm and leads to a smal ler d iaphragm displacement and a lower micro-

phone sensitivity. The lower the frequency the more significant the effect becomes.

The sensitivity will continue to fall with frequency. At very low frequencies the

slope rea ches a m a ximum of 20 dB per decade, see Fig.2.7, lower curve.

The frequency a t w hich the response is down by 3 dB is ca lled the Low er Limit ing

Frequency of the m icrophone. At B rüel &Kjæ r, 250 Hz is norma lly used as the Ref-

erence Frequency as this frequency lies well within the f lat test and most well-

defined pa rt of the frequency response chara cterist ic .

In some measurement circumstances, only the microphone diaphragm is exposed to

the sound field. This is often the case when the microphone is used for measure-

ments in small enclosures such as various types of acoustic couplers. When this isthe case, the response does not fall with decreasing frequency. In fact , i t increases

with fall ing frequency because the fract ion of st i f fness which is due to the react ive

pressure in the internal cavity, becomes smaller as this is equalised through the

vent, see Fig.2.7. The low frequency sensitivity increase is smaller for microphones

ha ving a low fra ct ion of a ir-st if fness.

The lower l imit ing frequency is a funct ion of stat ic pressure, as this determines the

compliance of the internal cavity. Generally, this effect can be ignored, but under

specific circumstances the response may change significantly. This may be the case

in pressurised tanks, diving bells and inside some aircraft . Examples of calculated

magnitude and phase responses are given in Fig.2.8 for an ambient pressure of 0.5,

1.0, 2.0 an d 10 bar a nd for a microphone with 10% a ir st i f fness. Note tha t t hecalculation of the curves did not account for the heat conduction effect of the cavity

walls. The curves are therefore not exact, but still provide a good illustration of the

influence of air pressure on the low frequency response.

Fig.2.7 L ow fr equency r esponse val i d for si t uat i ons where the stat i c pressur e equal i sat ion vent i s i nside (B) an d out si de (A) the sound fi eld

950906e 1 10 Frequency (Hz)100 1 k

2

4

dB

0

– 2

– 4

– 6

– 8

0.1

(A)

(B)

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BE1447–11 2 − 19

The low frequency phase response will also change with the stat ic pressure. Phase

response changes may be more severe than magnitude changes, especially in con-

nect ion with part icle velocity and intensity measurements.

Closely phase-matched pairs of microphone are used for such measurements. The

microphones of a pair are selected to be essentially equal and to change equallywith pressure. Their lower limiting frequencies should be the same. This also ap-

plies to the fraction of their air stiffness. Fig.2.9 shows the phase characterist ics

which correspond to the magnitude responses of Fig.2.8.

For general purpose types of measurement microphone, the lower limiting frequen-

cy is be tween 1Hz and 2Hz , but o ther types wi th longer t ime constants are avai la-

ble for measurements at lower frequencies. Microphones with higher cut-off

frequencies are also available. They may reduce possible disturbance from infra-

sound while doing low level sound measurements in other parts of the frequency

range .

The magnitude and phase response curves which are shown on the above graphsare calculated using a model shown in Sect ion 2.3.10.

Fig.2.8 The magni tu de of the low fr equency m icrophone response is inf luenced by the ambi ent pr essure. Th e responses shown ar e cal culat ed an d ar e al l norm ali zed at 250 H z. Th ey ar e val id for a microphone which has 10% air-st i f fness at nominal ambient pressure (101.3 kPa): a) 1 bar, b) 2 bar, c) 10 bar, d) 0.5 ba r

950908e 1 10 Frequency (Hz)100 1 k

– 3

0

3

6

9

dB

– 6

– 9

– 12

– 150.1

(c)(b)(a)(d)

(c)(b)(a)(d)

Vent unexposed

Vent exposed

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BE1447–11 2 − 21

the diaphragm sys tem is thus s igni f icant ly greater than that o f the diaphragm

itself. Typically, the a ir-ma ss ma kes betw een 10 a nd 50% of th e tota l system ma ss.

As the air mass varies with ambient pressure, i t changes the frequency response at

high frequencies. A microphone with a large fract ion of diaphragm mass should be

selected for applications where large pressure variations occur, for example, in div-

ing tanks, as the frequency response of such microphones changes less with ambi-

ent pressure than that of other microphones.

Other major des ign parameters are the diaphragm diameter and the diaphragm

damping resistance. For condenser microphones, in contradict ion to many other

types o f t ransducer , an opt imal d iaphragm damping may be obta ined and main-

tained over time. Therefore, such types of microphone may be used in the frequency

range around and even above the diaphragm resonance frequency.

The damping is caused by the movement of air in the sli t between the diaphragm

and the back-plate . Diaphragm movements lead to air movements in the sli t which

cause viscous loss. The damping resistance may be controlled by holes in the back-

plate . By changing the number and size of holes and by varying the back-plate 's

distance to the diaphragm, various degrees of damping may be obtained.

The influence of da mping is i l lustra ted by the curves show n in Fig.2.10. In relat ionto these, the resonance frequency was kept constant at 10kHz, which is the typical

resonance frequency for 1″ a nd for high-sensit ivity (50 mV/P a or –26 dB re 1 V per

Pa) 1/2″ microphones. The illustrated degrees of damping may all be obtained in

practice and they are utilized in microphones designed for different purposes.

Fig.2.10 I nf l uence of dampi ng on the high fr equency m icrophone r esponse (magn it ud e). The dampi ng i s du e to movement

of th e air in the sl i t between t he di aphr agm an d backpla te. Th e dam pin g depend s on th e m icr ophone design.Exam pl es of a low (a), cr i t ical (b) and a h igh (c) dam p- in g are shown

950792e

1000

a

b

c

Frequency (Hz)10000 100000

dB

30

20

10

0

– 10

– 20

– 30

– 40100

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BE1447–11 2 − 23

tensions. The phase characterist ics which correspond to the above magnitude char-

acterist ics are shown in Fig.2.12.

The above curves were worked out by using a simple mathematical model. The

parameters of the model correspond to those valid for a series of 1″ 1/2″ a nd 1/4″microphones which ma ke a pa rt of the Brü el &Kjæ r progra m. The sensit ivit ies and

frequency ranges therefore correspond to those valid for some real microphone

types.

The simple models discussed have been chosen to illustrate the influence of themain parameters which determine the microphone response. Other, less important ,

par am eters should be ta ken into a ccount t o rela te the m odels to microphones of the

real world. In part icular , 1/4″ microphones generally cover a wider frequency range

than est imated from the simple models. This is because a resonance between the

diaphragm mass and the compliance o f the a ir in the s l i t behind the diaphragm

may increase the response at higher frequencies and extend the frequency range of

these microphones.

In principle, any microphone could be improved with respect to frequency range if

the diaphragm mass could be reduced. A lower mass would increase the resonance

frequency and thus also the highest operat ion frequency. However, this would mean

that a th inner d iaphragm fo i l should be used, and that the tension in the dia-phragm material i tself would be increased accordingly. This might lead to sagging

and instabili ty in the diaphragm. Therefore, very strong diaphragm materials are

needed when good acoust ic performance and good long term stabili ty are required,

as is the ca se for m easurement microphones.

Fi g.2.12 Phase of fr equency r esponses (pressur e). The cur ves are val id for models of microphone wi th cri t ical damping

and di ffer ent di aphr agm d iameters (rel ati ve scale: 1 (a),0.5 (b), 0.25 (c)). The number s chosen for t he cal cul at ion

appr oxima te th e par ameter s of existi ng 1 ″, 1 / 2 ″ and1 / 4 ″

microphones

950905e

1 k 10 k Frequency (Hz) 100 k

30degrees

0

– 30

– 60

– 90

– 120

– 150

– 180100

(a) (b) (c)

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The above explanat ion shows that the microphone size, the sensit ivity and the fre-

quency range are t ied together and cannot be selected separately. Very often, the

user must make a compromise when select ing a microphone. Generally, small mi-

crophones w ork t o higher frequencies a nd crea te less disturba nce in the sound field,

but they also have lower sensit ivity and higher inherent noise and thus may not be

usa ble at the lowest sound levels of interest .

2.3.9 Microphone Sensit ivi ty

The sensitivity of a measurement microphone may either be expressed in Volts per

P a sca l (V/P a ) or in decibels referr ing t o one Volt per P a sca l (dB re 1 V/P a ). The ter m

“sensit ivity” , generally means the sensit ivity at the Reference Frequency, which is

most often 250 Hz, but in some ca ses this ma y be 1000 Hz. The ma gnitude of the

frequency response characterist ic represents the rat io between the sensit ivity at a

given frequency and that of the Reference Frequency. This ratio is generally ex-

pressed in d B.

The sensitivity of a microphone depends on the type of sound field. Sensitivity is

therefore generally referred to in terms of Free-field, Diffuse-field or Pressure-fieldsensitivit y, see 2.1.5 t o 2.1.7 a n d 2.5. However, at the reference frequency, the sensi-

t ivity is essentia lly equa l for a ll types of sound field.

I t should be noted that pr essur e-fiel d sensiti vi ty refers to the pressure at the dia-

phragm only (by definition). The fr ee-fiel d sensit ivi ty a n d di ffu se-fiel d sensiti vi t y a re

defined for pressure applied at both the diaphragm and pressure equalisat ion vent .

Condenser measurement microphone types generally have a sensit ivity between

1 µ V and 100 µV per Pascal. When designing and selecting a microphone for a

certain application the expected sound pressure level and microphone output volt-

age must be taken into account . A microphone with proper sensit ivity should be

selected. The sensitivity should not be so high that the microphone output signaloverloads the preamplif ier and it should not be so low that i t is exceeded by the

inherent noise of the succeeding amplifiers.

In general , the sensit ivity may be used for ranking microphones with respect to

their abili ty to measure low and high sound pressure levels . The higher the sensi-

t ivity, the lower the sound pressure levels that may be measured and conversely,

the lower the sensit ivity, the higher the sound pressure levels that may be meas-

ured.

The sensit ivity is thus not only l inked to the applicable frequency range as previ-

ously discussed. It is also linked to the dynamic range. The microphone designer

must work with this fact and compose a programme of microphone types which

meets the needs of the user.

Analysis of microphone system limitat ions at low levels shows that inherent noise

of the microphone itself must also be taken into account. This will be discussed in

connection with inherent noise of microphone systems.

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BE1447–11 2 − 25

2.3.10 Microphone Modelling by Eq uivalent Electr ic Circuits

Analysis of electric circuits has been a well-known and widely applied discipline for

ma ny y ear s. Today, very effective computer progra ms h a ve become ava ilab le for the

purpose. This makes the technique very interesting for both microphone designers

and for designers of acoustic systems that include microphones.

To use these tools in designin g microphones, a model must be ma de by converting

acoustic circuit elements to equivalent electric circuit components and by connect-

ing these in series and parallel corresponding to the acoustic circuit . There are two

main analogies, the impedance and the admit tance analogies. The impedance analo-

gy is the generally applied analogy for modelling microphone circuits.

An acoustic compliance which corresponds to reciprocal stiffness is converted to an

electric capacitance. The acoustic mass corresponds to an electric inductance and

a coust ic da mping is represented by a n electr ic resista nce. In such a model, pressure

corresponds to voltage, acoustic volume velocity to electric current and acoustic

displacement to electrical charge.

Combined acoustic, mechanical and electric constructions, like the condenser micro-

phone, may be modelled by simply connecting the acoustic and electric elements

properly under the condit ion that all elements are given in equivalent units . See

the table below.

Microphone designers may use very complex models which take many design de-

ta ils into a ccount a nd a llow calcula t ion of their influence on t he response. For users

or designers of acoustic systems that include microphones, simpler models are gen-

erally suff icient . Models which describe the acoust ic diaphragm impedance as a

function of frequency are frequently applied for determining the influence of the

microphone on the sound pressure of narrow channels or closed cavities, such as

couplers used for calibration of microphones or earphones.

Acoustic Parameter Unit Equivalent Electric Parameter Unit

Sound Pressure Pa = N/m2 Voltage V

Compliance m3 /Pa = m5 /N Capacitance F

Stiffness Pa/m3= N/m5 1/Capacitance

F

-1

Mass kg/m4 = Ns2 /m5 Inductance H

Acoustic Resistance Pas/m3 = Ns/m5 Resistance Ω

Volume Velocity m3 /s Current A

Volume Displacement m3 Charge As

Table 2.1 Acoust ic and Equi valent El ectr ic Param eters used for m odel l in g of condenser microphones

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The equivalent electric circuit shown in Fig.2.13 and the indicated component val-

ues explained in Table 2.2, form a model of a microphone. The example shown

corresponds to a microphone with a diaphragm system resonance of 10kHz which is

crit ically da mped (Qua lity fa ctor, Q = 1) l ike the diaphra gm of a pressure (pressure-

field) microphone.

Such a model may be used for calculat ion of the sensit ivity and the frequency

response (magnitude and phase) which may be found with and without sound pres-

sure at the stat ic pressure equalisat ion vent . I t may also be used to determine the

complex acoust ic diaphragm impedance as well as the electrical impedance. In addi-

t ion, the inherent electric noise of the microphone may be calculated as this may be

referred to th e noise of the resista nce elements (also known a s Nyq uist a nd J ohn-

son Noise).

This type of model is commonly used for calculation of the response of the micro-

phone, as previously described in this section. The model is also used for describing

other microphone properties. This is discussed in the following sections.

Fig.2.13 M icrophone model . Th e components of th e equival ent electr i cal cir cui t r epr esent stif fn esses, ma sses an d d am p-

i ng of t he el ectr o-mecha ni cal system . Th e r espon se of th e model depends on t he exposur e to soun d pr essur e of th e stat ic pr essur e equa li zati on vent (exposed: (3) conn ected to (1); un exposed : (3) to (2))

950933e

Rv

C2

ElectricTerminals

AcousticTerminals

PressureEqualization

Vent

Diaphragm

Common

C1 C3

Cd Ld Ls Rs

Cc

Cc1

3

2

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BE1447–11 2 − 27

2.3.11 Acoustic Impeda nce of Diaphra gm Sy stem

In cases where microphones are used in small cavit ies and narrow channels, i t may

be necessary to evaluate and correct for the influence of the microphone on the

a coust ic system.

This is usually done by using a model which is even simpler than that shown above

in Fig.2.13. The very simple model shown in Fig.2.14 may only be used if the

diaphragm (not the stat ic pressure equalizat ion vent) is exposed to the sound pres-

sure and if the microphone is essentially unloaded on the electrical terminals . Val-

ues of the circuit elements which correspond to those of the more complex model

are given in Ta ble 2.3. Such values are often stated by microphone manufacturers

for the purpose of impedance calculations.

The values of the diaphragm system (ds) elements may be calculated from those

given in Section 2.3.10 by using the formulae below:

Symbol Model Element Value Unit

Cd Diaphragm Compliance 0.314 × 10–12 m5 /N

Ld Diaphragm Mass 600 kg/m4

Ls Acoustic Mass of slit behind diaphragm 296 kg/m4

Rs Acoustic Resistance of slit behind diaphragm 56.2 × 106 Ns/m5

Cc Acoustic Compliance of internal cavity 2.83 × 10–12 m5 /N

Rv Acoustic Resistance of pressure equalisation vent 36 × 109 Ns/m5

C1 Acoustic Coupling Compliance 5.66 × 10–12 m5 /N

C2 Coupling Compliance/Capacitance –5.66 × 10–12 m5 /N or F

C3 Electrical Coupling Capacitance 5.66 × 10–12 F

Ce Electrical Capacitance (when diaphragm is blocked) 17 × 10–12 F

Table 2.2 Valu es of th e m icrophone model elements whi ch ar e shown i n Fig.2.13 . The model corr e- sponds to a mi crophone (50 mV/ Pa) havin g a cri t ical ly dam ped di aphr agm w ith resonance at 10 kH z

C d s

C d C c ⋅

C d C c +-------------------- L d s L d L s += = R d s R s =

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The diaphragm system impedance (Z ds ) may by calculated by using the formula

below:

2.3.12 Eq uiva lent Volume of the D iaphra gm S ystem

The acoustic impedance of a microphone diaphragm may be expressed in terms of

equivalent volume. The equivalent volume, which is complex, is a function of fre-

quency. At low frequencies i t is essentially real and constant , while i t varies with

frequency at high frequencies where the imaginary part dominates, see Fig.2.15.

The use of equivalent volume, instead of diaphragm impedance, often makes itmore easy t o eva lua te th e influence of a microphone on the sound pressure of small

acoustic systems, such as calibration coupler cavities. The equivalent volume of a

diaphragm is the volume of air which has the same compliance or impedance as

that o f the diaphragm.

The acoustic compliance (C a ) of a volume of gas is given by the following formula:

Fi g.2.14 Sim pl i f ied model r epr esenti ng the acoust ical im pedance of a m icr ophone. Some manu factur er s stat e th e model par ameter s for r el evan t m icrophone types

Symbol Model Element Value Unit

C ds Diaphragm System Compliance 2.83 × 10–13

m5 /N

Lds Diaphragm System Mass 896 kg/m4

R ds Diaphragm System Resistance 56.2 × 106Ns/m5

Table 2.3 Values of the sim pl i f i ed mi crophone model shown in Fig.2.14 . Th e model r epr esent s the acousti c di aphr agm i mp edan ce of the m icr ophone model shown i n Fig.2.13

950934e

Cds Lds Rds

Acoustic

Terminals

Z d s 1

j ωC d s -----------------+ j ωL d s +R d s Ns/m5=

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BE1447–11 2 − 29

Accordingly the compliance of a diaphragm system (C ds ) is:

The formula for calculat ion of equivalent diaphragm volume from diaphragm sys-

tem impedance is derived from these equat ions and from the general equat ion:

The Equivalent Diaphra gm S ystem volume is thus :

V e is complex as Z d is complex.

The equivalent diaphragm volume may be calculated as a funct ion of frequency by

using the formula below when the previously mentioned simple C–L–R model, see

Section 2.3.11, is considered

where :

C ds = Diaphra gm sys tem complia nce

L ds = D iaphragm sys t em mass

R ds = Diaphragm sys tem res is tance

where

γ = Ra tio of specif ic temperat ures of the ga s (1.402 for air )

P s = S t a t i c p ressure of t he gas in t he cav i t y

V = Vol um e of ca v it y

where V e = Equivalent d iaphragm volume

where Z ds = Diaphragm sys tem impedance

C a V

γ P s ⋅-------------=

C d s

V e γ P s ⋅-------------=

Z

1

j ωC -----------=

V e

γ P s ⋅

j ωZ d s ----------------=

V e

γ P s ⋅

j ω j ωC d s ( ) 1– j ωL d s R d s + +[ ]

------------------------------------------------------------------------------=

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Alterna t ively, th e complex equiva lent volume ma y be ca lculat ed from a nother set of

pa ra m et ers a s t he a bove eq ua t ion m ay be w r it ten a s:

where:

V e(l f ) = L ow frequency equivalent d iaphragm volume

f o = Dia phragm sys tem resona nce f requency

Q = Diaphragm sys tem qual i ty fac tor

The second set of parameters may be calculated from the f irst set as :

Both sets of parameters are used in pract ice. The complex equivalent volume is

especially applied in connection with the calibrat ion of Laboratory Standard Micro-

phones and in connection with measurements made on human and art if icial ears.

The calculated equivalent diaphragm system volume of the microphone model

shown in t he previous sect ion, is sh own in Fig.2.15.

Fi g.2.15 Real and i magin ary par t of Equi valent Volume calculated wi th t he values of Table 2.3.N oti ce that th e im aginar y part i s negative

V e f [ ] V e l f [ ] 1f 2

f 0

2----– j

f f 0

---- Q 1–⋅+

1–

⋅=

V e l f [ ] γ P s C d s f 0⋅ ⋅ 2π C d s L d s ⋅( )1–

Q L d s

C d s ---------- R d s

2–⋅= = =

950910e

100 Frequency (Hz)1 k 10 k 100 k

mm3

50

40Ve(r)

– Ve(i)

30

20

10

0

– 10

– 2010

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Ch a pter 2 — Microphone TheoryCombination of Microphone and Preamplifier


BE1447–11 2 − 31

In pract ice, the equivalent volume of measurement microphone diaphragms de-

pends on the type of microphone. The total range varies from about a tenth of a

cubic millimetre to some hundred cubic millimetres. The diameter of the micro-

phone diaphragm has a great influence on the volume (fourth power) . Pressure

microphones in a 1″ size have ty pical volumes of 130 to 160 mm 3, while correspond-

in g 1/2″ microphones ha ve a m uch smaller volume of approxima tely 10 mm 3. The

diaphragm volumes of 1/4″ a n d 1/8″ microphones are correspondingly smaller. The

equivalent volume is also a funct ion of the diaphragm tension, therefore, the high-

sensit ivity 1/2″ microphones which have lower diaphragm tension have greater

equivalent volume, typica lly 40 mm 3.

2.4 Combina t ion of Microphone a nd Preamplif ier

The condenser microphone generates electrical signals. These signals need to be

transferred to associated equipment such as an analyzer or recorder which may be

placed in some dista nce from th e microphone itself. B eca use th e microphone has a

very high electrical impedance it cannot withstand the load made up by the instru-

ment a nd t he cable which is necessary. To minimize the loading a nd t o ensure th a teven very long cables (perhaps several hundred metres) may be used, specific mi-

crophone preamplifiers are employed.

Some microphone syst em propert ies a re determined by the preamplif ier in combina -

tion with the microphone. This applies for the electrical frequency response func-

t ion, especially for the lower l imit ing frequency and for the dynamic range which is

limited by inherent noise a nd d istort ion.

2.4.1 Microphone Ca pac it a nce

The microphone is an electrical source with an impedance which is determined byits capacitance. The capacitance is mainly made up by the act ive capacitance be-

tween the diaphragm and the backpla te and by the s t ray capaci tance o f the micro-

phone housing.

However, the microphone capacitance is also influenced by mechanical properties of

the diaphragm system. This is especially the case for those microphone types which

have the highest sensitivities. At low frequencies, the electro-mechanical coupling

a dds to th e ca pacita nce (by up t o 15%) w hile it s ubtra cts capa cita nce above the

diaphra gm resonan ce (1–2%) w here the pha se of the d ia phra gm movements is op-

posite . Due to the low input capacitance of the preamplif iers used, these rather

small capacitance variat ions are generally ignored.

The capacitance of condenser measurement microphone types is a function of micro-

phone size a nd it va ries from a bout 3 pF for 1/8″ microphones to 70 pF for 1″ micro-

phones.

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2.4.2 Electrica l Frequency Response of Microphone a nd P reamplif ier

To minimize the loading effect on the m icrophone a s described a t t he sta rt of this

section, the microphone is screwed directly on a preamplifier. The preamplifier has

a high input impedance which is generally described in terms of input resistance

(t yp ica l ly 1 – 100 G Ω) a nd input ca pacita nce (ty pica lly 0.1– 1 pF). The electrical v olt-

age gain is generally very close to unity, corresponding to “0 dB”.

The preamplif ier should preferably withstand loading from even very long cables.

The out put resist a nce is ther efore low (typically 10 – 100Ω). As the amplifier output

is resist ive and the cable loading is ca pacit ive (typically 50 – 100 pF/m) the influ-

ence of the loading, i f any, will be most signif icant at the highest frequencies. Due

to the low output impedance of the preamplif ier , the input resistance and capaci-

ta nce of most succeeding inst ruments (1 MΩ a nd 50 pF) can be ignored.

Modern preamplif iers are able to transfer voltages within a very wide dynamic

range, from about 1 µV to 50 V, i.e. more tha n 150 dB .

The capacitance of the microphone which makes the electrical source may be re-garded as being essentially constant when the microphone is used with a modern

preamplif ier with a low input capacitance.

The combined electrical circuit of the microphone and the preamplifier is shown in

Fig.2.16. In addit ion, a set of typical circuit element values valid with a 1/2″ micro-

phone is given in the table below.

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BE1447–11 2 − 33

The electrical frequency response of the circuit is given by the formula below:

Circuit Element Symbol Typical Value

Open circuit microphone voltage voc 1 µV to 50V

Microphone Capacitance Cm 18 pF (1 / 2″ microphone)

Preamplifier Input Capacitance Ci 0.2 pF

Preamplifier Input Resistance Ri 10 GΩ

Amplifier Gain g 0.995

Preamplifier Output Resistance Ro 30 Ω

Cable Capacitance Cc 3 nF (corresponding to 30 m)

Output Voltage vo 1µV to 50 V

Table 2.4 Valu es of El ectr ical Cir cui t El ements of the sim pl i f ied m odel , see Fig.2.16 w hich r epr e- sent s th e m icr ophone capacita nce, preampl if ier and cable of a typi cal m i crophone system

( 1/2″ ). The model may be u sed for ca l cu l at i on of the electr i cal f r equ ency r espon se of a m icr ophone system. Oft en, onl y t he acousti c response is ta ken i nt o accoun t , as the el ectr ic r esponse i s general ly fl at ; see Fig.2.17 and Fig.2.18

Fig.2.16 Sim ple model for calculat i on of the electr ical frequency response of a microphone and its preampli f ier loaded wi th a cable. The el ectr ical r esponse shoul d be combi ned wi th t he acousto-mecha ni cal r esponse of the m icr ophone to obtai n t h e over-al l system r esponse

950892e

Microphone Preamplifier Cable

Ro

Ri

g

CcCi

Cm

VoVoc

v o v oc --------

C m

C m C i +---------------------

j ω C m C i +( )R i 1 j ω C m C i +( )R i +------------------------------------------------- g

1

1 j ωC c R o +------------------------------⋅ ⋅ ⋅=

G C m

C m C i +--------------------- g ⋅=

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The magnitude and phase of a typical electrical frequency response which corre-

sponds to the values given in the table are shown in Fig.2.17 a n d Fig.2.18 respec-

tively.

The constant magnitude rat io in the mid frequency range is determined by the

capa cita nce rat io (f irst fa ctor) an d by the a mplifier ga in (g). Their product is na med

“G ” in the B rüel &Kjæ r ca librat ion li terat ure an d on ca librat ion chart s . The low

frequency roll-off is determined by the input circuit and the high frequency roll-off

by t he output circuit .

Fi g.2.17 M agni tu de of the electri cal f r equency response cal culat ed w it h th e valu es of Table 2.4. Th e r esponse is fl at w it hi n a w i de ra nge in clu di ng th e fr equency ra nge wh er e acousti cal measur ement s are most commonly perf orm ed

Fi g.2.18 Phase of the electr ical f r equency response calculated w it h t he values of Table 2.4. The response i s fl at w it hi n a w id e r ange and meets the requi r ement s for most a cousti cal measur e- ments

G d B [ ] 20 logC m

C m C i +---------------------

g d B [ ]+⋅=

10 100 1 k

M a g n

i t u d e

( d B )

10 k

2

1

0

– 1

– 2

– 3

– 4

– 5

– 61 100 k 1 MFrequency (Hz)

950893e

10 100 1 k

P h a s e ( d e g . )

10 k

60

45

30

15

0

– 15

– 30

– 45

– 601 100 k 1 M

Frequency (Hz)950894e

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measure lower signal levels (depending on the type of acoustic signal). By using

bandwidths of 1Hz, levels of –35 to –25 dB may be measured in the audible part of

the frequency range. According to internat ional sound measurement standards,

measurements must be performed with a signal to noise rat io of at least 5dB. The

graph in Fig.2.19 shows how non-correlated system noise adds to the sound pres-

sure level and increases the instrument reading.

The noise of a measurement system is composed by microphone noise, preamplifier

noise and noise from the succeeding measurement amplifier. The graph, see

Fig.2.20, illustrates the contribution of each of these three sources for a typical 1 ″microphone system. The noise voltages of the preamplif ier and the measurement

am plifier were converted t o equiva lent SP L by dividing th e noise volta ge by the

microphone sensitivity. The noise from the measurement amplifier contributes to

the system noise at higher frequencies where it is of same order of magnitude as

the preamplifier noise. At low frequencies, the preamplifier noise dominates while

the microphone noise is domina t ing from a bout 200 H z to 10kH z.

Microphone Noise

The noise produced by the microphone is basicly due to thermal or Brownian move-

ments of the diaphragm and is thus a funct ion of the absolute temperature. In

connection with microphone design and selection for specific purposes, noise estima-

t ion or analysis may be made in a very pract ical way by using equivalent circuit

models. Acoustic resistances, which produce noise like electrical resistances, make

the sources of the microphone while the reactive circuit elements do not produce

any noise. There are two sources (resistances) in a microphone, see the equivalent

circuit model shown in Fig.2.13. The diaphragm damping res is tance and the s ta t ic

pressure equalisation resistance. The noise pressure produced by an acoustic resist-

ance is defined by the formula below.

Fig.2.19 Add i t ion of Noise

10

5

2

1

0.5

0.2

0.1

0.05

0.02

0.010 2

E r r o r ( S + N ) / S ( d B )

4 6 8 10 12

S + N reading (dB) - N reading (dB)

14 16 18 20

960238e

p n 4 k T R a ⋅ ⋅ ⋅ f ∆⋅=

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Microphone S yst em N oise

Noise spectra valid for microphone systems equipped with free-field microphones of

different sizes are shown in Fig.2.22. For smaller and less sensitive microphones, in

sizes such as 1/4″ a n d 1/8″, only the preamplifier noise needs to be taken into ac-

count, as this dominates over the microphone noise.

Syst em With E xtremely Low Inherent Noise

A specific method of lowering microphone system noise can be applied for the de-

sign of a system with extremely low inherent noise. The method is based on the

idea o f reducing the diaphragm damping res is tance as th is makes up the main

noise source of the microphone. This will lower the noise, but it will also create a

peak on the frequency response at the diaphragm resonance frequency. However,

this peak may be equalized by an electrical network which can be combined with

Fi g.2.20 Equi valent levels of i nherent noise (1/ 3 octave bandw id th) pr oduced by the elements of a system equi pped w it h a 1 ″ free-field m icrophone (50mV/ Pa). Th e m icrophone, th e pr eam pl i-

fi er an d th e measur ement am pl i f ier ar e al l sign if icant n oise sources in cer tai n par ts of th e fr equency ran ge

951155/1e

dB

re. 20 µPa

5

0

– 5

– 10

– 15

– 20

– 25

– 30

8 16 31.5 63 125 250 500 1 k 2 k 4 k 8 k 16 kFrequency (Hz)

a) Complete system

b) Preamplifier + Measurement Amplifier

c) Measurement Amplifier

31.5 k

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BE1447–11 2 − 39

the preamplifier. This technique, which requires careful control with the micro-

phone resonance frequency and Q-factor, has lead to the development of a system

w ith a n equivalent in herent noise level as low a s –2 dB (A), see Fig.2.23.

2.4.4 D ist or tion

Both the microphone and the preamplif ier may distort the output signal. The dis-

tort ion which is produced by the microphone is the dominat ing component withinthe major part of the dynamic range while preamplif ier distort ion may only be

detected close to the clipping limit at the highest operational levels.

Fi g.2.21 Th ir d O ctave N oise Spectr a of a system consistin g of a f r ee-field m icrophone ( 1 /2″, 50 mV/ Pa) and a hi gh qual i t y pream pli f i er. The el ectri cal pr eam pl i f i er n oise domi nat es at low fr e- quencies wh i le Br owni an m ovement s of the m i cr ophone di aphr agm cr eate th e most signi fi - cant noise at hi gh fr equencies. The colum ns to th e r igh t show L in ear (20 H z – 20 kH z) (L )

and A-weighted (A ) noise l evels for th e m icr ophone (M ), pream pli f i er (P) and combin ati on (C)

– 10

– 5

0

5

10

15

940718e

20

10 1 k 10 k100

Sound Pressure Levelre 20 µPa (dB)

Frequency (Hz)

M P C

Preamplifier

Microphone

20 k

Microphoneand

PreamplifierCombination

L

A

L

A

L

A

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Microphone Distortion

Microphone distort ion ( in t he frequency ran ge where t he dia phra gm d ispla cement is

st if fness controlled) , is caused by passive capacitance in parallel with the act ive

diaphragm capacitance. This passive capacitance is made up by the backplate-hous-

Fi g.2.22 Th i rd Octave N oi se Spectr a of fr ee-field m icr ophone system s. The lar ger an d m ost sensiti ve m icr ophones shoul d be used f or l ow l evel measur ement s. Th e m i crophone noise is most sign if icant in such system s. The preampli f i er noise is most sign if icant in system s wi th smal l and l ess sensiti ve m icr ophones

950941e

35

40

30

dB

re. 20 µPa

1/4" (4 mV/Pa)

1/2" (12.5 mV/Pa)

1/2" (50 mV/Pa)

1/1" (50 mV/Pa)

25

20

15

10

5

0

– 5

– 10

8 16 31.5 63 125 250 500 1 k 2 k 4 k 8 k 16 kFrequency (Hz)31.5 k 63 k

8/9/2019 be1447




BE1447–11 2 − 41

ing capacitance, preamplif ier input capacitance and to some degree by parts of the

diaphragm capacitance which are less act ive than others. Passive capacitance leads

to a dominat ing second harmonic distort ion which increases proport ionally with the

sound pressure and a less signif icant third harmonic component which increases by

the square of the pressure.

The microphone distortion is practically proportional to the parallel, or stray capaci-

ta nce. Br üel &Kjær ha s patent ed a m ethod for reduction of microphone system dis-

tort ion which implies the applicat ion of negat ive preamplif ier input capacitance for

equa lizat ion of the pa ssive pa rt of the microphone capa cita nce.

Microphone distortion is proportional to diaphragm displacement. Therefore, small-

er and less sensitive microphones produce less distortion than larger microphones

do at the same sound pressure. However, as the parallel capacitance of a small

microphone is relat ively larger than that of a larger microphone the reduction in

Fi g.2.23 Equi valent levels of i nherent noise (1/ 3 octave bandw idt h) pr oduced by t he elements of a low noise system wi th a specia l 1 ″ free-f ield m icrophone (100 mV/ Pa and low di aphr agm

dam ping). The mi cr ophone and th e pr eampl i f i er (20 dB gain) w hi ch contai ns a fr equency r esponse equa li zati on n etw ork, form th e mai n n oise sour ces. Th e system n oise level is –2 dB (A )

dBre. 20 µPa

5

0

– 5

– 10

– 15

– 20

– 25

– 30

8 16 31.5 63 125 250 500 1 k 2 k 4 k 8 k 16 kFrequency (Hz)

a) Complete system

b) Preamplifier + Measurement Amplifier

c) Measurement Amplifier

31.5 k

951156e

8/9/2019 be1447





distortion does not fully follow the sensitivity reduction. This can, for example, be

seen in the sensit ivity and distort ion differences between a 1/2″ a n d a 1/4″ micro-

phone. The difference in sensitivity is 22dB, while the difference in distortion is

only 15dB .

P reamplifier a nd M icrophone System Distor t ion

The preamplif ier distort ion may generally be ignored as this is much lower than

the microphone distortion. This is the case at levels up to a few decibels below the

upper operat ion limit where clipping occurs and makes the system unusable, see

Fig.2.24. The resul t s shown in the f igure are obta ined w i th a Br üel&K jær High

P ressure a nd L ow Frequency C a librat or, Type 4221.

Fig.2 .24 Di stor t ion of m icrophone (M ) and of m icrophone-pr eampl i f ier combinat ion (C). The preampl i f ier distort ion wh i ch pl ays th e m i nor r ole is just n oticeable at t he hi gh- est measur able levels. Th e di stort ion is val id for a fr ee-

field microphone ( 1/2″, 50m V/ Pa). I t is measur ed at

90 H z and i s r epr esent ati ve for th at par t of the fr equency r ange wh ere the diaph ragm di splacement is domin antl y cont r ol led by sti ffn ess

0.1

1

0.01

940498e

155145135125

Distortion (%)

SPL (dB)

10

3rd

Harmonic

C

M

M

C

2nd

Harmonic

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Ch a pter 2 — Microphone TheoryMicrophone Types Dedicated to Different Sound Fields


BE1447–11 2 − 43

Distor t ion Due to Large Paral lel Capacitors

Most often the preamplifier has only a minor influence on the microphone distor-

t ion a s i t only a dds 0.2 to 0.5 pF to i ts pa ssive pa ra llel ca pacita nce. However, when

a large passive capacitor is used for extending the frequency response to lower

frequencies this will have great influence on the distort ion which may increase by a

factor of five or more, see Section 2.4.2.

2.5 Microphone Types Dedica ted to Di f ferent S ound Fields

When a microphone is placed in the sound field which it is to measure, it will

influence the field and change the sound pressure. This change needs to be taken

into account as i t would otherwise lead to a measurement error. Depending on the

type of f ield and on the type of microphone the influence may be so small that i t is

insignif icant . However, i t may also amount to several decibels which would be an

unacceptable error for most measurements. Microphone types designed for specific

applicat ions may correct for the influence under certain circumstances, while in

other cases th e user must evalua te, a nd if possible, correct for t he influence.

Three different types of sound field are generally considered in connection with

acoustic measurements, namely the pressure-field, the free-field and the diffuse-

field. The influence of the microphone depends on the type of sound field, on the

microphone dimensions a nd t o a minor degree, on its dia phra gm im pedance.

2.5.1 Influence of the Microphone on th e P ressure-Field

A pressure-field generally occurs in a small closed cavity (see Section 2.1.5) which,

for example, may make a part of an art if icial ear used for the test ing of telephones

or hear ing a ids. To measu re the sound pressure in such a cavit y, the microphone isgeneral ly bui l t in to the coupler in a way that makes the diaphragm a par t o f the

coupler cavity wall . Because the diaphragm is not as st i f f as the wall of the coupler,

i t deflects due to th e sound pressure a nd loa ds t he cavity a coust ically.

The influence of the microphone depends on the size and shape of the coupler and

on the microphone diaphragm impedance. Very often, art i f icial ears are used up to

such high frequencies that standing waves occur in the coupler. Depending on the

coupler cavity shape, i t may be quite complicated to determine the influence of the

microphone. I t is simpler in ca ses wh ere the coupler m akes a cylindrical cavity w ith

the sound source and a microphone is mounted at each end. In this configurat ion

the coupler acts as an acoust ic transmission line which connects the source to the

microphone, see Fig.2.25. The transfer funct ion and the microphone influence maythen be determined by the general transmission line theory by taking its character-

istic impedance, its complex propagation coefficient and its length into account, see

Fig.2.26 (a).

At lower frequencies, where standing waves do not occur, the circuit may be further

simplified to take only the compliances into account. They represent the reciprocal

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stiffnesses of the source, the coupler cavity and the microphone diaphragm, see

Fig.2.26 (b) . In such cases i t is very pract ical to work with equivalent volumes of

the source and the loading microphone.

Most couplers a re equipped w ith a sta t ic pressure equ alisa t ion vent . The impedance

of this should be taken into account i f the model is also to be used at the lowest

frequencies.

The sound pressure attenuation due to the microphone is given by the following

formula:

Fig.2.25 Schematic diagram of coupler used for h eadphone testing

Fig.2.26 M odel of headphone coupl er using acoust ic tran sm ission l i ne (upper ci r cui t) and sim pl i f ied model ( lower ci r cui t) .Onl y th e fi rst m odel shoul d b e used at hi gh fr equencies.

Th e m icr ophone is r epr esent ed by i ts comp lex im peda nce (Z ds ) and by the l ow fr equency val ue of i t s equ i val ent

volum e V e (l f) r especti vely

Diaphragm

Coupler

Diaphragm

MicrophoneTelephone

Coupler Cavity

950939e

950940e

psource

Zsource

Csource

Ccoupler Cds

Zds

Za,0, γ , I0

a)

b)

psource

a t ten u a t i on d B [ ] 20V coup ler V e sou r ce , V e l f [ ]+ +

V coup ler V e sou r ce ,+------------------------------------------------------------------------------

log⋅=

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BE1447–11 2 − 45

where:

V coupler = coupler volume

V e,sour ce = equivalent volume of source

V e [l f ] = equiva len t volume of microphone d iaphragm sys t em

In practice, 1″ microphones are used with larger couplers (3 – 10 cubic centimetres)

which may be used for headphone test ing while1/2″ microphones are used with

smaller couplers of 1 to 3 cubic centimetres, for example, those designed for insert

earphone test ing.

As the equivalent diaphragm volume of a 1″ microphone is typically 0.16 cubic

centimetres the microphone will in pract ice at tenuate the sound pressure produced

in such a coupler by 0.5 dB to 0.15 dB, depending on its size.

For smaller couplers with 1/2″ microphones, the influence is typically smaller. The

microphone types may in practice be placed in one of two groups depending on their

equivalent volume, which may either be about 0.010 or 0.045 cubic centimetres.

Those with a low volume are most frequently applied in couplers. Here their influ-

ence is relat ively less than that of the larger microphones on the above mentionedcoupler sizes.

2.5.2 P ressure Field Microphone and Sensi t iv ity

The frequency response characteristic of a pressure-field microphone is optimised to

be as f lat as possible when its output voltage is referred to a uniform pressure on

the outer surface of i ts diaphragm.

Ideally, the diaphragm should be as st i f f as the walls of the coupler within which it

is applied. As this is not possible, i ts influence may be est imated and taken into

a ccount by using equ ivalent volume or tra nsmission line ca lculat ions.

2.5.3 Influence of Microphone on th e Measured Sound P ressure in a F ree-Field

A free-field exists where a sound wave propagates in a certain direct ion without

being disturbed by any reflecting objects (see Section 2.1.6). However, to measure

the sound pressure in a free-field, a microphone must obviously be placed in that

f ield. The microphone will change the sound field as i t will dif fract and reflect the

sound wave, see Fig.2.27. As a result , the pressure act ing on the microphone dia-

phragm will deviate from that of the measurement point in the undisturbed f ield

which was to be measured. The deviat ion may lead to a measurement error unless

a correction is made.

The ra t io be tween the pressure a t the diaphragm and that o f the undis turbed

sound field is a funct ion of the rat io between the microphone diameter and the

wavelength. Pressure rat io funct ions look alike for smaller and larger microphone

types, but they are shif ted within the frequency range depending on the diameter of

the microphone body. This is illustrated in Fig.2.28 which shows the order of mag-

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nitude of the pressure ratio valid for sound incidence perpendicular to the front of

the microphone (zero degrees) for different sizes of microphone.

For m ost pra ct ica l mea surements t he m icrophone diaphra gm needs t o be covered by

a protect ion grid. This grid will also influence the pressure at the diaphragm as i t

acts as an acoustic resonator. The influence of protection grids is generally very low

below 1kHz, but i t increases signif icant ly with frequency. Fig.2.29 shows a typica l

contribution of a 1/2″ protection grid to the pressure increase at the microphone

diaphragm (zero degree incidence).

The resulting influence of the body of a 1/2″ microphone and the protection grid is

shown in Fig.2.30 (upper curve). The influence of the microphone on the pressure of

a free-field is so great that i t needs to be taken into account to avoid considerable

measurement errors.

Fig .2.27 Sim pl i f ied i l lus t ra t ion of the di stur bance of a plane soun d wave caused by a m i crophone body. The pressur e at t he posi t ion of the di aphr agm deviates signi f icant ly fr om th at of the un di stu r bed fi eld a t h igh er f r equencies.Th is effect m ust be tak en i nt o account to avoid l ar ge and un accept abl e measur ement er r ors

950938e

Measurement Point

Microphone

UndisturbedSound Field

DisturbedSound Field

Sound

PropagationDirection

SoundPropagation

Direction

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BE1447–11 2 − 47

The influences of both microphone body and protection grid differ with the angle of

sound incidence on the microphone body. For a ll Br üel &K jær m icrophones the in-

fluence is analysed and stated for a number of specific angles of incidence. There-

fore, a correction may be made for the above effect, if the angle of sound incidence

is known.

Fig.2.28 Rati o between t he pr essur e at th e diaph ra gm posi t ion and the pressure of the undisturbed sound field. The

same pressure changes occur for bodies of larger and smal l er body d iam eter, but th e fr equency ra nge i s shi fted and is inversely pr opor ti onal t o th e di ameter of th e m i-

crophone body

Fig.2 .29 Typ ica l i n f lu ence of pr otect ion gr id ( 1 / 2 ″ microphone)

sound in cid ence perpend icular to the diaph ragm . The gr i d acts as an acousti c r esona tor

950960e 100 1 k 10 k

1/1" 1/2"

1/4"

100 k

– 5

0

5

10

dB

Frequency (Hz)

950944e

100 1 k Frequency (Hz)10 k 100 k

dB

10

5

0

– 5

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2.5.4 Free-Field Microphone a nd Sensit ivity

The correction for the influence of the microphone body on the sound field can be

made by post-processing of measured sound spectra, but the compensat ion might

also be built into the microphone itself. This is the case for the so called Free-field

microphone types which have a flat free-field frequency response characteristic to

sound waves that are perpendicular to the diaphragm (at zero degree incidence) .

The compensat ion is made by introducing a heavy damping of the diaphragm reso-

nance, see the lower curve in Fig.2.10, Section 2.3.8. By proper design, the degree

of damping may be chosen to give a decreasing diaphragm system sensit ivity with

frequency, see Fig.2.30, lower curve which corresponds to the above mentioned in-

creasing sound pressure on the diaphragm, see Fig.2.30, upper curve. This leads to

a frequency response characterist ic which is essentially f lat in a free-field when the

output voltage is referred to the sound pressure of the undisturbed free-field. The

product (or the sum, when decibels are applied) of the relative pressure increase

and the diaphragm system sensit ivity is constant over the frequency range, see the

middle curve shown in Fig.2.30.

The pressure increase on the diaphragm may be used for extending the frequency

range of free-field microphone types at higher frequencies. Therefore, free-field mi-

crophones cover wider frequency ranges than equally large and equally sensit ive

P ressure-field microphone ty pes wh ich ha ve a fla t pr essure-field response. The ex-

tension t ypica lly equa ls one octave.

The rat io between the diaphragm pressure and the undisturbed free-field pressure

is generally expressed in decibels. This ratio is essentially the same for all micro-

Fi g.2.30 Pressur e at di aphr agm posi t ion referr ed to the pr essur e of the un di stu r bed fi eld i nclud i ng in flu ence of protecti on gr id , O ° in cid ence (upper cur ve). Th e fr ee-fi el d r esponse of the m icr ophone (mi dd le curve) is fla t as the m icrophone is designed to have a pressure response (lower curv e) wh ich fal ls w it h f requency and compensates for the i ncr ease of pr essu r e. Th e cur ves of th e exam pl e ap-

pr oxim ate th ose val id f or a 1 / 2 ″ mi cr ophone

950943e

100 1 k Frequency (Hz)10 k 100 k

15

dB

5

10

0

– 5

– 10

– 15

8/9/2019 be1447




BE1447–11 2 − 49

phones of the same type, as their dimensions are the same, (although the rat io

depends slight ly on the diaphragm impedance as well) . Therefore, i t is determined

in connection w ith t he development of any new B rüel &Kjær microphone type. The

measured number is generally called the free-field correction.

As described above, the free-field correction corresponds to change in sound pres-

sure which is due to the presence of the microphone body in the sound field.

The free-field correction may, therefore, be used for determining the individual free-

field response characteristic of a microphone. This is done by adding the correction

to the individual pressure response or to the so called, electrostat ic actuator re-

sponse. In pract ice, this is a great advantage as those responses are less cost ly to

determine. This is especially t he case for t he a ctuat or response. Most B rüel &Kjær

free-field and diffuse-field corrections refer to the electrostatic actuator response.

2.5.5 Inf luence of the Microphone on t he Mea sured Sound P ressure in a Dif fuse

Field

The sound pressure of a certain point in a diffuse-field is created by waves which

over a certain t ime impinge to that point from all direct ions. To measure the pres-

sure, a microphone must be placed in the field. However, the microphone is not

equally sensit ive to sound waves coming from different direct ions as the pressure

change, due to the presence of the microphone and a possible protection grid, is

different for different angles.

Fig.2.31 shows free-field corrections for a 1/2″ microphone without protection grid.

These were measured for the a ngles betw een zero and 180 degrees in steps of

5 d eg r ees.

The above free-field corrections may be used for calculation of the diffuse-field cor-

rection; see the bold curve in Fig.2.31.

The diffuse field correction which represents the difference between the diffuse-field

and the pressure-field sensit ivity may be measured, but this is usually calculated.

The interna t ional st a nda rd ‘Ra ndom incidence and diffuse-field calibra t ion of sound

level meters’ IE C 1183 prescribes how t his should be done.

The calculat ion employs a weighted power based summing of the correct ion values

valid for the different angles of incidence. The weighting accounts for the non-equal

solid angles of incidence which are represented by the equally stepped angles at

w hich t he correct ions a re mea sured.

More weight is th us put on t he correct ions of the a ngles close to the 90 degrees

tha n on those valid for a ngles close to zero degrees. IE C 1183 defines the ca lcula-

t ion formula and the weighting factors.

8/9/2019 be1447





As with free-field characteristics, it is very easy to determine the diffuse-field char-

acteristic of a microphone by adding the diffuse-field correction to its individually

measured pressure-field response or electrostatic actuator response.

2.5.6 Dif fuse Field Microphone a nd Sensit ivity

Dedicated microphones for diffuse-field measurements are rare. A main reason for

this is that the diffuse-field correction or the pressure change created by the micro-

phone itself is so small that many pressure-field microphones also have good dif-

fuse-field characteristics.

Di f fuse-f ie ld chara cter is t ics w hich comply wi th s tan dards such a s ANSI S 1.4 may

also be obtained by mounting certain devices on free-field microphones. These devic-

es which at high frequencies increase the pressure at the diaphragm might either

replace the protection grids or be mounted on them.

Fig.2.31 Free-f ield corr ect ions (0 ° to 180 ° i n 5 °steps) val i d for a 1 / 2 ″ microphone without protection grid. The diffuse-

fi el d corr ecti on (bold curv e) is calcul ated accord in g to

IEC 1183

950959e

1.0 k Frequency (Hz) 100 k

4

8

12

dB

0

– 4

– 8

– 12

– 161 k

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Ch a pter 2 — Microphone TheoryLong Term Microphone Stability


BE1447–11 2 − 51

2.6 Long Term Microphone S t ab ilit y

To obta in va lid mea surements a ll the instru ments a pplied must be sta ble a nd relia-

ble, including the microphone. However, the microphone may be exposed to harsh

environments, outside of the normal environments where the analyser and record-

ing instruments are generally kept . In part icular , high temperatures imply a r isk of

a permanent change in sensit ivity.

Depending on the type of microphone there are two parameters which can be ex-

pected to change. One is the mechanical tension of the stretched diaphragm and the

other, which is only relevant for prepolarised microphones, is the electrical charge of

the electret . Both may decay over the t ime. Carefully controlled art if icial or forced

ageing procedures are therefore applied during production to stabilise these param-

eters. The stabilisat ion is not only relevant for high temperature applicat ions but

also in connection with laboratory standard microphones which are calibrated at

room temperature to within a hundredth of a decibel. They must therefore be very

stable.

A permanent decrease of the diaphragm tension implies an increase of the micro-phone sensitivity, while a decrease of the electret charge causes a decrease of the

sensitivity.

The speed of the relaxation processes which lead to permanent sensitivity changes

depends on temperature. At high temperatures the speed at which changes occur is

so high that i t can be measured. Under normal ambient condit ions the speed at

which changes occur is very low and is not direct ly measurable. The stabili ty at

room temperature may be est imated from high temperature measurements by ex-

trapolat ion using an Arhenius plot . This displays stabili ty as a funct ion the recipro-

cal Kelvin temperature.

Within a part icular type of microphone there may be a great spread between theunits . The high temperature stabili ty of some units may be up to ten t imes bet ter

than the est imated and specif ied value.

Very often the permanent and systematic changes which are to be expected are less

than the random changes which may occur due to mechanical shocks and heat

transients. This is especially the case for microphones with stainless steel dia-

phragms (Falcon range microphones) as they are signif icant ly less sensit ive to long

term h eat exposure tha n t he Nickel dia phra gms used by other types of microphone.

Minor random changes in sensit ivity may occur due to irreversible mutual displace-

ments of the microphone parts. Therefore, microphones which are used as reference

standard microphones, for example, for nat ional standards, should always be storedat room temperature.

For an externally polarized microphone, the diaphragm tension may change over

t ime. I t will decrease slight ly and lead to a small increase in the microphone sensi-

t ivity. The rate at which this occurs depends on the temperature and follows the

general rule for a material process:

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where t T is the t ime for a certain charge at the absolute temperature T , Q i s the

process activation energy, R i s the universa l gas constant and k i s a constant .

Transformed to logarithmic form this gives:

where K1 and K2 are constants which characterise the material process. The equa-

t ion shows a l inear relat ionship between log t T a n d 1/T.

For most B rüel &Kjær microphone types, the long t erm sta bility is described by the

sta bility v a lid at a Reference Tempera tur e (see microphone ty pe specificat ions) a nd

by a Stabili ty Factor which is a funct ion of temperature. The Stabili ty Factor de-

pends on the type of material and relaxat ion process.

The Stabili ty Factor is the rat io between the stabili ty at a given temperature and

tha t of the Reference Tempera tur e.

The long t erm st a bility is given by the follow ing formula:

where:

S Lon gTerm (T) = L on g Ter m S t a b ili ty a t t he t em per a t u re (T)

S Long Term (Tref) = Long Term S t ab i li t y a t t he re fe rence t empera t ure (Tref)

F stability (T) = S t a bilit y Fa ct or (r a t io b et w een s ta b ilit y a t t h e tem per a t ur es

(T and Tref)

The Stabili ty Factors of the Stainless Steel and Nickel diaphragms are shown in

Fig. 2.32 and 2.33 respectively.

Two Stabili ty Factors which are valid for the electret used by the Prepolarised

Microphones are shown in Fig.2.34. The factor that is valid for dry air uses 150°C

as the Reference Tempera ture, wh ile tha t va lid for hum id a ir (90% Relat ive H umid-ity) uses 50°C as the reference.

The sta bility a t th e Reference Tempera tu re should be foun d in the specification th a t

is valid for the type of microphone.

t T k exp Q

RT --------

×=

t T log K 1

K 2

1

T ----×+=

S LongTe rm T [ ] S LongTe rm T r ef [ ] F s t a b i l i t y ⋅ T [ ]=

8/9/2019 be1447




BE1447–11 2 − 53

Note, that the above calculat ion method leads to a rather rough est imates of dia-

phragm and e lect re t s t abi l i ty and that the s tabi l i ty o f most microphone uni t s are

actua l ly severa l t imes h igher tha n es t imat ed .

Fig.2.32 Stabi l i t y Factor for stainl ess steel al l oy diaphr agms (Fal- con m icr ophones). To obtai n t he stabi l i ty at any t emper a- ture multiply the reference stabi l i ty of 150 ° C (see m icr ophone specificati on) by the stabi l i ty factor

F ig.2 .33 Stab i l i ty Factor for n ickel d i aphragms (non-Fa lcon m i -

crophones. To obtain the stabi l i ty at any temperature multiply the reference stabi l i ty of 150 ° C (see microphone specif icati on) by th e stabi l i ty f actor

950898e

10 – 6

10 – 4

10 – 2

0 50

S t a b i l i t y F a c t o r

100 150 200 250 300

100

102

104

106

108

1010

Temperature (C)

Reference Point

950896e

10 – 6

10 – 4

10 – 2

0 50

S t a b i l i t y F a c

t o r

100 150 200 250 300

100

102

104

106

108

1010

Temperature (C)

Reference Point

8/9/2019 be1447


Ch a pter 2 — Microphone TheoryElectrostatic Actuator Calibration



2.7 E l ect r os t a t ic Act u a t or C a libr a t ion

2.7.1 I n tr od uct ion

The calibrat ion of microphones using an electrostat ic actuator is a widely applied

laboratory method for determinat ion of frequency response characterist ics of meas-

urement microphones. The actuator produces an electrostatic force which simulates

a sound pressure act ing on the microphone diaphragm. In comparison with sound

based methods , the ac tuator method has a great advantage . I t provides a s impler

means to produce a well-defined calibrat ion pressure over a wide frequency range

wit hout t he special fa cil i t ies of a n a coust ics laborat ory.

However, the actuator method cannot be used for determinat ion of the microphone

sensit ivity, as i ts absolute accuracy is not suff icient ly high. Therefore, an actuator

frequency response calibrat ion is in most cases combined w ith a n a bsolute sensit ivi-

ty calibrat ion at a reference frequency. This may be performed by using a piston-phone, a sound level calibrator or other means.

The actuator simulates a pressure-field or a pressure act ing direct ly on the micro-

phone diaphragm. It cannot simulate a free-field or a diffuse-field. Free-field and

diffuse-field corrections must therefore be available if calibrations valid for those

types of sound field are required.

Fig.2 .34 Stab i l i ty Factors as funct ions of temperatu re va l id for

th e electr ets used by Pr epolar i zed M icr ophones. M ul ti ply th e stabi l i ty val ue stat ed for t he reference temper atu r e wi th the stabi l i ty factor t o est i m ate the stabi l i t y at other tempera tu r es. The cur ve mark ed a) i s val id at 90% r ela - t i ve hum id i t y whi le b) is va l id for dr y a i r

10 – 6

10 – 4

10 – 2

0 50

S t a b i l i t y F a

c t o r

100 150 200 250 300

100

102

104

106

108

1010

Temperature (C)

Reference Point

950897e

Reference Point

a)

b)

8/9/2019 be1447




BE1447–11 2 − 55

The electrostatic force or pressure produced by the actuator is practically independ-

ent of environmental factors. This makes the actuator method well suited to envi-

ronmental test ing of microphones which may be performed at various temperatures,

pressures and even in gasses other than air .

2.7.2 E lect ros t a t i c Actua to r

An electrostat ic actuator is a st i f f and electrically conducting metal plate which

forms an electrical capacitor together with the microphone diaphragm. This must

be made of metal or of a metal coated material .

The actuator stands on isolat ing studs on the microphone housing in front of the

diaphragm. The dis tance between the ac tuator and diaphragm pla tes is usual ly

between 0.4 a nd 0.8 mm . The actua tor is perforated in order to minimize its influ-

ence on t he a coust ic pressure produced by t he diaphra gm, w hen th is is displaced by

the electrostatic pressure, see Fig.2.35.

When an electrical voltage is applied between the parallel actuator and diaphragm

plates a uniformly distr ibuted electrostat ic force is produced across the diaphragm.

The diaphragm reacts on this electrostat ic force or pressure as i t would react on an

equally strong sound pressure.

2.7.3 E lect ros t a t i c Ca l ibra t ion P ressure

The equivalent sound pressure produced by an electrostat ic actuator may be de-

fined by considering the fact that the stored energy on an electrical capacitor may

be expressed either in electrical or in mechanical terms. This leads to the following

equat ion:

Fi g.2.35 Electr ostat ic actu ator u sed w it h a 1 / 2 ″ microphone

E 2

C ⋅2

--------------- F d ⋅=

8/9/2019 be1447





where:

E = e lect r ica l vol tage betw een the pla tes

C = e lect r ica l capa cita nce betw een the pla tesF = force betw een the pla t es

d = p la t e di st a n c e

ε = dielectric consta nt of the ga s betw een plates (air = 8.85 × 10–12 F /m )

A = p l a t e a r e a

Rearranging the parameters leads to the following equivalent sound pressure act ing

on the plates:

where: p = electrosta t ic pressure

When a DC and a sinusoidal AC voltage are applied between the plates, i .e . be-

tween the actuator and the microphone diaphragm, the following expression is ob-

tained for the stat ic and dynamic pressure components:

where: E 0 = a pplied DC -volta ge

e peak = pea k va lue of a pplied AC-volta ge

e rms = rms va lue of a pplied AC-volta ge (e peak / )

p static

= produced sta t ic pressure

p dynamic = produced dyna mic pressure

ω = angular f requency

t = t ime

The equivalent sound pressure produced by the actuator at the frequency of the

applied electric signal may be derived from the above formula. However, it should

be taken into account that the area of the actuator, due to i ts perforat ion, makes

C ε A⋅

d -----------=

p F

A----

ε E 2⋅

2 d 2⋅

--------------= =

p ε

2 d 2⋅

------------- E 0

e peak ωt sin+( )2⋅ ε

2 d 2⋅

------------- E 0

22 E

0e peak ωt e peak

2 1 2ωt cos–

2----------------------------+sin⋅ ⋅+

⋅= =

p s t a t i c ε2 d

2⋅------------- E 02 e r m s 2+( )⋅=

p d y n am i c ε

2 d 2⋅

------------- 2 2 E 0

e r m s ωt e r m s 2

2ωt cos–s in⋅ ⋅( )⋅=

2

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BE1447–11 2 − 57

only a certain fract ion of the diaphragm area. The simulated sound pressure is ,

therefore, reduced accordingly and defined by the following formula:

where:

R area = rat io between actuator and diaphragm areas ( typically, 0.75).

The rat io of the second harmonic component and that of the fundamental frequency

becomes:

%

2.7.4 Electros ta t ic Actua tor Operat ion

An actuator measurement set-up is shown in Fig.2.36. The required DC-voltage is

supplied via a resistor and the AC-voltage is supplied via a capacitor. These compo-

nent values should be chosen to give a lower cut-off frequency which is 5 to 10

times lower t ha n t he lowest ca librat ion frequency. Their impedan ces should be suff i-

ciently high that the circuit does not create a safety r isk for the user.

Fig.2.36 Schematic di agram of m easur ement set-up for electr o- stat i c actuat or cal i brat ion

p d y n am i c r m s [ ]ε E

0e r m s ⋅ ⋅

d 2

------------------------------- R area ⋅=

d 2n d

e r m s

2 2E 0

------------------ 100⋅=

950937e

DC-voltage Supply

Actuator

Microphone

Preamplifier

Measurement

Amplifier

Recorder

10 MΩ

5000 pFAC-voltage Supply

8/9/2019 be1447





Typical vol tages are 800 V DC an d 30 V AC (rms). For a d is ta nce betw een the ac tu-

at or an d the diaphragm of 0.4 mm a nd a n ac tua tor-diaphragm area ra t io of 0.75, an

equiva lent sound pressur e of one P a scal or 94 dB w ill be produced. The second

ha rm onic distort ion w ill ma ke 1.3 %.

It is possible to operate the actuator without any DC-voltage. In this case the

frequency of the simulated sound pressure will be twice the frequency of the sup-

plied electrical signal, see the formula in 2.7.3 which defines the dynamic pressure.

However, this method has two disadvantages: f irst ly, a much lower sound pressure

ma y lea d to a n insufficient signa l to noise rat io a nd secondly, th e pressure produced

depends on the square of the supplied voltage. This may increase the uncertainty of

the measurement .

The calibrat ion of a microphone using an electrostat ic actuator implies a high AC-

voltage on the actuator and often, a very low output voltage from the microphone

being calibrated. This creates a r isk of making calibrat ion errors due to cross-talk

in the measurement set-up. This risk is especially great at high frequencies. The

calibration set-up should, therefore, be carefully checked and modified if necessary.

The check may be done by either setting the polarization voltages of the micro-

phone or actua tor to zero volts . The displayed signa l should then fa ll by 40 dB or

more depending on the required calibrat ion accuracy. I f this is not the case the

cross-talk signal might be reduced by proper selection of instrument ground connec-

tions.

2.7.5 Actua tor a nd P ressure-f ield Responses

In principle, the actuator and the pressure response of a microphone are dif ferent .

In pract ice, the dif ference may be insignif icant . I t may vary between less than

0.1 dB a nd a bout 1 dB depending on the a coust ic impeda nce of the microphone dia-

phragm system and on the radiat ion impedance which loads the outside of the

diaphragm. The higher the diaphragm impedance the smaller the dif ference.

For t he new er a nd for some of the older B rüel &Kjær microphone t ypes correct ions

are available for determination of pressure(-field) responses from measured actuator

responses; see examples for 1″ a n d 1/2″ microphones in Fig.2.37. As smaller micro-

phones ha ve higher dia phra gm impedances no correct ions a re necessa ry.

2.7.6 G enera l Note on Actua tor Cal ibrat ion

Brüel&Kjær give microphone correction values which are to be added to the measured

actuator response to obtain the required free-field, diffuse-field and pressure(-field) re-

sponses.

Measurement of the actuator frequency characterist ic should, generally, be per-

formed with the type of actuator specified with the free-field, diffuse-field and pres-

sure-field corrections as this leads to the highest calibration accuracy.

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8/9/2019 be1447




8/9/2019 be1447



BE1447–11 3 − 1

Chapter 3

Characteristics of Microphones

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesIntroduction to Characteristics



3.1 I n t rod uct ion t o C h a r a ct er ist ics

The previous chapter of this handbook has described the theory and principles be-

hind measurement microphones. In doing so, the way in which different micro-

phones are designed for different purposes has been explained.

The suitability of a microphone for a particular task is commonly described interms of a set of characteristics. This chapter describes these characteristics in

some detail to give a background to how and why different characterist ics are

measured. These characteristics are referred to in product-specific literature such

as Product Data sheets and Volume 2 of this handbook.

Characterist ics are normally described under the following headings:

— Th e C a lib r a t ion C h a r t

— S en sit iv it y

— Frequency Response

— Direct iona l Cha rac t er i st i cs

— D yn a m ic R a n ge

— Equiva lent Volume a nd Ca l ibra tor Load Volume

— C a pa cit a n ce

— Po la r i za t ion Vol t age

— L ea k a g e R es is t a n ce

— S ta bilit y

— Effect of Tempera ture

— E f fect o f Ambien t Pr essure

— E f fect of H u m id it y

— Effect of Magnet ic Field

— E lect romagne t ic Compat ib il it y

Similar headings are used in this chapter to provide a reference for the information

about specific microphones that is given in product-specific literature.

Information about the characterist ics of preamplif iers is not given in this Chapter,

but is included in Chapter 4.

3.1.1 Th e C a libr a t ion C ha r t a n d D isket t e

The calibrat ion chart is an important piece of documentat ion providing essential

information about the performance characterist ics of the microphone. A calibrat ion

cha rt is supplied with ea ch microphone delivered by B rüel &Kjær an d each ca libra-

t ion chart is individual to that microphone. The calibrat ion chart states both typical

8/9/2019 be1447


Cha pter 3 — Cha ra cterist ics of MicrophonesSensitivity


BE1447–11 3 − 3

and individual data that applies to the microphone cartr idge only, i .e . not a micro-

phone cart r idge a nd prea mplif ier combina t ion.

The open-circuit sensitivity of the microphone cartridge is an example of an individ-

ual and valuable piece of information given on the calibrat ion chart . I t al lows the

user to verify the performance of the cartr idge and, together with information on

the preamplif ier , to calibrate the measurement system.

The microphone calibration diskette provides individual frequency responses for

three types of sound field in 1/12 octave steps. This data can be used to reduce the

measurement uncertainty by correct ing the measurement data with these respons-

es, by using, for example, a spread-sheet. As this implies, a microphone optimised

for one type of sound field can be used in another type of sound field, provided that

suff icient ly deta iled frequency a na lysis is performed.

3.2 S ensit ivit y

3. 2.1 Open -cir cu it S e n sit iv it y (S o)

The open-circuit sensitivity is defined as the pressure-field sensitivity, valid with an

idealised preamplifier which does not load the microphone.

The open-circuit Sensitivity is a microphone specific parameter. The value stated on

the microphone Calibrat ion Chart is determined using the Insert Voltage Calibra-

t ion t echniq ue with the configura t ion described in IE C 1094-1. This sta nda rd a lso

describes the mechanical dimensions of both microphone and preamplifier.

F ig.3 .1 M icrophone and preamp l i f i er w i th ca l i b ra t i on char t and di skett e. Th e m icrophone and pr eampli f ier can be stored i n t h e same box

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesSensitivity



The open-circuit sens itivity, w hich is usua lly determ ined a t 250 Hz or 1000 H z, is

used for calibrat ion and monitoring of the microphone cartr idge. When the entire

measurement system must be calibrated, the influence of the preamplif ier should

be ta ken into a ccount , see 3.2.2.

3.2.2 Loaded Sens it i vit y (S c)

When the microphone cartridge is connected to the preamplifier, its input voltage is

at tenuated by the preamplif ier input capacitance (C i). This effect is valid over a

wide frequency ra nge, therefore, the capa cit ive loading of the cart r idge ha s no effect

on the relative frequency response.

The gain of the microphone and preamplifier combination (G) is also influenced by

the gain of the preamplif ier i tself (g) which is measured by connecting the genera-

tor directly to the preamplifier input. The loaded sensitivity, S c can thus be de-

scribed using th e open-circuit sensit ivity, so:

where:

C m = polarized microphone ca pacita nce as st a ted on the microphone calibra t ion

char t

C i = preamplif ier input ca pacita nce (a s given in the preamplif ier specif ica t ions)

G = ga in of the microphone a nd preampli fier combinat ion

g = gain of the pream pli fier (a s given in the prea mplif ier speci f ica t ions)

F ig.3 .2 C i rcu i t d iag ram of p reamp l i f i er and mi crophone comb i - nat ion

S c S o G d B [ ]+=

950574/1e

Microphone

g

Cm Ci

Preamplifier

G 20C m

C m C i +--------------------- g ⋅

d B [ ]log⋅=

8/9/2019 be1447


Cha pter 3 — Cha ra cterist ics of MicrophonesFrequency Response


BE1447–11 3 − 5

The interna l gain, g , of the B rüel &Kjæ r pream plif iers is typica lly a l i t t le less th an

unity (for example, 0.997≈ – 0.025 dB ). Typica l capa cita nce values for 1/2″ micro-

phones a nd prea mplif iers a re 20 pF a nd 0,2 pF respect ively. These values yield a n

overall ga in (G ) of (– 0,1dB ) + (– 0,025) = – 0,125 dB.

3.2.3 Correct ion-factors K and Ko

Some Brüel &Kjær measur ing am pli fiers a nd a na lysers d isplay t he ir input vol tage

in terms of dB re 1 µV. This fea tur e ca n be used for determ ining t he sound level by

adding a correct ion to the displayed value.

The correction is zero dB for a microphone with a sensitivity of 1 µV per 20 µP a

because 1 µV and 20 µPa are the reference values for the levels of the displayed

voltage and the sound pressure respectively. This microphone sensitivity equals

50m V per Pa w hich corresponds to – 26 dB re 1 V per Pa scal (microphone sensit ivi-

ties a re specified in dB rela tive to 1 V/P a ). For m icrophones wit h t his sensit ivity, the

instrument will display the sound level direct ly in dB.

For microphones with other sensitivities, the correction factor (K ) defined below should be added to the display reading. The correction factor K is defined as:

K = –26 – S c or K = K o – G [dB]

where K = correction fact or

S c = loa ded sensit ivity

K o = open-circuit correction fa ctor

G = ga in of the microphone an d preamplif ier combina t ion

The K o factor can be found on most Br üel &Kjæ r microphone calibrat ion chart s .

3.3 Fr eq uen cy Respon se

3.3.1 Introduct ion a nd Opt imised response

Individually measured frequency response calibrat ions are supplied with most

B rüel &K jær m icrophones. The frequency r esponse of a microphone depends on the

type of sound field in which the microphone is used.

In acoust ic measurements there are three main types of sound field:

Free-field

Pressure-field

Diffuse-field (equivalent to random incidence response)

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesFrequency Response



The microphone is optimised to have a flat frequency response in one of these

sound fields. This response is called the optimised response. The differences be-

tw een t he responses ar e only evident a t h igher frequencies. B elow 1000H z the

responses differ by, ty pica lly, less th a n 0.1 dB .

The determination of all responses is based on corrections added to individually

measured electrostat ic actuator responses above 200Hz. All measurement micro-

phones ha ve a r elat ively f lat frequ ency response from 10 H z to 1000 H z, independ-

ent of the sound field. According to IE C 651 and IE C 1094-4 stan da rds, one

frequen cy in t he 200 Hz to 1000 Hz ra nge is selected a s t he reference frequency, see

Fig.3.3. Br üel &Kjær norma l ly use 250 Hz (10 2.4 Hz) as the reference frequency. The

sensit ivity a t t he reference frequency is used to represent the “overall” sensit ivity of

the microphone.

For a full discussion about types of microphone designed for different sound fields,

see Section 2.5.

3.3.2 Low Frequency Response

In general , the data related to the low frequency response given in the calibrat ion

data is typical for the type of microphone cartr idge at the reference ambient pres-

sur e (101,3 kP a ) only.

The – 3 dB point on th e low frequency r esponse is proport iona l to the a mbient pres-

sure; in practice the influence is insignificant because the lower limiting frequency

is below the usual frequency response of interest . Note that the stated low frequen-

cy response is va l id when the diaphragm and s ta t ic pressure equal isa t ion vent are

exposed to the sound field.

Fi g.3.3 Th e fr equency response curve is composed of an in di v idu al h igh fr equency response and a typ ical low fr equency respon se. Th e cur ve i s norm al i sed t o 0 dB at t he r efer ence fr equency

dB

200950605e

5

0

– 5

–101 10 100 1k 10 k Frequency (Hz) 100 k

Reference

frequency

Low-frequency Response High-frequency Response

8/9/2019 be1447




BE1447–11 3 − 7

For rear-venting microphones the venting takes place through the preamplifier

housing.

In pract ice, the low frequency response of a measurement system is often deter-

mined by other factors, such as the electrical lower limiting frequency of the micro-

phone/prea mplifier combina tion or by a high-pa ss filter in t he condit ioning

amplifier.

All Brü el &Kjær m icrophones a re tested acoust ically to ensure that the low er l imit-

ing frequencies are within the production tolerances. This test cannot be performed

by an actuator because an actuator does not produce any sound pressure at the

vent .

3.3.3 High Frequency Response

To obta in a n individ ua l high freq uency response, ty pe specific a nd field dependent

correct ions are added to the individually measured actuator response for the micro-

phone. These actual corrections are measured during the development of each mi-

crophone type.

Fig.3.4 il lustrates how all frequency responses for each of the three sound fields are

obtained for the same microphone. This is done by simply adding the type specific

correct ion data to the individually measured actuator response.

3.3.4 Electros ta t ic Actua tor Response

For a descript ion of the electrosta t ic actua tor a nd its operat ion, refer to Sect ion 2.7.

Calibrat ion by an electrostat ic actuator is a convenient and accurate method for

determ ining ind ividua l frequency responses. To a minor degree, the mea sured re-sponse depends on the type of actuator applied. The corrections stated in Fig.3.4

are valid only for frequency response measurements using the specified type of

actuator.

The Electrostatic Actuator Phase Response

The phase response curves show n in B rüel &Kjær li terat ure a re norma lised to zero

degrees a t low frequencies. For a ll Br üel &Kjæ r externa lly polarized microphones

(posit ive charge) , the phase dif ference between the voltage and the pressure at low

frequencies is –180°. For a ll Br üel &Kjær prepola rized microphones w hich use a

negat ive charge, the shif t is 0°.

The 90° phase lag relat ive to the phase at low frequencies determines the reso-

nance frequency of the microphone.

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Ch a pter 3 — Cha ra cterist ics of MicrophonesFrequency Response



Fi g.3.4 Th e fr equency response cur ves val i d for an i nd ivi du al m i crophone ar e obtain ed on the basis of

th e in di vid ual ly m easur ed a ctu ator r esponse. The response, val id for d if ferent t ypes of soun d fi el d, i s obtai ned by ad di ng t he cor r ections, shown i n bold , to the actuat or r esponse

5 0 d B

– 2 0

1 k

1 0 k

1 0 0 k

1 0 0

F r e q u e n c y ( H z )

950389/1e

5 0 0

1 k

1 0 k

5 0 k

F r e q u e n c y

( H z )

1 5

– 1 0 0

θ °

5 0 0

1 k

1 0 k

5 0 k

F r e q u e n c y

( H z )

P r e s s u r e - f i e l d C o r r e c t i o n

R a n d o m - i n c i d e n c e C o r r e c t i o n

F r e e - f i e l d C o r r e c t i o n

C o r r e c t i o n

F r e e - f i e l d R e s p o n s e ( 0 ° i

n c i d e n c e )

R e s p o n s e

R a n d o m - i n c i d e n c e R e

s p o n s e

A c t u a t o r R e s p o n s e

A c t u a t o r R e s p o n s e

P r e s s u r e - f i e l d R e s p

o n s e

1 5

– 1 0 0

θ °

4 d B

d B

d B

0 – 1

1 k

1 0 k

1 0 0 k

1 0 0

F r e q u e n c

y ( H z )

5 0 d B

– 2 0

1 k

1 0 k

1 0 0 k

1 0 0


5 0 d B

– 2 0

1 k

1 0 k

1 0 0 k

1 0 0


5 0 d B

– 2 0

= = =

+ + +

=

+

1 k

1 0 k

1 0 0 k

1 0 0


0 ° i n

c i d e n c e

R a n d o m - i n c i d e n c e

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BE1447–11 3 − 9

3.3.5 F ree-field Res pon se

For background information on the free-field response of a microphone, refer to

Section 2.5.4.

To determin e the m icrophones perform a nce in a free sound field, a correction is

added to the actuator response. This correction is denoted as the “Free-field Correc-

tion”. This correction must not be confused with corrections used with sound cali-

brators.

3.3.6 Random Incidence Response

The random-incidence response is the response of a microphone in a diffuse sound

field.

A diffuse sound field exists at a given location if the field is created by sound waves

arriving more or less simultaneously from all direct ions with equal probabili ty and

level.

A diffuse sound field may be created within a room with hard sound reflect ing walls

and which essentially contains no sound absorbing materials .

Sound fields with a close resemblance to a diffuse-field may be found in environ-

ments such as factories where many simultaneous sound or noise sources exist or

in buildings with hard walls , for example, in halls or churches.

The diffuse-field or ‘random incidence’ sensitivity of a microphone refers to this type

of field, even if, in most cases, the diffuse-field sensitivity is calculated from meas-

urements performed under free-field conditions. The calculation method is described

in the internat ional standard “Random-incidence and Diffuse-field calibrat ion of

Sound Level Meters” IEC 1183.

The random-incidence corrections for Falcon-range microphones have been calculat-

ed a ccording t o IE C 1183-1993 using t he free-field corrections fr om 0° to 360° inci-

dence in 5° steps. For other ty pes of B rüel &K jær m icrophone, 30° s teps are applied

according to IEC 651.

The random-incidence response is determined by adding the random-incidence cor-

rect ions to th e a ctuat or r esponse.

3. 3.7 Pr e ss ur e-field R es pon se

The pressure-field response of a microphone refers to uniformly distributed pres-

sure on the diaphragm.

This response is often regarded as being equ a l to the a ctuat or response becau se the

difference between them is small compared to the uncertainty related to most meas-

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesDirectional Characteristics



urements. The difference is due to the radiat ion impedance which loads the dia-

phragm during the actuator response measurement , see Sect ion 2.7.

The pressure-field response may be determined by adding the pressure-field correc-

t ion to the individually measured actuator response.

The pressure-field correct ions are determined during the intensive analysis that is

part of the development of ea ch part icular B rüel &Kjæ r microphone type.

The pressure-field response is measured using the reciprocity method according to

the IE C 1094-2 stan da rd. This method is the most a ccura te ca librat ion method

available.

3.4 D ir ect ion a l C h a r a ct er ist ics

The direct ional characterist ic is the relat ive sensit ivity variat ion as a funct ion of

angle of incidence. This can be represented graphically by polar plots, see Fig.3.5 .

The same information is, in principle, given in the free-field correction curves. Thedifference in the representation is that the free-field corrections are given at fixed

angles of incidence, while the direct ional characterist ics are given at f ixed frequen-

cies.

The directional characteristic is relevant if the microphone is used for free-field

measurements.

Fig.3.5 Typical di rect i onal character i st ics for a 1 / 2 ″ m icrophone norm ali sed to 0 ° i ncid ence

950600e

0 °

3 3 0 °

3 0 0 °

270°

2 4 0 °

2 1 0

°

1 8 0 °

1 5 0 °

1 2 0 °

6 0 °

3 0°

05 – 5 – 10 – 15 – 20 5 0 – 5 – 1 0 – 1 5 – 2 0

– 25 9 0 °

0 °

3 3 0 °

3 0 0 °

270°

2 4 0 °

2 1 0

°

1 8 0 °

1 5 0 °

1 2 0 °

6 0 °

3 0°

05 – 5 – 10 – 15 – 20 5 0 – 5 – 1 0 – 1 5 – 2 0

– 25 9 0 °

5 kHz

10 kHz

20 kHz

40 kHz

θ°

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Cha pter 3 — Cha ra cterist ics of MicrophonesDynamic Range


BE1447–11 3 − 11

The directional characteristics of a 1″ microphone will resemble those shown in

Fig.3.5 , but at half the frequency. Accordingly, the frequency is multiplied by two

or four to represent a 1/4″ or 1/8″ microphone respectively.

3.5 D yna mic Ra nge

The dyna mic ran ge specified for t he B rüel &Kjær microphones is l imited by:

the equiva lent inherent n oise level (dB SP L) which defines th e low er l imit

the 3 % distort ion level (dB SP L) which defines the upper l imit .

3.5.1 I n her en t Noise

The inherent noise of the cartr idge is determined by the thermal movement of the

diaphragm. This is specif ied either as inherent noise or as cartr idge thermal noise,

see Section 2.4.3 for a discussion of inherent noise.

Because the microphone cartr idge is always used with a preamplif ier , the inherent

noise of the combination is composed of both microphone and preamplifier noise.

The combined noise level may be calculated by the following formulae:

where:

Ln(Mic ) = ca r t r idge therma l noise level [dB SP L]

pn(Mic) = ca r t r idge thermal noise (Pa )

pn (PA) = equivalent preamplif ier noise pressure

L n (Combined) = combined noise level (dB SP L)

en(PA) = prea mplifier noise volta ge (V)

p r ef =

p n M i c ( ) p r ef 10L n M i c ( )

20-----------------------⋅=

p n PA( )

e n PA( )

S c -------------------=

L n Comb i n ed [ ] 10p n 2 M i c ( ) p n

2+ PA( )

p r ef 2

--------------------------------------------------log⋅=

p r ef 20 106–Pa ⋅=

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Ch a pter 3 — Cha ra cterist ics of MicrophonesDynamic Range



The noise data (L n(Mic) and en(PA) are given in the respective type specifications. It

is important to note that the noise levels must be for the same frequency band-

widths.

3.5.2 Ma x im um S ou nd P r es su re L evel

The dynamic range of condenser microphones is so great that for most pract icalsituat ions the user will not encounter any limitat ion due to the maximum permissi-

ble sound pressure level.

The maximum output of the microphone is limited by the displacement of the dia-

phra gm . To ensure correct opera tion, th e microphone should n ot be exposed t o

sound pressure levels exceeding the stated Maximum Sound Pressure Level (peak).

This corresponds to a peak out put volta ge of 40 to 50% of the polar iza tion volta ge.

Above this level, the output becomes heavily distorted (clipping occurs). In addition,

an externally polarized microphone will temporarily loose its charge and will need

some time to recover. However, even if the maximum sound pressure is exceeded,

for exam ple, by up to 10 dB, t he microphone will not suffer perma nent da ma geprovided it is used wit h a B rüel &Kjær pream plif ier. This is becau se the preamplif i-

ers are constructed so that the discharge that occurs when the diaphragm touches

the backpla te does not ha rm t he diaphragm.

The microphone is always used with a preamplif ier , therefore the limits for this

should a lso be ta ken into account . The ma ximum output voltag e from t he preampli-

fier depends on the supply volta ge. To utilise the wid e dyna mic ra nge of th e micro-

phone, the prea mplifier should be operat ed a t a supply volta ge of 100 V. Even so,

the pream plif ier m a y be t he limit ing fa ctor.

While the microphone has a distortion proportional to the sound pressure level (3%

distort ion level is stated) , the preamplif ier has a very low distort ion until a level ofa few dB below the clipping point where the distort ion suddenly increases. The

maximum output peak level from the preamplif ier is usually a few volts lower than

half the total supply voltage. The actual supply voltages are stated in the product

da ta sheet for the power supply.

Often it is convenient to express the preamplif ier maximum output in terms of

equivalent peak sound pressure level. The equivalent peak sound pressure can be

found from th e follow ing equa t ion:

where:

SPL peak = equivalent peak sound pressure level of th e preamplif ier

e peak = Maximum output volta ge of the prea mplifier (V)

SPL peak m ax [ ] 20e peak

S c p r ef ⋅---------------------

d B [ ]log⋅=

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Cha pter 3 — Cha ra cterist ics of MicrophonesEquivalent Diaphragm Volume


BE1447–11 3 − 13

S c = loa ded m icrophone sensitivit y (V/P a )

p r ef = reference sound pressur e ( P a )

3.6 E q uiva l en t D ia ph r a gm Volu me

The equivalent diaphragm volume is that volume of air which has the same compli-an ce as th e dia phragm a t a s t a t ic pressure of 101.3 kPa .

Equivalent diaphragm volume is used in connection with coupler calibrat ion of mi-

crophones and for evaluat ing the loading which the microphone presents to small

couplers. See Section 2.3.12 for more deta iled informa tion.

3.7 C a l ibr a t or L oa d Volu me

The calibrator load volume is the sum of the equivalent diaphragm volume and the

air volume enclosed by the outer surface of the protect ion grid and the diaphragm.See the relevant data sheet for typical values.

The calibrator load volume is used to evaluate and correct the loading of micro-

phones w hen used on calibra tors a nd pistonphones.

3.8 C a pa cit a nce

When a condenser microphone is included in an electrical circuit , it may be consid-

ered as being a purely capacitive component.

The capacitance is determined by the distance between the diaphragm and the

backplate , and by stray capacitance between the backplate and the microphone

housing.

The capacitance of the microphone and its variat ion with frequency is a funct ion of

the polarisation voltage, see Fig.3.6 . The stated values of microphone capacitance

a re va lid for nomina l polariza t ion volta ge at 250 Hz (genera lly 200 V for externa lly

pola rised m icrophones an d 0 V for prepolarized m icrophones. The capa citan ce of th e

microphone can be used for the evaluation of loaded sensitivity (S c) lower limiting

frequency a nd preamplif ier n oise.

The stability of the microphone is closely related to its capacitance, i.e. changes in

capacitance reveal changes in microphone sensitivity and frequency response. This

relat ionship is exploited in th e B rüel &Kjær pa tented Ch a rge Inject ion Ca librat ion

technique for monitoring the condition of a microphone (see Section 4. 8).

20 106–⋅

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Cha pter 3 — Cha ra cterist ics of MicrophonesPolarisation Voltage


BE1447–11 3 − 15

The sensit ivity of the ca rtr idge is essentia lly proport iona l t o the cha rge, see Fig.3.8.

A reduction in polarization voltage, and hence sensitivity, can be a practical expedi-

ent to avoid overloading preamplif iers in situat ions where there is a combinat ion of

high levels, high frequencies and long cables.

B rüel &Kjær instrum ents supply a posit ive pola rizat ion volta ge for externa lly pola r-

ized microphones. This type of microphone therefore produces a negative voltage for

a positive pressure.

3.9.2 P repolar ized Microphones

Prepolarized microphones contain a stable charge in the electret layer on the back-plate, see Section 2.3.4. All B rüel &Kjær prepolar ized microphones a re nega t ively

charged. They therefore produce a positive voltage for a positive pressure.

If an external polarisat ion voltage is accidentally applied to the prepolarized micro-

phone, no perma nent h a rm is done. However, th e sensit ivity is signif ica nt ly reduced

by 10 dB or more as long as t he externa l polariza t ion is sustained. The result ing

Fi g.3.7 Exam ple of th e fr equency response dependency wi th polar isat ion vol t age. The cur ves are

norm al ised t o th e nom i nal val ue of 200 V. Thi s exampl e i s for a 1 / 2 ″ mi crophone

w i th hi gh sensit iv i ty. Th e depend ency is l ess for 1 / 2 ″ð ðm i crophones w i th lower sensit iv it y

100 1k 10k 100kHz

-2

-1

0

1

2

Response (dB)

940606e

28 V

150 V

250 V

2.5

-2.5

Frequency (Hz)

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesLeakage Resistance



polarisat ion voltage is the sum of the external and internal polarizat ion voltages

which are of opposite sign.

3.10 Lea kage Res is t ance

Leakage resistance is the electrical resistance between the centre terminal and the

housing of the microphone. For several design reasons, preamplifiers use high resis-

tors for the polarization voltage supply. Therefore to avoid a reduction of the polari-

zat ion voltage, and so ensure accurate measurements, the leakage resistance of the

microphone must be at least a thousand t imes greater than the polarizat ion voltageresistance of the preamplifier. This requirement must be fulfilled even under severe

environmental condit ions, for example, in condit ions of high humidity and high

temperature.

These high va lues impose str ingent dema nds on design, ma terials a nd production of

microphones. Br üel &Kjær microphones a re tested to th ese requirements at 90%

relat ive humidity. Note that the surface of the microphone insulator should not be

exposed to contaminat ion, for example, from dust and hair , as this may lead to a

low leakage resistance.

If microphones, produced to lower leakage resistance requirements, are used with

high-qua lity B rüel &Kjær prea mplif iers there will be a r isk of insta bility in sensi-tivity.

For prepolarized microphones, the leakage resistance is far less critical. It need only

be about ten t imes greater than the resistance of the preamplif ier polarizat ion re-

sistance in order not to significantly influence the lower limiting frequency of the

microphone and preamplifier combination.

Fig.3 .8 Change in sensi t i v i ty as a funct ion of polar i sa t ion vol t - age at 250 H z

10 20 50 100 200 500

Polarization Voltage (V)

– 25

– 20

– 10

0

5

dB

950608e

5

– 15

– 5

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Cha pter 3 — Cha ra cterist ics of MicrophonesStability


BE1447–11 3 − 17

3.11 S t a bilit y

The stabili ty of a measurement microphone is a very important feature. I t is one of

the feat ures th a t dist inguishes measu rement m icrophones from other microphones.

Changes in the parameters of a microphone are dealt with here under “ Irreversible

Cha nges” and “Revers ible Chan ges” .

3.12 I rrevers ib le Cha nges

3.12.1 Long-term sta bil ity

The diaphragm of a microphone has a certain, high mechanical tension which will

decrease as a funct ion of heat and t ime. A decrease in tension leads to a permanent

cha nge in t he sensit ivity of a microphone. At n ormal r oom temperat ure th is effect is

of the order of 1 dB per 1000 year s. At eleva ted t emperat ures the effect is a ccelera t-

ed, see Section 2.6 for deta ils.

3.12.2 Ha ndling

The mechanical stabili ty of the microphone is determined by its abili ty to withstand

mechanical effects , for example, a force applied to the diaphragm clamping ring or

unpredictable mechanical shocks, such as i f the microphone is dropped onto a hard

surfa ce. Brü el &Kjæ r microphones are designed an d tested to w ithsta nd such ef-

fects. However, it should be noted that microphones are delicate precision measur-

ing instruments, especially those designed for laboratory use, and should be treated

carefully.

Special care should be taken when the grid is removed; avoid touching the dia-

phragm as i t is easily damaged by sharp points or part icles. Some microphones

have “screwed on” diaphragms and in this case touching the clamping ring may

change the diaphragm tension causing subsequent changes in sensit ivity and fre-

quency response. In addit ion, care should also be taken not to stress the diaphragm

by having different stat ic pressure on the front and the back side of the diaphragm

(normally avoided by having the Pressure Equalisat ion Vent in the sound field) .

This may also happen when mounting and dismounting the microphone from a

small coupler or cavity. Here the microphone may be subjected to a large vacuum

causing heavy loading of the diaphragm. This could cause changes in sensit ivity

and frequency response.

3.12.3 Short-term St a bil ity

Over the li fet ime of a microphone it is very l ikely that some minor variat ions in

sensitivity will occur due to thermal or mechanical shock. These changes occur due

8/9/2019 be1447


Ch a pter 3 — Cha ra cterist ics of MicrophonesReversible Changes



to set t l ing of the relat ive posit ions of the mechanical parts . However these changes

will generally n ot exceed 0.1 dB a nd a re th erefore negligible for m ost a pplicat ions.

The short term stability of a microphone is very high once the microphone is accli-

matised and used in stable ambient environments. Usually the microphone will

susta in th e sensit ivity w ithin 0.01 or 0.02 dB under such sta ble environments. This

is important when the microphone is used as a laboratory reference.

3.13 Revers ib le Cha nges

Reversible changes occur as a result of environmental influences. Correction factors

are available for the three main influences: temperature, ambient temperature and

humidity.

3.13.1 Effect of Tempera t ure

The sensit ivity of the microphone is only slight ly affected by the ambient tempera-

ture. I t is usually not necessary to compensate for this influence, unless the micro-

phone is subjected to very high or very low temperatures. After quick changes in

temperature the microphone should be allowed to acclimatise for at least 15 min-

utes a t t he a mbient condit ions to ensure correct operat ion.

B rüel &Kjæ r specify a temperat ure coefficient at 250 Hz a nd gra phs of sensit ivity

variat ions as funct ion of temperature. These can be used to compensate for thedeviation in sensitivity. The deviation is read directly from the graphs. The temper-

ature coefficient depends on the frequency. Fig.3.9 a n d Fig.3.10 show how changes

occur in the frequency characterist ics at various temperatures.

The ma gni tude o f the in f luence on t he sensi t iv ity a t 250 Hz is typica l ly – 0.002 to

– 0.008 dB/°C. See microphone type data for more details .

Fig .3.9 Exampl e of revers ible changes. Typ ica l var i a t ion in 0 ° – i nci dence fr ee-fi el d r esponse (norm al ised at 250 H z) as a fu ncti on of temper atu r e, relat iv e to th e r esponse at 20 °C

950610e Frequency (Hz)

1 k 10 k 50 k

1.0

Response (dB)

– 1.5

– 1.0

– 0.5

0.0

0.5

500 Hz

1.5

– 10 °C

+ 50 °C

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Cha pter 3 — Cha ra cterist ics of MicrophonesReversible Changes


BE1447–11 3 − 19

3.13.2 Effect of Ambient P ressure

The ambient pressure influences the sensitivity of the microphone. The microphone

sensit ivity and frequency response stated is in most cases valid at an ambient

pressure of 1 a tm osphere = 101.325 kPa . The ambient pressure is sometimes re-

ferred to as stat ic pressure.

The microphone is designed w ith a vent t o equ alise th e pressure inside a nd outside

the microphone, so it only detects deviations from the equilibrium, which is the

sound we want to measure. The output from the microphone is, however, affected by

variat ions in ambient pressure. This is due to changes in air st i f fness and air

density which affect the impedance of the cavity behind the diaphragm.

The ambient pressure varies with alt i tude, and it also varies over t ime at the same

location. With the exception of few locations, these variations do not usually exceed

the range 80 to 120kPa (only ± 20 kPa relat ive to one at mosphere). Those micro-

phones with the greatest sensit ivity to ambient pressure will rarely give rise to a

correction of more th a n 0.4 dB. S ee microphone type specificat ions for m ore deta ils.

Fig.3.11 shows an example of the variat ion in sensit ivity as a funct ion of ambient

pressure at the reference frequency of 250Hz. The slope of the curve at 101kPa is

specif ied as the pressure coefficient and is determined by the rat io between the

diaphragm st if fness and the st if fness of the air in the internal microphone cavity.

The pressure coefficient may be used to add corrections to the sensitivity of the

microphone. However, i f a sound calibrator is used to calibrate the entire measure-

Fig.3.10 Exam ple of r eversible chan ges. Typical vari at ion in actuator r esponse (norm al ised a t 250 H z) as a fun cti on of temperat ur e, relat i ve to th e r esponse at 2 0 °C

1

– 1

– 2

2

0

950611e

50 k1 k

3

4

10 k500

300° C

200° C

100° C

Response (dB)

Frequency (Hz)

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Ch a pter 3 — Cha ra cterist ics of MicrophonesReversible Changes



ment system, the change in sensit ivity of the microphone is automatically taken

into account.

The graph in Fig.3.12 shows the variat ion in frequency response due to changes in

am bient pressure below one a tm osphere. These gra phs ma y b e used to ma ke correc-t ions of the frequency response. For sm all va riat ions in a mbient pressure a bove one

at mosphere, the chang e in frequency response corresponds t o tha t below one a tmos-

phere, but with the opposite sign.

Fig.3 .11 Exampl e of the var i a t ion in sensi t i v i ty as a funct ion of am bient pressur e

Fig.3.12 Typical variat ion in f requency r esponse (norma l i sed at 250 H z) fr om t hat at 101 kPa, as a fun ct ion of change in am bient pressur e

1 10 100 1 kAmbient Pressure (kPa)

– 6

– 4

0

dB

950615e

– 2

2

4

950613e

1k 10kFrequency (Hz)

– 1

0

2

Correction (dB)

1

3

500 50k

– 10kPa

change

– 20kPachange

– 40kPa

change

8/9/2019 be1447


Cha pter 3 — Cha ra cterist ics of MicrophonesReversible Changes


BE1447–11 3 − 21

3.13.3 Effect of Humidity

B rüel &Kjæ r m icrophones have been tested for effects of humidity a ccording t o

IE C-68-2-3 st a nda rd for Ba sic E nvironm enta l Testing P rocedures.

In general , humidity has no influence on the sensit ivity and frequency response of

the microphone. However some microphones have a layer of quartz on the dia-

phragm which absorbs moisture. This leads to a decrease in tension of the dia-

phragm and a corresponding increase in microphone sensitivity. The magnitude of

this effect is t ypically 0.4 dB /100% rela tive h um idity. S ee microphone t ype specific

informa tion for m ore details .

The situat ions where one should be aware of humidity problems are where sudden

changes in temperature and humidity occur, for example, when going from a warm,

humid environment to a cool air-conditioned building. The opposite situation is not

so crit ical because any condensat ion that may occur will only affect the outside of

the ins t rument .

However, if condensation occurs, it will usually result in some electrical leakagewhich obviously results in a malfunction of the microphone and preamplifier. The

moisture will at tenuate the sensit ivity of the microphone and as a side effect , in-

crease the inherent noise level, see Section 3.10.

3.13.4 Effect of Vibrat ion

The vibrat ion sensit ivity of the microphone (normal to the diaphragm) is well de-

fined as i t is determined by the mass of the diaphragm. The vibrat ion sensit ivity is

much smaller in all other direct ions. Preamplif iers and electrical adaptors and alike

may also contribute to the vibrat ion sensit ivity of the measurement channel. The

vibrat ion sensit ivity usually varies with the vibrat ion direct ion. The magnitude of

this effect is of the order of 65 dB (SP L) for 1/ms −2.

3.13.5 Effect of Magnetic Field

The Brü el &Kjær m icrophones a re designed with m a terials tha t provide a very low

sensit ivity to magnetic f ields. The latest Falcon RangeTM microphones have signifi-

cantly lower sensit ivity to magnetic f ields than earlier microphones.

3.13.6 Electroma gnetic Compat ibility

A microphone cartridge is a passive and well shielded component. Therefore theelectromagnetic compatibili ty ent irely depends on the equipment connected to the

ca rtr idge. See Sect ion 4.7, for more information on this subject.

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8/9/2019 be1447



BE1447–11 4 − 1

Chapter 4

Characteristics of Preamplifiers

8/9/2019 be1447


Ch a pter 4 — Cha ra cterist ics of P ream plif iersIntroduction to Characteristics of Preamplifiers



4.1 In t roduct ion to Cha rac ter is t ics of P rea mplifiers

4.1.1 Defini t ion of a Microphone P reamplif ier

A microphone preamplif ier is an impedance converter between a high impedance

microphone and its following cable. A low output impedance is necessary to drive

long signa l cables.

4.1.2 Selection of a Microphone Prea mpli fier

In principle, microphone preamplifiers have more or less identical electrical charac-

terist ics i .e . a gain of unity and a frequency range of a few hertz to more than

200kHz. The most obvious difference between preamplifiers is the diameter, with

the most common diameter being 1/2″. For acoustical reasons, it is usual to select a

preamplif ier with t he sam e dia meter as t he microphone to be used. Brüel &Kjær

produce 1/2″ a n d 1/4″ preamplif iers. Adaptors are available to connect these to 1/8″ or

1″ microphones.

Apart from diameter, other important select ion parameters include the transmission

principle, (for example, current, voltage or digital signals) system verification facili-

t ies, phas e cha ra cterist ics, inherent n oise an d current supply req uirements.

4.1.3 C on t en t s of t h is C h apt er

Certain characterist ics are commonly referred to in discussion of the performance

and design at tr ibutes of preamplif iers. This chapter describes these characterist ics

in some detail . The information is intended to promote both a general understand-

ing of prea mplif iers a nd to support th e inform at ion given in Volume 2 of this ha nd-

book.

4.2 Fr eq uen cy R espon se

The frequency response of a microphone preamplifier typically covers a range from

a few her tz and up t o approxima te ly 200 kHz, wh ich is far great er tha n the a udible

range of humans. Within most of this range, the amplif ier acts as a buffer with a

near perfect flat frequency response. The responses at the extremities of the fre-

quency range are more complex and are described in Sect ion 2.4 and here, in more

detail , under separate headings.

4.2.1 L ow Fr eq uen cy R espon se

Usually the low frequency response of a microphone and preamplif ier combinat ion

is determined by the stat ic pressure equalisat ion system of the microphone. There

is however, another important factor to be considered. The electrical low frequency

8/9/2019 be1447


Cha pter 4 — Ch a ra cterist ics of Pr eam plif iersFrequency Response


BE1447–11 4 − 3

response of the m icrophone capa cita nce in combinat ion w ith t he input im pedance of

the preamplifier.

This electrical response at low frequencies is determined mainly by the highpass

filter (R-C circuit), created by the capacitance of the connected microphone (C m ) and

the input impedance of th e preamplif ier (Ri ), giving the –3 dB cut-off frequ ency:

The typical electrical low frequency responses are normally shown with capacitanc-

es equivalent to common 1/4″, 1/2″ a n d 1″ microphones (typica lly 6 pF, 15 pF a nd

50 pF). While the m icrophone capa cita nce is a ra ther simple a nd w ell defined prop-

erty, the preamplifier input impedance can be more complex.

Normally, the input impedance consists of a resistive impedance of approximately

20 G Ω in combina t ion with sma ll stra y capa cita nces of a bout 0.2 pF. In conjunction

with the microphone, this results in a 1 st order highpass filter, as mentioned above,

with a minor capacit ive at tenuat ion of the microphone signal.

Some preamplifiers use a boot-strapping technique where there is feedback from

the output signal to the input of the amplif ier . This reduces the alternat ing voltage

across the components, result ing in lower input currents and subsequently in a

higher impedance. This technique can be used to achieve a very low cut-off frequen-

cy, as well as good phase linearity. Note that with some preamplif iers which use a

bootstra pping technique, a ga in peaking a t frequ encies under 20 Hz ca n occur. In

combinat ion with low frequencies and perhaps inaudible signals , this can result in

an overload of the system.

Fig.4.1 shows typical electrical low frequency responses for two different types of

preamplif ier , one with a simple resist ive input impedance and one with a complex

input impedan ce obta ined by bootst ra pping.

Also shown in Fig.4.1 is a solution for lowering the electrical cut-off frequency of

the preamplif ier . This is done by simply adding stray input capacitance to the

preamplif ier . Special adaptors may be used to obtain this effect , but this obviously

also has the effect of lowering the sensit ivity for the system. Such a microphone

and preamplif ier system is useful for measuring low frequency sound.

4.2.2 High Frequency Response

Normally, the high frequency response of a microphone and preamplifier combina-

tion is determined by the acoustical high frequency cut-off of the microphone. How-

ever, the electrical high frequency response of the combined preamplifier and cable

loading must also be considered.

f 3–1

2π R i C m ⋅ ⋅-------------------------------=

8/9/2019 be1447


Ch a pter 4 — Cha ra cterist ics of P ream plif iersFrequency Response



The electrical high frequency response is determined by different properties of the

preamplifier in combination with the capacitive load of the connection cable. These

propert ies are the output impedance, the maximum output current capacity and the

ma ximum output s lew ra t e .

The normally mentioned “Frequency Response” will be considered here as the re-

sponse obtained when the dynamic propert ies of the preamplif ier are negligible.

This response is also known as the “small signal” response. The opposite, “large

signal” response will be discussed in S ect ion 4.3: “Dy na mic Ra nge” .

The small signal, electrical high frequency response of the preamplifier is deter-

mined by the low pass f i l ter created by the output impedance of the preamplif ier

a nd t he capa cita t ive loa d of the connection ca ble.

The output impedance is determined by protection components built into the

preamplifier output circuit stage. This protection consists of a current limiting re-

sistor and for some preamplif iers, a f i l ter that protects the preamplif ier electronic

circuit against high frequency electromagnetic noise picked up by the cable. Thisfi l ter includes a series inductor, which in combinat ion with the cable capacitance

ca n cause ga in pea king in the 100 kHz to 200 kHz frequency ra nge, as i l lustra ted in

Fig.4.2. The advantage of this system is that i t enables the preamplif ier to be used

where radio interference can be expected.

Fig.4 .1 Elect r i cal low fr equency r esponse of pr eampl i f iers wi t h var ious mi cr ophone and adaptor combinat ions: a, preampl i f i er wi th bootstrappin g; b, c and d, pr eampl i f iers w i th 1st ord er hi gh pass fi l ter. M icrophone capacitan ce: (a) 6 pF (b) 20 pF, (c) 6 pF (d) 20 pF i n combin ati on wi th a 80 pF stra y capaci t ance adaptor

950962/1e 0.1 Frequency (Hz)1

d

10 100

dB

10

0

– 10

– 20

– 30

– 40

– 50 0

a

b

c

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Cha pter 4 — Ch a ra cterist ics of Pr eam plif iersDynamic Range


BE1447–11 4 − 5

4.3 D yna mic Ra nge

The dynamic range for the microphone and preamplif ier combinat ion is also dis-

cussed in Section 2.4 a n d 3.5. This total dynamic range is primarily l imited by the

preamplifier. This section concentrates on the preamplifier and its associated meas-

urement chain.

The dynamic range of the preamplif ier is the rat io between the maximum and the

minimum output voltages. The lower limit is defined by the self-generated noise ofthe amplif ier and the upper l imit is set by the distort ion created at high output

levels due to clipping of the signal.

The typical dynamic range of a preamplif ier varies from about 1 to 4 µV (A-weight-

ed) to a pproxima tely 35 V with ma ximum preamplif ier supply voltage. This gives a

dyna mic ran ge of up to about 140 – 150 dB . The locat ion of this ra nge with respect

to sound pressure level, is mainly dependent on the sensitivity of the selected mi-

crophone. The selection of the microphone depends on the actual measurement re-

quirements, see Chapter 5.

The remainder of this section describes some of the different mechanisms which set

the limits at both ends of the dynamic range.

4.3.1 U pper lim it of D y na m ic R a n ge

The parameters that determine the combined frequency response of the preamplif i-

er and cable also determine the response and behaviour at high signal levels . These

Fig.4 .2 El ect r i ca l h igh frequency responses for smal l signa l of pr eam pl i f iers wi th di fferent cable capacitan ces. Th e cable

capaci t ance is typical l y 100 pF/ m

950966e

10 k 100 k 1 M – 20

– 15

– 5

0

5

5

300 pF

300 nF

30 nF

3 nF

10

dB

Frequency (Hz)

8/9/2019 be1447


Ch a pter 4 — Cha ra cterist ics of P ream plif iersDynamic Range



parameters are the maximum output vo l tage , the current and the s lew ra te o f the

signal.

4.3.2 Max imum Volt ag e

The limitat ion set by the maximum output voltage is due to a clipping of the signal

which occurs when the peak of the output signal reaches a maximum level set bythe supply voltage, minus a voltage-drop determined by the preamplifier construc-

tion. See the specifications for the relevant preamplifier for details.

Clipping is responsible for th e ma ximum outp ut a t lower freq uencies. To ma ke the

most of the dynamic operation range of the condenser microphones, the supply

volta ge has t o be quite high i .e. 100 – 120 V.

If the input signal exceeds the limits set by the supply voltage, an abrupt genera-

t ion of harm onic distort ion w ill result

The maximum sound pressure level that can be handled by the microphone pream-

plifier can be calculated by:

where:

SPL peak = pea k a coust ical sound pressure level in dB re 20 µP a (1 P a = 94 d B )

e peak = peak output voltage of the pream plif ier in V

S c = loaded sensit ivity of th e microphone in V/Pap o = pressure level for sta ted microphone sensit ivit ies = 1Pa .

Note: The pea k signa l is typica lly 3 to 10 dB higher tha n t he RMS va lue (for a

pure tone 3dB, for a noise signal typically 10dB).

4.3.3 Ma x im um C u rr en t

A second limitat ion is the maximum output current . This current is normally deter-

mined by the design of the output stage in the amplifier, however, the current

capacity of the power supply could also be a limiting factor.

The current limitation should be considered when high frequencies, long cables and

relat ively high signal levels are combined. The relat ion between the maximum

sound pressure level, the frequency and cable load for a given current capabili ty is

given by the followin g formula:

SPL peak m ax ( ) 94 20e peak S c p o ⋅-----------------

d B [ ]

log+=

8/9/2019 be1447




BE1447–11 4 − 7

where:

i peak = ma ximum current capaci ty of the preamplif ier or (i f lower) of the pow-

er supply in A.

C L = total ca pacita t ive load presented by the connection cable in F. Typically

50 to 100 pF/m.

po = pressure level for s t a t ed microphone sens it ivi t y = 1 Pa

f = a p pl ied m a x im um fr eq u en cy.

4.3.4 Ma xim um S lew R a t e

The third l imitat ion is due to the slew rate which is defined as the rate of change ofoutput volta ge (i.e. de/dt). The slew r a te limit a tion is caused by th e intern a l cur-

rents and capacities inside the preamplifier. This is typically the limiting factor for

the output-voltage and frequency when short cables are used.

The slew ra te only requ ires at tent ion in specia l situa t ions, for example, w here com-

bined very high frequencies and signal levels occur. The limitation is described by:

where:

de /d t = m a xi mu m s lew r a t e, V/s

f ma x = m a xi mu m f req u en cy of in t er es t

The influence of these three limitat ions (voltage, current and slew rate) are shown

in Fig.4.3. The upper limit s a re defined here by a dist ortion level of 3%. Comm on to

all these limitat ions is the fact that an excess will create a sudden rise in the

distort ion level. Contrary to this , the microphone exhibits an almost l inear relat ion-

ship between sound pressure level and distortion (see Chapter 3 for details). There-

fore, the contribution of the preamplif ier to the total distort ion can pract ically be

ignored until one of the mentioned limits occur.

SPL peak m ax ( ) 94 20i peak

2π f C ⋅ L S c p o ⋅ ⋅ ⋅-----------------------------------------------

d B [ ]log+=

SPL peak m ax ( ) 94 20d e d t ⁄

2π f m ax S c p o ⋅( )⋅---------------------------------------------- d B [ ]log+=

8/9/2019 be1447





4.3.5 L ow er L im it of Dy na m ic R a nge

The lower l imit of the dynamic range of the preamplif ier is set by the inherent

noise. The noise is primarily generated by two independent sources: resistor noise

N R and transistor noise N FET .

These two noise sources can be considered as being located in the passive and

a ct ive pa rt of the pream plif iers input circuit respect ively, a s show n in Fig.4.4.

The N R -noise is the thermal noise created by the high value resistors in the input

circuit (R i). Thermal resistor noise is characterised as white noise i.e. the same

magnitude for all frequencies and is proport ional with both resistance and absolute

F ig.4 .3 M aximu m ou tpu t vol tage vs f requency show ing the in f l u - ence of pr eampl i f ier l i m it ati ons caused by: a) maxim um suppl y volt age, b) sl ew r at e. Th e cur ves, for d i fferent ca-

ble lengths and l oads, are al l caused by cur rent l im i ta- t ion

Fig.4 .4 Schemat i c d iagram of preampl i f ier showi ng noise sour c- es

1 k 10 k 200 k

10

50

1100 k

Total Supply Voltage 120 V ab

a

Total Supply Voltage 28 V

3 0 m

F i x e d C a b l e

F i x e d C a b l e

9 0 m

3 0 n F

3 0 n F

1 0 0 n F VRMS

950309/1e Frequency (Hz)

200

40

b

950393/2e

NR

Ri

Cm

Cc

~

NFET

8/9/2019 be1447




BE1447–11 4 − 9

temperature. However, in the preamplif ier , this resistor noise is shunted by the

capacitance of the microphone (C m ). This has the effect of low-pass filtering the

noise signal, result ing in a noise spectrum as seen in Fig.4.5, which shows the noise

spectr um for dif ferent combina t ions of ca pacita nce and resistan ce.

In the frequency range where the preamplif ier is used, this low pass f i l tering caus-

es a noise decrease when the input resistance increases due to the low pass f i l ter-

ing effect . For this reason, modern preamplif iers are designed with high input

resistances.

The input resista nce is determined by t wo resistors; one used t o esta blish the polar-

isation voltage for the microphone and the other, to set the DC-working point for

the preamplifier. Resistors of too high a value can give practical problems, both

with respect to DC-stabili ty and with inconvenient long stabilisat ion t imes for the

complete measuring-system.

The second noise source, the transistor noise N FET , is related to the act ive part ofthe amplifier input stage, which consists of a Field Effect Transistor (FET). The

FET noise has three different origins: channel noise, (creating white noise), materi-

al impurit ies, (creat ing pink noise) and leakage current , which in combinat ion with

the input resistors creates white noise “coloured” by the input impedance. The in-

fluence of th e leaka ge current w ill be mentioned u nder S ection 4.6: E ffect of Tem-

perature.

Fi g.4.5 N oise spectr al densi ty , for di f ferent combinat ions of m icrophone capaci t ances and

in put r esistan ces

10 – 9

10 – 8

10 – 7

10 – 6

10 – 5

10 – 4

V/ Hz

960272e

10 k 100 k1 k1001010.100.01

Frequency (Hz)

15 G, 6 pF

30 G, 20 pF

15 G, 20 pF

V H z ⁄

8/9/2019 be1447





Under normal environmental condit ions, only the white noise source is relevant .

This white noise source has the same nature as the previously mentioned resistor

noise, but here the resista nce is ty pically 1 t o 2k Ω. The microphone capacitance

does not have any pract ical influence on frequency distr ibution of this noise and, as

seen in Fig.4.6 , this noise component becomes responsible for the noise from about

1kHz and above .

Due to coupling capacities (shown in Fig.4.8 a s C c ), a fraction of the FET noise is

coupled forward to the high impedance input of the preamplif ier , result ing in an

increase in the noise level. The noise contribution from this mechanism depends on

the capacitat ive at tenuator formed by the microphone capacitance C m and the cou-

pling capacities C c . This explains why the higher frequency noise also depends on

the capacitance of the microphone.

Note that the noise spectra shown in Fig.4.6 a s , w hich is comm only used

in electronic engineering, but not in the field of acoustics where a representation as

shown in Fig.4.7 is more usual. Here, the total noise is shown for a constant rela-

t ive bandwidth ( third octave) in combinat ion with two different microphone capaci-

tances.

Fig.4.6 Spectr a of noise sour ces in pr eampl i f i ers

V H z ⁄

950961e

0.1 1 10 100

10 – 4

V/ Hz

10 – 5

10 – 6

10 – 7

10 – 9

10 – 8

0.01 1000 10000 100000 Frequency (Hz)

Effect of

increasein temperature

Thermal

generated

resistor noise

White noise(from FET)

Flicker noise

(from FET)

20 Hz to 200 kHz (Bandwidth - 206 kHz)

20 Hz to 20 kHz (Bandwidth - 23 kHz)

A-Weighting (Bandwidth - 13 kHz)Effect of increase in

microphone capacity

Thermal resistor noise+ microphone capacity

Effect of increase in

cross coupling capacity

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Cha pter 4 — Ch a ra cterist ics of Pr eam plif iersPhase Response


BE1447–11 4 − 11

4.4 P ha se Response

The pha se response is th e dif ference betw een t he pha se of the output a nd the input

signals, expressed as a function of the frequency.

All Br üel &Kjær prea mplif iers ar e designed to keep the pha se of the output signa l

essentially equal to the input signal, but for the reasons described in Sect ion 4.2 a

phase deviat ion for low and high frequencies can occur. From about 10Hz to above

100 kHz, th e magn itude response is genera lly f lat , wh erea s the corresponding phase

response is close to zero degrees from ty pica lly 100 Hz to 10 kH z, see Fig.4.8.

The low frequency pha se response is determined by t he m icrophone ca pacita nce and

preamplif ier input resistance, while the cable load in combinat ion with the output

impeda nce determines t he pha se response a t t he high frequencies.

For some applications, for example, for sound intensity measurements, it is impor-

tant that the phase di f ferences be tween a number o f measurement channels are

very small . I t is recommended that specially developed types of preamplif ier are

used for this kind of measurement . By minimizing the influence of the resist ive

part of the preamplifier input impedance, it is possible to obtain more closely

matched phase responses between a number of channels.

4.5 E f fect of Tem per a t u r e

The specif icat ions of preamplif iers are normally valid within a working temperature

range f rom – 20°C t o + 60 °C. Some preamplif iers are designed with components and

Fi g.4.7 Typical thi rd octave noise spectr a for preampl i f iers noise connected to tw o di f fer ent m icrophones (dumm ies, 6 pF and 20 pF)

1 µV

6 pF 20 pF

10 µV

0.1 µV

2 5

3 1

. 5 4 0

5 0

6 3

8 0

1 0 0

1 2 5

1 6 0

2 0 0

2 5 0

3 1 5

4 0 0

5 0 0

6 3 0

8 0 0

1 k

1 . 2

5 k

1 . 6

k 2 k

2 . 5

k

3 . 1

5 k

4 k

5 k

6 . 3

k 8 k

1 0 k

1 2

. 5 k

1 6 k

2 0 k

H z A

L I N

950964e

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Ch a pter 4 — Cha ra cterist ics of P ream plif iersEffect of Temperature



materials that allows them to be operated at high temperatures. However, there are

always some limitat ions that should be taken into considerat ion.

First ly, at high temperatures, the failure rate of the device increases. At tempera-

tures above 100 – 125o this increase is dramatic and the preamplif ier should only beused at such temperatures for short term measurements.

Another considerat ion concerns the output power which causes internal heat ing of

the semiconductors. In combinat ion with high external temperature, this heat can

destroy the output transistors. The preamplif ier can deliver the specif ied current ,

but i f this is done for a long t ime at a high temperature, the heat will destroy the

preamplifier.

I f i t is necessary to measure at temperatures which exceed the specif ied values

guara nteed by B rüel &Kjær a nd i f a lower ma ximum output can be accepted, the

preamplif ier supply voltage may be reduced to decrease the risk of overheat ing the

circuitry. In such circumstances, the use of a 1/2″ preamplif ier is recommended aspreamplif iers of this size are more eff icient at losing heat than 1/4″ preamplifiers.

For preamplif iers working at high temperatures, an increase in the noise level is

caused by an increase in the bias current in the preamplif iers. This very small bias

current of a few pA, produces a noise spectrum equal to the resistor-noise. At nor-

mal temperatures this noise is negligible but a temperature rise of 7oC causes a

doubling of the noise contributions and so a change from 25 oC to 75oC will increase

the noise level by approximately 40dB. That is enough to make it comparable to

the resistor-noise. At even higher temperatures, this noise is the most dominant

component. This effect of temperature is shown in Fig.4.6 . High temperature noise

da ta a re given in B rüel &Kjær type-specific documenta t ion.

F i g.4.8 Phase r esponses for tw o di ffer ent types of pr eampl i f i er. A f ir st or der i npu t cir cuit gives a 90 °ph ase shi ft a t l ow fr equencies, wh er eas a second ord er i npu t cir cui t (bootstr ap) gives a 180 °phase shi ft. T he latt er can be optim ised for very l ow ph ase shift for f r equencies above 10 H z

950965e

0.1 1 10 100

180

Degrees

135

90

45

0

– 45

0.01 1 k 10 k 100 kFrequency (Hz)

1 M

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Cha pter 4 — Ch a ra cterist ics of Pr eam plif iersEffect of Magnetic Fields


BE1447–11 4 − 13

4.6 E ffect of M a g net ic F ield s

The design of the preamplif ier ensures that the influence of external magnetic

fields is negligible. In pract ice, this means that no influence can be detected within

a measurement accuracy of 0.0dB, when the preamplif ier is exposed to a magnetic

field of 100 A/m .

4.7 E lect r om a g n et ic C om pa t i bilit y

The electromagnetic compatibility (EMC) of a product which contains electronic

components is the abili ty of the product to funct ion, as intended, without disturbing

and without being disturbed by other electronic equipment .

Some electromagnetic disturbances have existed for many years, for example,

through electrostat ic discharge, l ight ing transients and mains voltage f luctuat ions.

The recent interest in EMC, however, is due to the huge growth in the use of

electronic equipment; from microcomputers operating at radio frequencies to mobile

telephones using pulse modulation. Such devices emit electromagnetic noise at ra-dio frequencies which can interfere with equipment that has insufficient immunity.

At the same time, electronic circuits are being integrated in all sorts of electrical

appliances, from washing machines to burglar alarms, making these products more

susceptible a nd vulnerable t o electr omagnetic disturba nce.

The following sect ions give a short introduction to EMC requirements, with an

emphasis on those a spects releva nt to m icrophone pream plifiers.

4.7.1 The Europea n EMC Di rect ive

Requirements and limits regarding the emission of radio frequencies have existedfor many years. Until recently, l i t t le at tent ion was paid to the fact that delicate

electronic circuits are easily disturbed by strong external signals . In addit ion to the

emission requirements, the European Union EMC direct ive now makes immunity a

mandatory requirement . The direct ive states that electrical and electronic equip-

ment must be suff icient ly immune to disturbances of various kinds. All electrical

and electronic devices must comply with the EMC direct ive in order that they can

legally be sold in Europe.

4.7.2 Th e C E la b el

The presence of a CE label on a product indicates that i t complies with all relevantEuropean Union Direct ives. The CE label is aff ixed by the manufacturer (or an

authorised European representat ive) and indicates that product complies with the

requirements of the EMC direct ive and other direct ives as applicable. Precisely

what the relevant requirements are will depend on the product , but for all electron-

ic devices, the requirements include electromagnetic compatibility. Microphone

preamplif iers are CE labelled, but devices such as microphones and cables are pas-

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Ch a pter 4 — Cha ra cterist ics of P ream plif iersElectromagnetic Compatibility



sive components and therefore do not need to be CE labelled. They are however,

subjected to thorough EMC test ing together with their associated equipment , for

example, cables are tested with their associated preamplif iers. In many cases, the

cables have been specially developed (for example, with braiding patterns) to obtainthe specif ied E MC propert ies a s defined by t he ma nufa cturer.

4.7.3 EMC Tes t Fac ilit i es a t B rüe l &Kjær

In recognit ion that EMC requirements are now an important part of the develop-

ment of high q ua lity electronic equipment , Br üel &Kjæ r ha ve invested in fully

equipped EMC test facil i t ies. Certain tests are conducted at external, accredited

test ing labora tories. B rüel &Kjær products fulf i l the toughest generic EMC sta nd-

ards for both emission and immunity. These standards are:

EN 50081-1 G eneric emission sta nda rd. Residentia l comm ercia l an d light in dustry

En 50082-2 Generic immunity standard. Industrial environment

Detailed EMC specif icat ions are given in the Product Data sheets for all

Br üel&K jær products .

Fig.4 .9 GTEM (Gigaher tz Transversal E lect r omagnet ic ) test cel l at Br üel & Kjær’s EM C test l abora- tory: measur in g rad io fr equency sign al s – em issi on and i mmun it y

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Cha pter 4 — Ch a ra cterist ics of Pr eam plif iersMonitoring and Calibration Techniques


BE1447–11 4 − 15

Ca use a nd Cure of E lectroma gnet ic Introduced Noise.

The reasons for the sensitivity of devices to electromagnetic noise are often quite

simple to identify, but the effects can be difficult to avoid.

The connection cable can pick up signals from the electromagnetic field by acting as

an antenna while the semiconductors in the electronic circuit act as rect if iers and

demodula te t he AM signal from t he RF -ca rrier frequency. I t is then very dif f icult t o

separate this demodulated signal from the measurement signal. The best solut ion is

to prevent the RF-signal reaching the semiconductors. This can be done in different

ways. The most common method is a lowpass f i l tering of the signal going into the

electronic circuit.

I t is of course, important , that both ends of the cable are connected to devices that

are able to avoid demodulation of the RF-noise. This means that connecting a

preamplif ier with high immunity to an old measuring amplif ier that is not con-

structed to achieve RF-immunity, will not give the expected immunity for the system.

Fig.4.10 shows th e immunity improvement th at can be obta ined w i th a preamplif ier

constructed to fulfil the EMC-requirements, compared to an earlier version. These

measurements show the noise signal generated in the preamplif ier when it is ex-

posed to a n EMC field as described in the EMC sta nda rds (a f ield strength of 3 –

10 V/m, a modulat ion of 80% AM a nd a carr ier frequency of 80 – 1000MH z).

4.8 Monit or ing a nd Ca libra t ion Techn iq ues

Tw o different verifica t ion techniqu es are a va ilable for B rüel &Kjæ r pream plif iers.

These are either the Insert Voltage Calibrat ion (IVC) facil i ty or the Charge Injec-

t ion Calibrat ion (CIC) facil i ty. Each has a part icular area of applicat ion. The princi-

ple of both t hese techniqu es is shown in Fig.4.11.

Fig.4.10 Pr eampl i f ier noise when exposed to electr omagnetic f i eld ,before (left) and af ter EM C im pr ovement s (ri ght). The 0 dB li ne corr espond s to the inh er ent noise level of the pr eam pli f i er. The x-axis cor responds to t he car r ier fr e- quency (20 M H z to 1 GH z)

950956/1e

50

40

dB

30

20

10

0

50

40

dB

30

20

10

0

3 4 5 6 8 102 2 3 4 5 6 8 MHzMHz103 3 4 5 6 8 102 2 3 4 5 6 8 103

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Ch a pter 4 — Cha ra cterist ics of P ream plif iersMonitoring and Calibration Techniques



The Insert Voltage Calibrat ion method is primarily intended for use in calibrat ion

laboratories for determining the open-circuit sensitivity of condenser microphones.

The open-circuit sensit ivity is t he sen sitivit y (V/P a ) of t he m icrophone w orking t o

an infinitely large electrical impedance, i.e. the same as that of an ideal preamplifier.

The Insert Voltage Calibration technique may also be used to provide a field-check

of a measurement system including a preamplif ier and cables. However, the method

does not account for the mechanical parameters of the microphone cartr idge which

determine the acoustical properties of the measurement setup. The method is suffi-

cient to verify the electrical part of a measurement system, but i t is not sat isfactory

for verifyin g th e microphone cart ridge. To be a ble to verify the complete system ,

B rüel &Kjær h a ve developed and pa tented a techniqu e called Cha rge Inject ion Ca li-

bra t ion (CI C).

However, the IVC technique is st i l l the standardised system that should be used for

calibration of laboratory microphones.

The Charge Inject ion Calibrat ion (CIC) technique represents a great improvement

for remote test ing of a measurement setup compared to the IVC technique. The

system is based on a relat ive measurement of the capacitance of the microphone

cartridge, which is a reliable indicator of the microphones condition.

4.8.1 Inser t Volt a ge Ca l ibra t ion

Insert Voltage Calibrat ion is a standardised method of determining the open circuit

voltage and open circuit sensit ivity of a transducer. Insert Voltage Calibrat ion is a

subst itut ion method where the inserted voltage subst itutes the open circuit voltage

produced by the transducer, see chapter 6 for more details. Insert Voltage Calibra-

Fig.4 .11 Charge I n ject ion Cal ibr a t ion and I nser t Vol tage Cal ibra t ion. The for mul ae are va l id for the m id an d hi gh frequency ra nge

940528/1e

Cm Cc

Ci R1

PreamplifierMicrophone Cable

CIC

IVC

Generator

g

Cm

Ci R1

Typical Valves : Cm = 15 – 20 pF Ci = 0.3 pF Cc = 0.2 pF g ≈ 1

e o

e o

e o

e i

e o

e i

e i

e i

Cc

Cm + Ci + Cc

= g ( )

Cm

Cm + Ci

= g ( )g

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BE1447–11 4 − 17

t ion can be used to monitor a complete acoustic system, but it only checks the

function of the preamplifier, cable and the conditioning amplifier. Therefore, Insert

Voltage Calibrat ion is not the best choice as i t does not give information about the

condition of the microphone. As an example, a short-circuited microphone would

create a cha nge of about 0 .1 dB with a n In ser t Vol tage Ca l ibra t ion sys tem, wh i le i t

would be hundreds of t imes greater with the charge inject ion calibrat ion method

described in the following section.

4.8.2 Charge In ject ion Ca libra t ion

The Br üel &Kjær pat ented Cha rge Inject ion Ca librat ion (CI C) technique ena bles a

complete measurement chain to be verified, including the microphone. As the name

implies, the method uses frequency independent injection of charge into the micro-

phone a nd prea mplif ier input circuit .

The patent includes the measurement method and the pract ical realisat ion of a

high qu a lity, s ta ble ca pacita nce which is built into t he preamplif ier.

The main applications are the monitoring of remote microphones and microphonearrays. The principle of operation is shown in Fig.4.11. The built-in capacitance is

very sma ll , typica lly 0.2 pF. This sma ll capa citor ma kes an a t t enua tor together w ith

the impedance of the combined microphone and preamplifier input circuit . A voltage

supplied at the CIC input will be at tenuated, and can be monitored at the pream-

plif ier output . The rat io between the output and input voltages can be used to

monitor the stabili ty of the whole measurement system, including the microphone,

preamplif ier and cables. A simplif ied formula valid in the mid and high frequency

range is given in Fig.4.11. A more general formula is given here:

where:

e o = out put volt age

e i = in put volt a ge

C c = C IC ca pa cit a nce

C i = input capac it ance of preampli fier

C m = ca p a ci t a n ce of m i cr op hon e

R i = i np ut r e si st a n ce of pr ea m p lif ier

g = pr ea m plifier a m plifica t ion ≈ 1

As indicated by the formula and as shown in Fig.4.12, the method can be used to

monitor the preamplif ier input resistance at low frequencies and the microphone

capacitance in the mid and high frequency range.

e o

e i -----

C c

C c C m C i + +

----------------------------------- g 11

j ωR i C m C c C i + +( )-----------------------------------------------------+

1–⋅ ⋅=

8/9/2019 be1447





The acoust ical equivalent level to the signal introduced through CIC can, for the

mid frequency ra nge, be ca lculat ed a ccording t o:

where:

S c = load ed sensit ivity for the microphone (e.g . 12.5 mV/Pa )

p o = pressure level for s ta ted microphone sensi t iv i ty (1 Pa )

C m = microphone capaci tance (e.g. 15pF)

C c = C I C ca p a ci t a n ce (t y pi ca l ly 0 .2 p F)

The CI C m ethod shows t ha t t he microphone capa cita nce varies w ith freq uency. This

phenomenon is explained in Section 3.8.

Use of the CIC System

For acoust ical systems, frequent use of a precision acoust ical calibrator would be

the ideal means of verif icat ion. Although this can involve pract ical and economical

disadvantages, for example, dif f iculty of access, the t ime involved and disassembly.

Used in the r ight way, the CIC technique has the advantage that i t can be used to

increase the interval between cost ly acoust ical calibrat ions. However, an acoust icalcalibration can never be completely replaced by an electrical test facility.

F i g.4 .12 M easu red r a t i o e o / e i as a fun cti on of fr equency for a1 / 2 ″ mi cr ophone (50 mV / Pa) and

pr eampl i f i er, wi th and w i t hout polar i zat ion vol tage

– 39

– 38

– 37

– 36

– 35

–34

– 33dB

1 10 100 1k 10 kFrequency (Hz)

100 k

960273e

Without polarization voltage

With polarization voltage

SPL C I C 94d B 20e i

S c p ⋅--------------o

C c C c C m +----------------------

⋅

log+=

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BE1447–11 4 − 19

How to Monitor Using CIC

The procedure is a s follow s:

1. Ins t a l l t he sys t em a nd per form a n a cous t ica l c a l ib ra t ion .

2. Immediate ly a f terwa rds , measure the ra t io betw een the output and input vol t -

ages of each measurement channel.

3 . Store the measurement resul t s as re ference ra t ios and the sys tem is ready for

use.

4. Verif icat ion of the system can now be performed a s often a s necessary by com-

paring the present measured rat ios with the stored reference rat ios.

5 . For normal temperature and pressure, var ia t ions w i th in 0.2 dB could be expect-

ed. Under controlled conditions, for example, in special test cells, a repeatability

of bet ter than 0.1dB can, and should, be obtained.

For results which vary more than expected, the system should be checked with anacoust ical calibrator . Frequent init ial measurements will create a database valid for

the actual set-up on which the threshold for acceptance can be based. As experience

and confidence is built up, the interval between acoust ical calibrat ions can be ex-

tended.

Note, that some types of microphone have a deliberate variat ion of capacitance as a

funct ion of temperature which will be reflected in the measured rat ios.

4. 8.3 C I C I n pu t S ig na l R equ ir emen t s

Test Lev el

A test signal close to the a llowed ma ximum limit is recommended in order to obta in

a good signal to noise rat io between the at tenuated calibrat ion output signal and

the signal produced by the acoust ical background noise. I f available, use f i l ters for

the measurement of the test signal to improve the repeatabili ty of the test meas-

urement. This will lead to more stable results.

For a 1/2″ microphone (15 pF) the a t t enuat ion ra t io will be in the ra nge of − 35 d B t o

− 40 dB. This mean s tha t for a test signa l of 10V, an output of 180 mV to 100 mV is

obta ined. To est ima te w hether ba ckground noise ha s a n influence on t he results , i t

is worth n oting th at a test signa l of 10V using a m icrophone wit h 50 mV/Pa sensi-

t ivity corresponds to a sound pressure level of more th an 100 dB.

There are no special requirements for the long term stability of the test level,

provided that the rat io between the output and input voltage is determined.

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Test Fr equ encies

Even if the system has the possibili ty to measure over the entire frequency range,

it is recommended to l imit the amount of data by only using two test frequencies.

Us e one in the m id frequency ra nge (for exa mple, 1000 Hz) and one a t a low fre-

quency, for example, 20Hz.

The measurement at low frequency has a higher sensit ivity to possible problemscaused by humidity ( leakage) , whilst the mid-frequency measurement monitors the

sta bili ty of the m icrophone ca rtr idge.

Faul t D iagnos is wi th C IC

Those who do the monitoring of the measurement system do not need to know the

reasons for the observed changes in the rat io between the output and the input

signals . However, those who perform the maintenance and fault f inding may f ind

the following examples of the use of CIC helpful.

The following examples are obtained using a white noise signal as the CIC input .

Norma l Working Condition:

Fig .4.13 N orm al work ing condi t ion . N ot ice the at tenuat ion of appr oxim ately 40 dB in th e m id fr equency range. The low fr equency rol l -off i s caused by th e pr eampl i f ier i npu t r e- sistance

960268e

Input signal

Output signal

Hz

– 40 dB

0 dB

eo /ei

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BE1447–11 4 − 21

Dia phra gm Torn or Missing

Microphone Short Circuited

Fig.4 .14 N o mi crophone at tached or d iaphr agm torn or mi ssin g.Th e outpu t level is signif icant ly i ncreased du e to r edu ced

m icr ophone capacitan ce

Fig.4.15 M icrophone short ci rcui t ed. The output level i s signi f i - cantl y reduced r el ati ve to the norm al cond it ion

960269e

Input signal

Output signal

Hz

– 40 dB

0 dB

eo /ei

960270e

Input signal

Output signal

Hz

– 40 dB

0 dB

eo /ei

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Disconnected or Broken Cable

Fi g.4.16 Di sconnected or broken cable. The outpu t l evel wi l l change si gni fi can tl y depend in g on th e di stan ce betw een th e condi t i oni ng am pl i f ier and the break i n t he cable. A: cable br oken near t o power suppl y. B: cable broken near

to th e mi cr ophone

960271e

Input signal

A

Hz

B

– 40 dB

0 dB

eo /ei

8/9/2019 be1447



BE1447–11 5 − 1

Chapter 5

Selecting a Microphone

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Ch a pter 5 — S electing a MicrophoneGuidelines on Selecting Microphones



5.1 G uidel ines on Se lect ing Microphones

When select ing a measurement microphone it is important to f irst understand the

measurement requirement and how this imposes demands on the performance of

the microphone. This is necessary because, although measurement microphones are

precision instruments that are optimised for part icular measurement tasks, they

st il l offer a wide operat ional range.

In fa ct , such is the versa t i l i ty of B rüel &Kjær m icrophones, tha t t he user ma y be

tempted into a “that one will do” philosophy when selecting a microphone, simply

because a microphone comes within the required general performance parameters.

I f , however, the user has a good understanding of the measurement requirement ,

then it is possible to choose the “optimum” microphone for the measurement task in

hand .

For most uses, the type of sound field is the main parameter to consider. This

divides the possible choices into roughly two groups of microphones: free-field or

pressure-field measurements.

Other fac tors , such as the measurement environment , the in ternat ional s t andards

which may need to be adhered to and the type of polarisat ion charge may also need

to be considered. These and other main considerat ions are discussed in more detail

in th is chapter.

B ut f irst , a s a prelude to a ny specif ic select ion guidelines, i t should be stressed tha t

select ion considerat ions cannot be taken in isolat ion. Many of the parameters are

inter-dependent. To illust ra te t his point, exam ples of tw o sepa ra te, but in ter-linked

considerations are given. The first being frequency response, the second being that

of dynamic range. Three diagrams il lustrate this point .

Fig.5 .1 U pper l im i t i ng frequency response of 4 typ ica l m easur e- ment m i crophones of d if fer ent sizes 1/8″, 1/4″, 1/2″ and 1 ″

950745e

1 2 4 8 2010 40 80 160

1"

1/2"

1/4"

1/8"

Lower Limiting Frequency Upper Limiting Frequency

8/9/2019 be1447


Cha pter 5 — Select ing a MicrophoneGuidelines on Selecting Microphones


BE1447–11 5 − 3

The above f igures show that i f , for example, measurements at very high frequencies

are required, this will automatically l imit the choice of microphone to one with a

fair ly high, lower l imit of dynamic range.

Once the optimum microphone has been selected in terms of primary selection pa-

rameters, there will most probably be several other considerat ions which are rele-

vant to the measurement requirement , for example, the physical robustness of the

microphone for the measurement environment . This can be il lustrated by compar-

ing two different types of microphone.

A 1/2″ microphone for laboratory s tandard ca l ibra t ion and a 1/2″ microphone for

general use may appear to have similar performance parameters on paper, but

actually have quite dif ferent physical characterist ics . The mechanical design of the

laboratory standard microphone makes it very well suited for pressure reciprocity

calibrat ion, but the almost unprotected diaphragm makes this microphone far too

frag ile for g enera l use.

Fig.5 .2 Dynami c range of the same 4 measur ement m icrophones.The lower l imi t is given in dB(A). The upper l imi t is given i n dB at th e level at w hi ch 3 % total h arm onic di stort i on occurs

F ig.5 .3 Graph show ing rela t i onsh ip between upper l im i t i ng f requency ran ge and i nh er ent noi se. The 4 dot s repr esent th e 4 sizes of m i cr ophone in or der fr om 1 ″ (bott om l eft)

to 1/8″ (top ri ght)

950746e

160140 18010 20 30 40 50

1"

1/2"

1/4"

1/8"

dBA dB 3% Total Harmonic Distortion

Upper limiting frequency, kHz

I n h e r e n

t N o

i s e ,

d B

950747e

0 0

10

20

30

40

50

60

20 40 60 80 100 120 140

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Ch a pter 5 — S electing a MicrophoneWhat to Consider



With this background, the following section gives some of the main considerations

when selecting a microphone.

5.2 Wha t t o C onsider

5.2.1 Frequency Response

Although particular types of microphone are optimised for particular purposes, they

st il l hav e a wide opera t ional r a nge, as explained by t he Freq uency R esponse/Dy-

na mic Rang e inter-relat ionship in Sect ion 5.1. Frequency response should therefore

be considered in relation to other selection requirements such as the type of sound

field.

5.2.2 Type of Sound Field

A good way of narrowing down the choice of microphone is to consider the type of

sound field in which measurements are being taken.

For measurements to be made away from reflect ing surfaces or in acoust ically well

damped indoor environments, for example when making outdoor measurements

with a sound level meter or indoors in an off ice offering a lot of natural acoust ic

damping, a free-field microphone offers the best choice.

Meanwhile, for measurements to be made in small closed couplers or close to hard

reflective surfaces, a pressure field microphone is a more appropriate choice. An

applicat ion which il lustrates such usage is where a set of pressure sensing micro-

phones a re posit ioned a t dif ferent points a cross a n a ircraft wing. A complete picture

of the pressure variat ions across the wing surface can then be established.

For measurements in enclosed areas where reverberations are likely, pressure field

microphones adapted for random incidence measurements offer the best choice. This

is because the random incidence response of a pressure-field microphone is much

“flat ter” or constant across the frequency range, than that of a free-field response

microphone. This is something that can be observed by comparing the random inci-

dence response of a pressure field with that of a free-field microphone using the

graphs in Volume 2 of this handbook. See also chapter 2 Section 2.5 for an explana-

tion of how different types of microphone are dedicated to different sound fields.

5.2.3 L imit s of D yn amic R an ge

The lower limit of dynamic range is dictated by the inherent noise of the micro-

phone and preamplif ier combinat ion. The upper l imit of dynamic range dictated by

the ma ximum s ound pressure level (3% tota l ha rmonic distort ion). Due t o the very

wide dyn a mic ran ge of the m icrophones, it is n orma lly either the lower or the upper

limit of dynamic range that is of interest .

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Cha pter 5 — Select ing a MicrophoneWhat to Consider


BE1447–11 5 − 5

An example applicat ion for measurement microphones where the lower l imit of

dynamic range has to be considered is that of the determinat ion of sound power of

light ar ma tur es for use in off ice environm ents. Levels a s low a s 10– 12 dBA ma y

have to be measured.

An example application for measurement microphones where the upper limit of

dynamic range has to be considered is that of measurements of exhaust systems on

engine test cells. Here, high sound pressu re levels (140 – 150 dB ) ma y be encoun-

tered. However, in addit ion to high sound pressure levels , high temperature may

also be encountered. In such a case, i t may be necessary to use a probe microphone

However, this type of microphone does not have the highest upper l imit of dynamic

range. Alternatively, where it is possible to use more conventional, externally polar-

ised microphones, the upper limit of dynamic range of these microphones can be

extended slightly by reducing the polarisation voltage to 28 volts.

5.2.4 Microphone Vent ing

As the microphone is only able to withstand a fair ly small stat ic pressure dif ference

between the front and the rear side of the diaphragm, it is important to considerthe choice of side or rea r vented microphone in relat ion t o measur ement situ a t ion.

There are basically two different types of stat ic pressure equalisat ion channels: rear

vented, where the microphone is vented through the rear and via the preamplif ier

and side vented, where the pressure equalisat ion channel is located on the side of

the microphone housing just in front of the thread for the protection grid.

Rear vented microphones have the advantage that they can be used wi th a dehu-

midifier . However for certain applicat ions it is necessary to use a side vented type

of microphone with its pressure equalisat ion close to the diaphragm. This is impor-

tant when the microphone is f lush mounted in an air duct where there is typically

a large stat ic pressure dif ference between the inside and the outside of the duct .

5.2.5 P h a s e R es pon se

Phase response should be considered when choosing microphones for sound intensi-

ty measurements and here it is not normally the absolute phase response that is

important , but the relat ive phase response between a pair of microphones. This is

beca use the pha se response char a cterist ics ha ve to be closely ma tched. Special pa irs

of microphones, wit h m a tched pha se responses, are a va ilable.

5.2.6 P ola r is a t ion

There are two different types of microphone construction, one that employs an ex-

ternal voltage supply to polarise the backplate to diaphragm air gap (externally

polarised) and one where the polarisat ion charge is stored in an electret layer on

the backplate of the microphone (prepolarized).

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Ch a pter 5 — S electing a MicrophoneWhat to Consider



Generally there are only small dif ferences between the specif icat ions for externally

polarized and prepolarized microphones, but these dif ferences make them suitable

for different purposes.

Prepolarized microphones are used for portable sound level meters where their

lightweight and lack of a requirement for a polarizat ion voltage supply is an obvi-

ous requirement. Prepolarised microphones also offer slightly better performance in

very hum id environments (see cha pter 3 L eaka ge resistan ce).

Alternatively, externally polarized microphones are generally more useful for gener-

al f ield and laboratory use and for high temperature measurements. Also, for spe-

cial measurements, externally polarised microphones offer a broader range to

choose from.

5.2.7 S t a n da r ds C om plia n ce

When select ing a microphone, i t is normally a requirement to consider whether the

microphone fulf i ls certain standards, for example, the ANSI S1.12 standard for Lab-

oratory Measurement microphones or the IEC 651 standard for sound level meters(including microphone). As can be gathered from the above example, standards gen-

erally relate to the type of applicat ion for the microphone. In addit ion, a further

range of levels specif ied by type numbers exist within a standard, for example the

IEC 651 standard for sound level meters has types 0 to 3. Type 0 relates to labora-

tory reference standard requirements while type 3 is mainly for f ield applicat ions.

Most B rüel &Kjær microphones ar e type 0 and t ype 1.

The standards and their associated type levels also specify the performance toler-

ances to which microphones and associated equipment must conform. This conform-

ance is stated in product l i terature.

B rüel &Kjæ r microphones ar e designed to come w ithin 50 to 70 % of the requiredtolerances depending on the applicat ion. In the case of tolerances relat ing to the

use of sound level meters the effect of the sound level meter in the sound field is

also ta ken into a ccount w hen designing a nd producing microphones.

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Cha pter 5 — Select ing a MicrophoneWhat to Consider


BE1447–11 5 − 7

Standards Relevant to Measurement Microphones:

5.2.8 E n vir on men t

When select ing a microphone the environment where measurements are to be made

should be considered. Some parameters which should be considered are as follows:

Robustness

In a protected laboratory environment all measurement microphones can be

used, but more robust general purpose microphones are required for field use.

Tempera tu re

At norma l tempera tures (– 30°C t o + 125°C) all microphones may be used. At

high temperatures (up to 300°C) Falcon Range microphones should be used and

at very high temperatures, above 300°C, a probe microphone should be em-

ployed. The tip of the probe on the probe microphone can withstand up to

700 °C.

Atmosphere

In normal air , al l microphones may be used, but for measurements where corro-

sive industrial gasses exist , for example, when making measurements in indus-

trial chimneys, the corrosion resistant Falcon RangeTM microphones should be

used.

Humidi ty

In normal humidity, all microphones can be used, but for high humidity, prepo-

larized microphones offer greater reliability. This is because they are more re-

sistant to the at tenuat ion of the polarizat ion voltage which can occur at high

humidity levels.

Standard Application Date

IEC 651 Sound Level Meters 1979

IEC 1094 Measurement Microphones Part 1:

Specifications for laboratory stand-ard microphones

Part 4: Specifications for Working

Standard Microphones

–

ANSI S1.12 Measurement Microphones

Type L: Reference

Type XL: As is but no outside diam-

eter specified

Type M: Sound Pressure Magnitude

Type H: Small diffraction errors

1967

ANSI S1.4 Sound Level Meters 1983

Table 5.1 Stand ard s Appl i cable to Measur ement M icrophones

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Ch a pter 5 — S electing a MicrophoneSelecting The Right Accessories



5.2.9 Microphone Arra y Applica t ions

When many microphones are to be used, for example, for spat ial t ransformation of

sound fields, the size and price per channel are the most important parameters. For

this purpose, a specially designed microphone with built-in preamplifier can be used

as an in tegra l par t o f an array .

5.3 Select ing The Right Accessor ies

Fi g.5.4 Range of m icrophone accessori es: wi ndscr eens, mi cro-

phone holder, tu r bul ence scr een, w in dscr een wi th bir d spik es, r ai n cover an d nose cone

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Cha pter 5 — Select ing a MicrophoneSelecting The Right Accessories


BE1447–11 5 − 9

For most types of microphones the use of appropriate accessories can effectively

extend the applicat ion range of the microphone, part icularly when making outdoor

measurements. Accessories are therefore described here with respect to the two

main threats to effect ive microphone operat ion: wind, or air turbulence, and humid-

ity.

5.3.1 Low Wind Speed, Random D irect ion

Outdoor measurements are often disturbed by wind noise. An easy way of reducing

the effect of wind noise is to mount a wind screen on the microphone (and pream-

plifier/S ound L evel Meter). The w ind screens a re ma de from a porous polyur etha ne

foa m. They wi l l a t tenuat e the wind noise by 10 to 12dB a t those wind speeds gen-

era lly consider ed a ccepta ble for outdoor t esting (0 m/s t o 6 m/s).

5. 3.2 H ig h Win d S peed , K n ow n D i rect ion

Acoustic measurements in wind tunnels are normally very dif f icult due to aerody-

namically induced noise around the microphone. When the microphone is exposedto high wind speed in a known direct ion the disturbance can be reduced by using a

nose cone. The nose cone replaces the normal protection grid. It has a streamlined

shape with a highly polished surface that gives the least possible aerodynamically

induced n oise.

Fig .5.5 N ose cones in d i f ferent s izes to f i t

1 / 8 ″ , 1 / 4 ″, 1 / 2 ″ and 1 ″ m icrophones

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Ch a pter 5 — S electing a MicrophoneSelecting The Right Accessories



5.3.3 Tu rb ulen t P r es su re F lu ct u a t ion s

The turbulence screen is designed to a t t enuat e noise from tur bulence w hen m easur-

ing airborne noise in situat ions where turbulence may occur, such as in ducts and

in wind tunnels.

5.3.4 H umidit y

The microphone may be protected against humidity in dif ferent ways depending on

the type and durat ion of the measurements.

Sh ort Term P rotection

Short term protect ion against humidity when making outdoor measurements in

unfavourable weather can be performed by mounting a dehumidifier between the

microphone and the preamplifier.

The funct ion of the dehumidifier is to ensure that only dry air reaches the interiorcavity of the microphone, thus preventing condensation. This is done by allowing

air to pass to the back vent of the microphone through a cavity f i l led with sil ica gel.

The dehumidifier therefore only works with rear vented microphones.

The dehumidifier is normally used in combinat ion with a wind screen. The assem-

bly should be mounted horizontally in order to let possible water droplets run off

the microphone diaphragm.

Long Term P rotection

For long term outdoor measurements, a more comprehensive combination of acces-sories is recommended consisting of a raincover, a windscreen and a dehumidifier.

The raincover is designed to be mounted in place of the normal protection grid. As

well as offering rain protect ion, i t serves as an electrostat ic actuator which can be

employed for remote calibration.

A special wind screen, with stainless steel bird spikes, and which allows the use of

the rain cover is recommended.

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BE1447–11 6 − 1

Chapter 6

Calibration

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Ch a pter 6 — Ca librat ionIntroduction



6.1 Int roduct ion

The most important parameter for any measurement device is sensit ivity. The sen-

sit ivity can be defined as the rat io of the output parameter to the input parameter

(the m easur an d). To determine the sensit ivity is t o ca librat e the mea surement d e-

vice. All the informa tion tha t follow s in t his chapter is ba sed on this definit ion.

For a transducer, sensit ivity is measured in terms of units of electrical output

(volts, ampere etc) per unit of the physical input parameter (pressure, acceleration,

distance etc). In line with this convention, the sensitivity of a microphone is gener-

ally given in terms of volts per pascal . Pascal is defined as one Newton per square

m et re (N/m 2), i.e. a unit of pressure.

These fundamental units provide a f ixed reference for the calibrat ion of a measure-

ment device. This reference is essential as i t al lows measurements, including cali-

brat ions, to be compared - measurements which could have been made by dif ferent

people, in different locations under different conditions. The units must be referred

to in a known and agreed way. This is well defined and monitored on an interna-

t ional basis . The accuracy of the calibrat ion must also be known i .e the device andmethod used to calibrate a microphone must perform the calibrat ion with a known

uncertainty.

I f these condit ions are fulf i l led the calibrat ion is called traceable because the cali-

brat ion can be re l iably t raced back through the measurement chain , u l t imate ly to

the fundamental units of measurement . The first or highest l ink in the measure-

ment chain is normally a device in a primary calibrat ion laboratory, since these

establishments usually have the most accurate measurement equipment . Normally

the establishment to which a calibrat ion can be traced is stated as a reference for a

calibrat ion and as already mentioned, the terms of reference are monitored between

calibrat ion establishments. See Sect ion 6.5 for more information on traceability.

I t is important to note that traceabili ty is not in i tself an indicat ion of high accura-

cy, but i f the uncertainty is known then the calibrat ion can be compared with other

valid measurements. Therefore a calibrat ion is not useful, unless the related uncer-

ta in ty is known .

Other Definit ions

Definit ions are available which may provide a variat ion on the above. However they

genera lly ha ve some ma in principles in comm on, as seen by the following exam ples:

The first comes from the ISO publication, The In tern at i onal Vocabular y of Ba sic and General Term s in M etr ology :

“Ca librat ion. The set of opera t ions th a t esta blish, under specif ied condit ions,

the relat ionship between values of quantit ies indicated by a measuring in-

strument or a measuring system, or values represented by a material meas-

ure, and the corresponding values realised by standards” .

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Cha pter 6 — Ca librat ionIntroduction


BE1447–11 6 − 3

The important point in this definition is the reference to “corresponding values

realised by standards” in the last part of the rather long sentence. This supports

the argument that fundamental to calibrat ion is a solid and definable reference.

The next definition from the European Space Agency also supports this:

“Calibration. A comparison of two instruments or measuring devices, one of

which is a s t andard o f known accuracy t raceable to nat ional s t andards to

detect , correlate , report or eliminate by adjustment any discrepancy in accu-racy of the instrument or measuring device being compared with the stand-

ard . ”

This definit ion uses the word “comparison” to explain how something unknown is

referred to (or compared with) something known. However, the reference is clearly

def ined as a measurement ins t rument that is ‘h igh ’ in the measurement chain and

tra ceable to nat ional s t an dards .

Why Calibrate?

A calibration is performed:

— To be sure of ma king correct measurements.

— To prove tha t m easurement methods a nd equipment are a ccura te , for example,

to prove that a measurement complies with the requirements of nat ional legisla-

t ion, standards bodies and customers.

— To verify the stabili ty of the mea surement equipment , including equipment used

to perform ca librat ions.

— To account for loca l measur ement condit ions, for exam ple, var iat ions in a mbient

pressure and temperature.

— To ensure product qua lity.

— To build confidence in measurement results .

S u m m a r y

— Ca libra t ion is to de termine the sensi t ivi ty o f a mea surement device.

— The funda menta l units of measur ement (volt , am pere etc) provide the ult ima te

reference for measurement s, allow ing different measu rements t o be compared.

— The accura cy (or uncerta inty) of the calibrat ion mu st be know n. Tra cea bility is

necessary, but not sufficient.

— Ca libra t ion creat es conf idence in the measurement result .

— Devices throughout the measurement cha in must be rel iable an d s table wi th in a

known uncertainty.

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Ch a pter 6 — Ca librat ionCalibration of Microphones



6.2 C a l ibr a t ion of Micr oph on es

This sect ion explains the common terms and methods used in connection with the

ca librat ion of meas urement microphones.

The calibrat ion can either be performed in the f ield or in a calibrat ion laboratory.

These calibrat ion situat ions are described here under separate headings.

6.3 Field C a libra t ion

Field calibrat ion is performed at the measurement locat ion using a calibrated refer-

ence sound source, such as a pistonphone. This ensures the traceability of absolute

sound level measurements. The fact that the measurement is traceable is important

if the measurement must be recognized by legal authorit ies or i f compliance with

internat ional standards is claimed. See Sect ion 6.5 for a discussion on traceability.

I t is advisable to perform a f ield calibrat ion before and after a measurement , for

example, by using a sound level calibrator. This gives confidence in the measure-ment result by verifying the stabili ty of the entire measurement system. Calibra-

t ion before and after a measurement is also something which is prescribed by

various sound measurement standards to ensure the validity of the measurement .

Even when making a re la t ive measurement , i t i s s t i l l advisable to ca l ibra te to

ensure correct operat ion of the measurement system. This is because calibrat ion is

by far the easiest way to check that set t ings, adjustments and postprocessing ana-

lyzers are correct.

Most Sound Level Calibrators are portable, easy-to-use and characterized by the

production of a well defined sound pressure at a single frequency, usually in the

ra nge of 200H z to 1 kHz. Some ca librat ors a re so ca lled Mult itone Calibra tors

which provide a number of pure tones at single frequencies.

When using calibrators that produce a single frequency, the calibrat ion is str ict ly

only valid at this reference frequency. However, microphones are generally manufac-

tured to provide a f lat frequency response which means that they will give the

same electrical output at all frequencies in the f lat frequency range for sound pres-

sures of equa l ma gnitude. Therefore calibra t ion a t a single frequency is suff icient in

most situat ions.

See Section 2.3.9 for more on microphone sensitivity and the reference frequency.

To perform calibra t ions a cross th e entire frequency r a nge, a Mult itone calibra tor

may be used to check the performance of the measurement system.

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Cha pter 6 — Ca librat ionLaboratory Calibration


BE1447–11 6 − 5

In multi-channel microphone systems, or where microphones are difficult to access,

an acoust ical calibrat ion is sometimes impract ical to perform. In these situat ions a

verif icat ion method can be used to provide a quick and easy method of checking the

function of each measurement channel. All the verif icat ion methods have their own

advantages and disadvantages. Three common verif icat ion methods are:

— The Actua tor Method

— The Inser t Vol tage Ca l ibra t ion Method

— The Charge Inject ion Ca l ibra t ion Method

See chapter 4 and Sect ion 6.6 for deta ils.

6.4 La bor a tor y C a libra t ion

Laboratory calibrat ion is a common expression for the type of calibrat ion that can-

not be performed in the f ield. Laboratory calibrat ion is an indoor method, prefera-

bly performed in a dedicated and well-controlled environment.

The laboratory calibrat ion methods are normally more accurate than the f ield cali-

brat ion methods. This is part ly due to the type of equipment used for calibrat ion

and part ly due to the stable laboratory environments. Calibrat ions in the f ield are

especially affected by temperature variat ions, wind and humidity.

While f ield calibrat ion is usually applied to an entire measurement system, labora-

tory calibrat ion also covers the calibrat ion of separate devices such as microphones

F ig.6 .1 Sound Level Ca l i b ra tor u sed for f i el d ca l i b ra t i on o f measur ement m icrophones

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Ch a pter 6 — Ca librat ionLaboratory Calibration



and calibrat ion devices. Microphone calibrat ions are usually performed at calibra-

t ion laboratories on a regular basis . As with f ield calibrat ion, this provides evidence

of stabili ty and ensures traceabili ty.

Standards relat ing to calibrat ion usually define laboratory recalibrat ion intervals of

1 year, which apply to both the calibrator and the measurement system, for exam-

ple, sound level meters. In other cases the recalibrat ion interval is determined by

the users es t imate . I t is a dvisa ble to s tar t wi th a 1 year in terva l , which can t hen be

extended when sufficient evidence of stability is obtained. The mode of use of the

device should always be taken into account when determining recalibrat ion inter-

vals ; the harsher the mode of use, the more frequent the recalibrat ion should be

because of the increased probability of changes in the performance of the device.

Not surprisingly, the most accurate calibrat ion methods are the most dif f icult and

most t ime consuming an d correspondingly t he m ost expensive. D ifferent calibra t ion

and test laboratories use dif ferent calibrat ion methods. However, for the customer,

it is not the method which is so important , but the accuracy (or uncertainty, see

Sect ion 6.3) stated by the calibrat ion laboratory, and of course, the price. I t is also

important for the customer to consider whether traceable calibrat ion, see Sect ion

6.5, is suff icient , or whether an accredited calibrat ion is required.

6.4.1 Pr i mar y C a l ibr a t i on L ab or a t or ies

Primary laboratories are nat ionally recognised laboratories which have the respon-

sibility of maintaining, developing and promulgating the highest levels of metrology.

6.4.2 Accredited Cal ibrat ion La borat or ies

Accredited calibrat ion means that the calibrat ion has been performed by an accred-

ited calibra t ion la bora tory.

To achieve “accredited sta tus” , the la bora tory mu st be a pproved by a n externa l

accreditat ion body which also performs an audit on a regular basis . The laboratory

must have the ir qual i ty assurance manual , ca l ibra t ion procedures , uncer ta in ty

budgets and technical personnel approved by the accreditation body. This means

that accredited laboratories can only offer accredited services which are within the

range approved by the accreditat ion body. Examples of accredited calibrat ion labo-

ratories are: the Danish Primary Laboratory of Acoust ics DPLA, (which is joint ly

run by B rüel &Kjær a nd the Technical U nivers i ty o f Denmark) a nd th e

Br üel&K jær Ca l ibra t ion La bora tory.

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Cha pter 6 — Ca librat ionLaboratory Calibration


BE1447–11 6 − 7

6.4.3 Ca libra t ion a t the Brüel &Kjær Fa ctory

B rüel &Kjæ r performs th ousands of calibrat ions every yea r a s part of the produc-

t ion of measurement equipment . These are performed under laboratory condit ions

although they are often referred to as “ factory calibrat ions” because they are an

integral part of the production process. All microphones and sound calibrators (in-

cluding pistonphones) leave the factory in a calibrated state. This is documented on

an individual ca l ibra t ion char t s t a t ing t raceabi l i ty to DPLA and NIST (Nat ional

Inst itute of Sta nda rds a nd Technology, U SA).

The methods used for factory calibration of microphones are as follows:

Open-circuit S ensitivity

The open-circuit Sensit ivity is determined using a preamplif ier with an Insert volt-

age calibrat ion facil i ty. An unknown microphones is calibrated by the comparison

method using a reference standard microphone in a small acoustical coupler. The

reference standard microphone is calibrated by DPLA using reciprocity calibrat ion

according to IEC 1094.1.

Frequency R esponse

The frequency response relat ive to the sensit ivity at 250Hz is measured for each

microphone using the a ctuat or method see Sect ion 6.6.5. To obt a in oth er responses,

the corresponding correction, for example the free-field correction, is added to the

actua tor response.

Ca pacitan ce of Microphone Ca rtr idge

The capacitance of the microphone cartridge, when mounted on a preamplifier, is

measured using the patented Charge Inject ion Calibrat ion technique. The measure-

ment system is checked regularly with a calibrated reference capacitor .

Lower Limiting Frequency

The Lower Limit ing Frequency is measured using a low frequency calibrator which

exposes the equalizat ion vent of the microphone to the same sound field as the

diaphragm. A reference level is measured at a high frequency and the frequency is

then lowered until the output is reduced by 3 dB.

P ha se Mat ch (Int ensity Microphone Pa ir)

A special acoustical sound chamber has been designed to ensure exposure of equal

sound pressure level, at all frequencies, both at the diaphragm and at the equaliza-

tion vent of both microphones. The phase match of the microphones is then meas-

ured by the comparison method using a dual channel frequency analyser. The phase

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Ch a pter 6 — Ca librat ionCalibration Hierarchy, Traceability and Uncertainty



response of the microphones are compared at all frequencies in the specified range

to ensure compatibili ty with IEC 1043 requirements.

6.5 Ca lib ra t ion H iera rchy, Traceab ilit y a nd U ncer t a in t y

Calibrat ion hierarchy is a representat ion of the links between the primary calibra-tion and the succession of intervening calibrations down to the end-user, for exam-

ple a pr imary ca l ibra t ion a t DPLA, a secondary ca l ibra t ion a t a service centre and

a tert iary calibrat ion by the end-user.

Traceability is defined in the I nter nat i onal Vocabular y of Basic and Gener al Ter m s in M etr ology as “ the property of the result of a measurement or the value of a

standard whereby it can be related to stated references, usually nat ional or interna-

t ional standards, through an unbroken chain of comparisons, all having stated un-

certaint ies” .

F ig.6 .2 Ca l i b ra t i on H iera rchy ; the na t i ona l acoust i ca l l abora to- r ies use in ter compar ison m eth ods (Round Robin) to ensure thei r t raceabi l i ty

960290e

Sound and VibrationLaboratories

eg. CalibrationServices

Other National

AcousticLaboratories

StandardsInstitutes

PhysicalParameters

National AcousticLaboratoty

(Accredited)

Round Robin Test

DPLA

Calibration Hierarchy

Users ofSound and

VibrationEquipment

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Cha pter 6 — Ca librat ionCalibration Methods


BE1447–11 6 − 9

The uncertainty of a measurement is defined as the parameter associated with the

result of a measurement that characterises the dispersion of the values that could

reasona bly be a t t r ibuted to the measurand .

The accuracy or a measurement is the closeness of the agreement between the

resul t o f a measurement a nd a t rue value of the measura nd. Note tha t “ a ccura cy” is

a qualitative concept. The term “precision” should not be used for “accuracy”.

In the ISO publicat ion Gui de to the Expr ession of Un cer tai nt y in M easur ement , i t is

recommended that uncertainty is stated in terms of 2 standard deviat ions (2-sig-

ma) . This means that 95%of the ca l ibra t ions wi l l be wi th in the s ta ted uncer ta in ty

range for a normal distr ibution funct ion.

Normally, the uncertainty decreases the higher up in the hierarchy the chain the

calibrat ions are performed, with absolute calibrat ion methods based direct ly on the

physical units at the top of the hierarchy. This posit ion is usually covered by na-

t ional acoust ical calibrat ion laboratories such as DPLA. Calibrat ion laboratories op-

erat ing at lower levels use comparison or subst itut ion methods based on reference

stan dards ca l ibra ted by h igher ra nking laborat or ies .

As seen in Fig.6.2 DP LA obta ins tra ceab le a ccredited ca libra t ions of physica l units

from other calibrat ion laboratories. DPLA is also accredited by the Danish Trade

a nd Indust ry body DANAK w hich a ccredits la bora tories a ccording to D S/EN 45001,

Gener al Cr it eri a for th e Oper ati on of Test La bor atori es , 45002 General Cri ter ia for th e evalu ati on of Test L abor atori es and 45003 Gener al Cr i t er i a for Or ganisat ions wh ich issue la bor atory accr edi tat ions .

6.6 C a libra t ion Met hods

This section gives an overview of calibration methods. These are listed in Table 6.1with an est imate of the expected uncertainty that can be obtained using the various

methods.

Method Uncertainty

Reciprocity Calibration 0.03 to 0.05 dB

Comparison Method 0.06 to 0.14 dB

Substitution Method 0.06 to 0.14 dB

Pistonphone

Sound Level Calibrator

0.07 to 0.3 dB

Actuator Frequency Response 0.1 to 0.5 dB

Table 6.1 U ncer ta i n t i es (two standar d d ev ia t ions) rela ted to vari ous cal i brat i on m eth ods

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Ch a pter 6 — Ca librat ionCalibration Methods



6.6.1 Reciproci ty Ca l ibrat ion Method

This is the most accurate calibrat ion method for determinat ion of the open circuit

sensit ivity of the microphone ca rtr idges. The sensit ivity ca n be obta ined either a s a

pressure sensitivity or as a free-field sensitivity, by using a coupler (cylinder) or an

anechoic chamber respectively. Certain physical requirements of the microphone

must be fulfilled to perform the calibration in a coupler, for example, the mechani-

cal configuration as described in IEC 1094-1.

The reciprocity method is an absolute method, which means that i t requires the

measurement of a number of fundamental physical units such as electrical voltage

and impedance, length, temperature, humidity and also ambient pressure. But noreference sound pressure is required.

The method determines the unknown sensitivities of three microphones simultane-

ously. At least two of the microphones must be reciprocal. This means that they can

be used both as receivers (microphones) and as transmitters (sound sources).

Fig.6 .3 Recipr oci ty cal ib r a t ion. Mi crophones are held “face to face” by a spri ng-l oaded yoke

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BE1447–11 6 − 11

The coupler properties must be known to a high degree of accuracy.

To conclude a complete calibra tion, th ree mea surem ents of receiver volta ge an d

transmit ter current rat ios must be performed in three different setups ( inter-

cha nged microphones). The th ree rat ios a re then used to solve thr ee equa t ions w ith

three un know ns: t he sensit ivit ies of the m icrophones.

To obta in reliable results , clea n a nd st able environments a re required. P ra ct ice at

performing the calibrat ion is also important . The method is described in detail in

IEC 1094-1, Pr essur e Cali br ati on and IEC 1094-3, Fr ee-field Cal ibr ati on .

6. 6.2 S u bs t it u t ion met h od

The subst itut ion method involves the measurement of a device in a given measure-

ment set-up. The device is replaced (substituted) by a reference device, preferably of

the same type and the measurement is repeated. Thus the rat io of the sensit ivit ies

of the devices are obtained directly.

This method is well suited for both microphones and sound pressure calibrators. Ifthe measurement and reference objects are of the same type, the measurement

uncertainty is reduced due to identical measurement condit ions. The measurement

capabili ty requirements are also reduced, as only a small part of the dynamic range

is used i.e. there is no need to know the absolute level.

Any sound source used for the calibration of microphones must obviously be very

stable during the measurement and must not be affected by dif ferences in micro-

phone configurations. In this case, the method is well suited for calibration of free-

field microphones, provided that a suitable reference microphone is available.

This method is often confused with the comparison method described below.

6. 6.3 C ompar is on M et h od

In the comparison method, both the measurement- and the reference objects are

present at the same t ime and are exposed to the same sound pressure. As a result ,

a simultaneous measurement can be performed. In principle something unknown is

compared with something known. The method is often confused with the subst itu-

tion method described above.

The method reduces the number of error sources, and also reduces the stability

requirements in situat ions where external sound sources are used. I t also covers

the compressor loop principle used in a number of sound level calibrators, where areference microphone inside the calibrator constantly monitors the sound pressure.

In this situat ion the reference microphone must be very stable as i t is the “known”

object.

This method is also used for calibrat ion and checking of sound intensity measure-

ment equipment , which ideally requires two identical measurement channels (both

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phase and magnitude) . In a calibrat ion situat ion, two microphones are subjected to

the same sound pressure field inside a coupler. Calibration is performed by applying

a well known sound pressure at a single frequency, and then adjust ing both chan-

nels to show the correct sound pressure simultaneously. The checking of the pres-

sure-residual intensity index is performed by applying a broad band noise

spectrum. Both microphones are subjected to the same signal which in turn means

that there is no phase dif ference between the signals at the microphones and hence

no sound intensity should be detected. A measurement in this situat ion represents

the false intensity generated by the measurement system itself due to the phase

mis-match between measurement channels. Comparing the actual sound pressure

level with the lowest measurable intensity represents the measurement capabili ty

of the intensity instrument , see IEC 1043.

6.6.4 Sound P ressure Ca libra tor Method

The purpose of using a sound pressure calibrator is to get a well defined sound

pressure with a certain microphone. This makes the calibrators equally suited for

calibrat ion of single microphones as well as ent ire measurement channels. In most

cases, the calibrator has only a single tone frequency in the range 200 to 1000Hz,at w hich t he ca librat ion is performed, (IE C 942 ‘Sound Ca librat ors’) but mu lt itone

calibrators are also available, usually with frequencies in steps of one octave.

When using the calibrator for microphone calibrat ion, the output from the micro-

phone is measured with the well defined sound pressure from the calibrator applied

to its front . The sensit ivity is determined by dividing the output voltage by the

sound pressure.

When the calibrator is used to calibrate the entire measurement channel, the well

defined sound pressure is applied to the front of the microphone and a proper

adjustment is made to give the correct reading of the measurement display or out-

put volta ge.

If the frequency of the calibrator is so high that the sensit ivity in the pressure f ield

and free f ield environments are not the same, i t should be noticed that sound

calibrators always establish a pressure f ield. As a result , a free f ield calibrat ion can

only ca n be performed by a pplying a suita ble correct ion.

6.6.5 Act u a t or met h od

The electrostat ic actuator is well suited for calibrat ion of a relat ive frequency re-

sponse of microphones with a metall ic or metalised diaphragm. It consists of a

meta ll ic grid posit ioned close to the dia phra gm (approx. 0.5 mm). By a pplying800 V DC a nd 100 VAC t o the a ctuat or, electrosta t ic forces equiva lent t o a s ound

pressure of a pproximat ely 100 dB re 20 micropasca l ar e esta blished. The actua tor is

not suited for absolute calibrat ion due to the extreme dependency of the equivalent

sound pressure level on the distance between actuator and diaphragm.

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The equivalent sound pressure is only applied to the diaphragm and not to the

ambient pressure equalisat ion vent so that the response measured at low frequen-

cies only applies when the vent is not exposed to the sound field.

The actuator method is a reliable method for determinat ion of the microphones

relative frequency response under laboratory conditions. The response obtained

with the actuator does not however correspond to any of the acoust ical sound fields.

Although there is no difference between the actuator response and the pressure

field response at low frequencies and only minor difference at higher frequencies for

microphones with high impedance diaphragms. I t should, however be noted that

different types of actuators will give slightly different frequency responses, even for

the same microphone.

The frequency responses of the microphone in pressure-, random and free sound

fields are determined by adding actuator and microphone type-specific corrections

to the individual actuator response.

The disadvantages of the method are that care is required to posit ion the actuator,

tha t t he sys tem uses h igh vol tages a nd tha t t he gr id must be removable.

6.6.6 Inser t Vol tage Ca libra t ion Method

Insert voltage calibrat ion is a technique which can be used for two purposes:

1. In ca l ibra t ion laborat or ies i t is used to assess the open c ircuit sensit iv i ty of

microphone cartridges.

2. I t can provide a convenient mean s for checking in the f ield the electrica l sensi-

t ivity of a complete sound m easuring system, including preamplif iers a nd ca bles.

However, the method does not account for the mechanical parameters which

determine the acoustical properties of the microphone cartridge itself.

The method requires a special pream plif ier t ha t ca n isola te t he microphone housing

from the preamplifier housing. This makes it possible to apply an electrical signal

( the insert voltage) direct ly to the microphone diaphragm (housing) . In the calibra-

tion the microphone is first subjected to a sound pressure of a known level and

frequency (say 94dB at 1kHz). This causes the microphone to generate an internal

voltage Vo (corresponding exactly to the open circuit microphone voltage) which,

when loaded by the preamplif ier , produces an output voltage V at the preamplif ier

output. The sound source is then switched off and the insert voltage V1 of the same

frequency is applied (such as the internal reference voltage of a measuring amplif i-

er) . The level of the insert voltage is adjusted so that the voltage measured at the

pream plifier output is a ga in V.

Provided that this voltage V is noted, when the microphone and preamplif ier are

used remotely from the measuring equipment , or i f for other reasons it is conven-

ient to apply a direct sound pressure to the microphone, the insert voltage method

can be used to adjust the sensit ivity of the equipment . This will provide a system

calibrat ion which relies only on the value of V remaining constant .

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When the method is used for verif icat ion of measurement channels, an init ial cali-

brat ion is usually required, af ter which a reference level is measured with insert

voltage. Each t ime a verif icat ion of the channel is required, a new measurement

wit h insert volta ge is compared w ith t he reference level.

The disadvantages of the method are that the system is subject to disturbance from

electrical noise and that faults in the microphone cartr idge cannot be detected.

6.6.7 Cha rge Inject ion Cal ibrat ion Method

This method is developed for monitoring of microphone channels and requires a

preamplif ier with a small , extremely stable, built- in capacitor which makes it possi-

ble to apply an electrical signal to the preamplif ier (and microphone) input termi-

na l. The B rüel &Kjær pat ented charge-inject ion ca librat ion m ethod is based ondetect ion of changes in impedance at the input terminal. Each verif icat ion measure-

ment is compared to an init ial reference measurement .

The pin used for the CIC method must be connected to ground potential or to the

pream plifier output w hen the microphone is used for norma l mea surem ents. To use

the charge injection calibration facility, a test signal, for example, an electrical

broad band noise signal, is applied to the capacitor terminal, preferably with no

sound on the microphone. The preamplifier output is then measured.

Changes in the measured outputs reflect changes in the microphone and preamplif i-

er input combination. The method is very effective for detecting small changes in

microphone capacitance. See chapter 4 for details.

Fi g.6.4 Pri nciple of th e I nser t Vol t age Cal i brat i on m eth od

820196/1e

V1 = V0 = microphoneopen-circuit output voltage

V = k V0

V = k V1

If the microphone were not loaded by

a preamplifier the open-circuit outputvoltage would be V0

Insert Voltage V1 applied inseries with microphone

Preamplifier

Preamplifier

P

If the microphone were not loaded by

a preamplifier the open-circuit outputvoltage would be V1

Sound sourcestopped

V0

P

If V is same in

both cases then

Open-circuit sensitivity =

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BE1447–11 I n d e x – 1

Index

4160 microphone 1 – 3

4180 microphone 1 – 3

AAccessories 5 – 8

Accredited calibration laboratories 6 – 6

Accuracy 6 – 2

Acoustic compliance 2 – 2 8

Acoustic im pedan ce 2 – 2 7, 2 – 2 8

Acoustic resistance 2 – 3 6

Actuat or method 6 – 1 2

Air turbulence 5 – 9

Air-stiffness 2 – 1 8

Amplifier gain 2 – 3 4

ANSI S1.12 5 – 7

ANSI S1.4 5 – 7

BBackp la t e 1 – 9, 2 – 8

In tegrated 2 – 8

Backplate to d iaphragm dis tance 2 – 8

Bird spikes 5 – 8

B ol t z manns Co ns t an t 2 – 3 7B oot-stra pping technique 4 – 3

CCalibraat ion

Int ercomparison method 6 – 8

Calibra t ion 2 – 5 4, 3 – 2

Accredited laboratories 6 – 6

Accuracy 6 – 3, 6 – 9

Actuator 2 – 5 8

Actua tor method 6 – 5

Definition 6 – 2

Field 6 – 4

Hierarchy 6 – 8

In t e rna t iona l s t andards 6 – 8

Laboratory 6 – 5

Measurement channel 6 – 1 2

Recalibrat ion interval 6 – 6Reference 6 – 1 1

Reference units 6 – 3

Sensit ivity 6 – 3

Sound source 6 – 1 1

Traceability 6 – 2, 6 – 4, 6 – 8

Uncer ta in ty 6 – 8

Calibra t ion char t 1 – 2, 3 – 2

calibrat ion chart 1 – 2

Calibrat ion equipment 1 – 3

Calibrator load volume 3 – 1 3

Capaci tance 2 – 8, 2 – 1 3, 2 – 3 1, 2 – 3 2,

2 – 3 7, 2 – 4 3, 3 – 1 3, 6 – 7

var ia t ions 2 – 1 1

Capaci tance ra t io 2 – 3 4

CE label 4 – 1 3

Charge Inject ion Calibrat ion 4 – 1 5, 6 – 7

Ch a rge inject ion ca librat ion 1 – 4, 6 – 5

Ch a rge inject ion calibra t ion method 6 – 1 4

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Index


Brüel & KjærI n d e x – 2

C I C 6 – 1 4

Compar ison Method 6 – 1 1

Correction

Angle of incidence 2 – 4 7

Microphone body 2 – 4 8

Correction-factor 3 – 5

Corrections 2 – 4 5, 2 – 5 8

Coupler 2 – 4, 2 – 4 3, 6 – 1 0

DDANAK 6 – 9

Danish Primary Laboratory of Acoust ics

(DPLA) 1 – 5

Dehumidifier 5 – 1 0

Design 2 – 7

Description 2 – 7

Design pa ram eters 2 – 7

Diameter

Sensit ivity 2 – 2 2Diaphragm 2 – 8

Air stiffness 2 – 1 5

Da mping resis tance 2 – 2 1, 2 – 3 8

Diameter 2 – 2 1, 2 – 2 2

Frequency ra nge 2 – 2 3

Mass 2 – 2 0

Tension 2 – 9, 2 – 2 0

tension 1 – 1 0, 2 – 5 1

thickness 2 – 8

Diaphragm mat e r i a l 2 – 9

Diffuse Field 2 – 4 9

Diffuse Field Microphone 2 – 5 0Diffuse sound field. 3 – 9

Diffuse-field 2 – 5

correction 2 – 4 9

Diffuse-field correction 2 – 4 9, 2 – 5 0, 2 – 5 4

Diffuse-field measurements 2 – 2

Diffuse-field response 2 – 5 8

Direct ional characterist ics 3 – 1 0

Distort ion 2 – 3 9, 2 – 4 3

Microphone D istort ion 2 – 4 0

Preamplif ier and microphone system 2 – 4 2

Distortion level 3 – 1 1

D P L A 6 – 6, 6 – 8

Dyna mic Range 3 – 1 1

Dyna mic r ange 2 – 3 1, 2 – 3 2, 3 – 1 1, 5 – 2

Limits 5 – 4

EElectret 2 – 1 3, 2 – 1 5

Series ca pacitor 2 – 1 4

Electrical resistance 2 – 3 6

Electroma gnetic compatibility 3 – 2 1, 4 – 1 3

Electrosta t ic Actua tor 2 – 5 4, 2 – 5 7

P ressur e-field response 2 – 5 8

Electrostat ic actuator 2 – 5 5, 6 – 1 2

P ha se response 3 – 7

Response 3 – 7

Elect rosta t ic Ca l ibra t ion P ressure 2 – 5 5

Electrostat ic calibrat ion pressure 2 – 5 5

Electrosta t ic pressure 2 – 5 5

E MC 4 – 1 3

EMC requirements 4 – 1 3

EN 50081-1 4 – 1 4

En 50082-2 4 – 1 4

Environment 5 – 7

Equivalent d ia phragm volume 2 – 2 9

Equivalent electric circuit 2 – 2 6

Eq uivalent electric circuits 2 – 2 5

Equivalent sound pressure 3 – 1 2

Equivalent Volume 2 – 2 8, 3 – 1 3

Equivalent volume 2 – 3 1

Diaphragm d iamet e r 2 – 3 1

External polarisat ion source 2 – 1 1

Externa lly polarised m icrophones 3 – 1 4

Externa lly pola rized m icrophones 5 – 6

FFalcon Range microphones 5 – 7

Falcon range microphones 1 – 4

FET noise 4 – 9

Field Effect Transistor 4 – 9

Free-Field 2 – 4 5

Free-field 2 – 4

Free-field correction 2 – 4 9, 2 – 5 4, 3 – 9

Free-Field Microphone 2 – 4 8

Free-field microphone 2 – 2 2, 2 – 3 8, 2 – 4 8,2 – 5 9

Free-field response 2 – 4 9, 3 – 9

Fr ee-field sensit ivity 2 – 4

Frequency Response 5 – 4

Frequency response 2 – 9, 2 – 1 4, 2 – 1 7, 2 –

32, 2 – 4 8, 5 – 2, 6 – 7

Electrical 2 – 3 3, 2 – 3 4

free-field 2 – 4 8

Magni t ude and phase 2 – 2 2, 2 – 2 6

pressure 2 – 3 7

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Index


Brüel & KjærI n d e x – 4

Nose cone 5 – 8, 5 – 9

Nyquis t a nd J ohnson Noise 2 – 2 6

OOpen Circuit Sensit ivity 3 – 3

Open-circuit sensit ivity 3 – 3, 6 – 7

Optimised response 3 – 5Output resistance 2 – 3 2

PP ara l le l capa ci tors 2 – 4 3

Particle velocity 2 – 2

P ass ive capaci tan ce 2 – 4 0

Phase mat ch 6 – 7

P ha se response 5 – 5

Polar plot 3 – 1 0

POlar isa t ion

resistor 2 – 1 1

Polar isa t ion 5 – 5

f ield st rength 2 – 1 4

Polarisat ion resistor 3 – 1 4

P olar isa t ion Voltage 3 – 1 4

Electret 3 – 1 4

P olar isa t ion vo lta ge 2 – 1 0, 2 – 1 4

Resistor 3 – 1 4

P olar iza t ion vo lta ge 2 – 1 0, 2 – 1 4, 2 – 3 5,2 – 5 8

Polarzat ion 2 – 1 1

Preamplif ier

Built-in preamplifier 5 – 8

Ca librat ion Technique 4 – 1 5

Current l imita t ion 4 – 6

Dynam ic Range 4 – 5

Effect of temperature 4 – 1 1

Electromagnetic noise 4 – 1 5

Frequency Response 4 – 2

G a i n 3 – 4

High frequency response 4 – 3

input impedance 2 – 3 2

Low frequency response 4 – 2

Lower limit of dynamic range 4 – 8

Maximum acoust ica l s ignal 4 – 6Maximum current 4 – 6

Maximum output current 4 – 6

Maximum output voltage 4 – 6

Maximum slew ra te 4 – 6

Noise level 4 – 1 2

Noise spectrum 4 – 9

Output impedance 4 – 4

P ha se Response 4 – 1 1

P ream plif ier a nd microphone combinat ion 2 –

31

P ream plif ier n oise 2 – 3 7

Preamplif iers

Character is t ics 4 – 2

Effect of ma gnetic f ields 4 – 1 3

Prepolarised microphones 2 – 1 4

Pre-polarization principle 2 – 1 1

Prepolarized microphone 2 – 1 3

Prepolarized microphones 3 – 1 5, 5 – 6

P ressur e coefficient 3 – 1 9

P ressure equal isa t ion 5 – 5

Pressure Field Microphone 2 – 4 5

Pressure sensing condenser microphones 2 – 5

Pressure sensit ivity 2 – 4

Pressure-Fiel 2 – 4 3

Pressure-field 2 – 4

Pressure-field calibration 2 – 4

P ressur e-field correction 3 – 1 0

P ressur e-field microphone 2 – 4 8, 2 – 5 0, 2 –

59

Pressure-field response 3 – 9

P r imary ca l ibra t ion la bora tor ies 6 – 6

Properties of microphones 2 – 7

P rotect ion grid 2 – 4 6

RRa in cover 5 – 8

Raincover 5 – 1 0Ra ndom incidence 2 – 4 9

Random Incidence response 3 – 9

Rear-vented microphones 2 – 1 6

Reciprocity calibration method 6 – 1 0

Reference Frequency 2 – 2 4

Reference frequency 3 – 6

Requirements

environmenta l influences 2 – 6

Mat er ia l 2 – 9

Performance 2 – 6

Resistance 2 – 3 2, 2 – 3 5, 2 – 3 6

Damping 2 – 3 8

Reversible changes 3 – 1 8

RF-signal 4 – 1 5

SSelection

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Index

Documents

be1447