SIST EN 61094-2:2009

Electroacoutstics - Measurement microphones - Part 2: Primary method for the pressure calibration of laboratory standard microphones by the reciprocity technique (IEC 61094-2:2009)

This part of International Standard IEC 61094
– is applicable to laboratory standard microphones meeting the requirements of IEC 61094-1 and other types of condenser microphone having the same mechanical dimensions;
– specifies a primary method of determining the complex pressure sensitivity so as to establish a reproducible and accurate basis for the measurement of sound pressure. All quantities are expressed in SI units.

Elektroakustik - Messmikrofone - Teil 2: Primärverfahren zur Druckkammer-Kalibrierung von Laboratoriums-Normalmikrofonen nach der Reziprozitätsmethode (IEC 61094-2:2009)

Electroacoustique - Microphones de mesure - Partie 2: Méthode primaire pour l’étalonnage en pression des microphones etalons de laboratoire par la méthode de réciprocité (CEI 61094-2:2009)

La CEI 61094-2:2009 est applicable aux microphones étalons de laboratoire répondant aux prescriptions de la CEI 61094-1 et aux autres types de microphones à condensateur présentant les mêmes dimensions mécaniques et spécifie une méthode primaire de détermination de l'efficacité en pression complexe de manière à établir une base reproductible et exacte pour la mesure de la pression acoustique. Cette deuxième édition annule et remplace la première édition publiée en 1992. Cette deuxième édition constitue une révision technique. Cette édition inclut les modification techniques majeures suivantes par rapport à l'édition précédente:
- une mise à jour de l'Article 6 afin d'être en conformité avec les exigences du Guide ISO/CEI 98-3;
- une amélioration de la théorie de la conduction thermique en Annexe A;
- une révision de l'Annexe F: Propriétés physiques de l'air humide.

Elektroakustika - Merilni mikrofoni - 2. del: Primarna metoda za kalibriranje tlaka laboratorijskih standardnih mikrofonov z recipročno tehniko (IEC 61094-2:2009)

General Information

• Status: Published
• Publication Date: 20-Apr-2009
• ICS: 17.140.50 - Electroacoustics
• ICS: 33.160.50 - Accessories
• Technical Committee: I11 - Imaginarni 11
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 15-Apr-2009
• Due Date: 20-Jun-2009
• Completion Date: 21-Apr-2009
• Ref Project: EN 61094-2:2009 - Electroacoustics - Measurement microphones - Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique

Relations

• Replaces: SIST EN 61094-2:2002 - Measurement microphones -- Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique
• Effective Date: 01-Jun-2009
• Revised: SIST EN 61094-2:2002 - Measurement microphones -- Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique
• Effective Date: 06-Mar-2012
• Replaces: SIST EN 61094-2:2002 - Measurement microphones -- Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique
• Effective Date: 29-Jan-2023
• Amended By: SIST EN 61094-2:2009/A1:2022 - Electroacoustics - Measurement microphones - Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique (IEC 61094-2:2009/AMD1:2022)
• Effective Date: 24-Nov-2020
• Replaces: SIST EN 61094-2:2002 - Measurement microphones -- Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique
• Effective Date: 07-Jun-2022

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN 61094-2:2009
01-junij-2009
1DGRPHãþD
SIST EN 61094-2:2002
(OHNWURDNXVWLND0HULOQLPLNURIRQLGHO3ULPDUQDPHWRGD]DNDOLEULUDQMHWODND
ODERUDWRULMVNLKVWDQGDUGQLKPLNURIRQRY]UHFLSURþQRWHKQLNR,(&
Electroacoutstics - Measurement microphones - Part 2: Primary method for the pressure
calibration of laboratory standard microphones by the reciprocity technique (IEC 61094-
2:2009)
Elektroakustik - Messmikrofone - Teil 2: Primärverfahren zur Druckkammer-Kalibrierung
von Laboratoriums-Normalmikrofonen nach der Reziprozitätsmethode (IEC 61094-
2:2009)
Electroacoustique - Microphones de mesure - Partie 2: Méthode primaire pour
l’étalonnage en pression des microphones etalons de laboratoire par la méthode de
réciprocité (CEI 61094-2:2009)
Ta slovenski standard je istoveten z: EN 61094-2:2009
ICS:
17.140.50 Elektroakustika Electroacoustics
33.160.50 Pribor Accessories
SIST EN 61094-2:2009 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST EN 61094-2:2009

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SIST EN 61094-2:2009

EUROPEAN STANDARD
EN 61094-2

NORME EUROPÉENNE
April 2009
EUROPÄISCHE NORM

ICS 17.140.50 Supersedes EN 61094-2:1993


English version


Electroacoustics -
Measurement microphones -
Part 2: Primary method for pressure calibration
of laboratory standard microphones
by the reciprocity technique
(IEC 61094-2:2009)


Electroacoustique -  Elektroakustik -
Microphones de mesure - Messmikrofone -
Partie 2: Méthode primaire Teil 2: Primärverfahren
pour l’étalonnage en pression zur Druckkammer-Kalibrierung
des microphones étalons de laboratoire von Laboratoriums-Normalmikrofonen
par la méthode de réciprocité nach der Reziprozitätsmethode
(CEI 61094-2:2009) (IEC 61094-2:2009)



This European Standard was approved by CENELEC on 2009-03-01. CENELEC members are bound to comply
with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard
the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and notified
to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: avenue Marnix 17, B - 1000 Brussels


© 2009 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61094-2:2009 E

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SIST EN 61094-2:2009
EN 61094-2:2009 - 2 -
Foreword
The text of document 29/671/FDIS, future edition 2 of IEC 61094-2, prepared by IEC TC 29,
Electroacoustics, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as
EN 61094-2 on 2009-03-01.
This European Standard supersedes EN 61094-2:1993.
EN 61094-2:2009 includes the following significant technical changes with respect to EN 61094-2:1993:
– an update of Clause 6 to fulfil the requirements of ISO/IEC Guide 98-3;
– an improvement of the heat conduction theory in Annex A;
– a revision of Annex F: Physical properties of humid air.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
(dop) 2009-12-01
national standard or by endorsement
– latest date by which the national standards conflicting
(dow) 2012-03-01
with the EN have to be withdrawn
Annex ZA has been added by CENELEC.
__________
Endorsement notice
The text of the International Standard IEC 61094-2:2009 was approved by CENELEC as a European
Standard without any modification.
__________

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SIST EN 61094-2:2009
- 3 - EN 61094-2:2009
Annex ZA
(normative)

Normative references to international publications
with their corresponding European publications

The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.

NOTE  When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD
applies.

Publication Year Title EN/HD Year

IEC 61094-1 2000 Measurement microphones - EN 61094-1 2000
Part 1: Specifications for laboratory standard
microphones


1)
ISO/IEC Guide 98-3 - Uncertainty of measurement - - -
Part 3: Guide to the expression of uncertainty
in measurement (GUM:1995)




1)
Undated reference.

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SIST EN 61094-2:2009

---------------------- Page: 6 ----------------------

SIST EN 61094-2:2009
IEC 61094-2
®
Edition 2.0 2009-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE


Electroacoustics – Measurement microphones –
Part 2: Primary method for pressure calibration of laboratory standard
microphones by the reciprocity technique

Electroacoustique – Microphones de mesure –
Partie 2: Méthode primaire pour l’étalonnage en pression des microphones
étalons de laboratoire par la méthode de réciprocité

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
X
CODE PRIX
ICS 17.140.50 ISBN 2-8318-1030-4
® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale

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SIST EN 61094-2:2009
– 2 – 61094-2 © IEC:2009
CONTENTS
FOREWORD.4
1 Scope.6
2 Normative references .6
3 Terms and definitions .6
4 Reference environmental conditions .7
5 Principles of pressure calibration by reciprocity .7
5.1 General principles .7
5.1.1 General .7
5.1.2 General principles using three microphones .7
5.1.3 General principles using two microphones and an auxiliary sound
source .7
5.2 Basic expressions .8
5.3 Insert voltage technique .9
5.4 Evaluation of the acoustic transfer impedance.9
5.5 Heat-conduction correction.11
5.6 Capillary tube correction.11
5.7 Final expressions for the pressure sensitivity .12
5.7.1 Method using three microphones .12
5.7.2 Method using two microphones and an auxiliary sound source .12
6 Factors influencing the pressure sensitivity of microphones.13
6.1 General .13
6.2 Polarizing voltage.13
6.3 Ground-shield reference configuration.13
6.4 Pressure distribution over the diaphragm .13
6.5 Dependence on environmental conditions .14
6.5.1 Static pressure .14
6.5.2 Temperature.14
6.5.3 Humidity .14
6.5.4 Transformation to reference environmental conditions .15
7 Calibration uncertainty components .15
7.1 General .15
7.2 Electrical transfer impedance .15
7.3 Acoustic transfer impedance .15
7.3.1 General .15
7.3.2 Coupler properties.15
7.3.3 Microphone parameters .16
7.4 Imperfection of theory.17
7.5 Uncertainty on pressure sensitivity level.18
Annex A (normative) Heat conduction and viscous losses in a closed cavity .20
Annex B (normative) Acoustic impedance of a capillary tube.23
Annex C (informative) Examples of cylindrical couplers for calibration of microphones .26
Annex D (informative) Environmental influence on the sensitivity of microphones .31
Annex E (informative) Methods for determining microphone parameters .34
Annex F (informative) Physical properties of humid air.37

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SIST EN 61094-2:2009
61094-2 © IEC:2009 – 3 –
Figure 1 – Equivalent circuit for evaluating the acoustic transfer impedance Z .9
a,12
Figure 2 – Equivalent circuit for evaluating Z’ when coupler dimensions are small
a,12
compared with wavelength.10
Figure 3 – Equivalent circuit for evaluating Z’ when plane wave transmission in the
a,12
coupler can be assumed .10
Figure C.1 – Mechanical configuration of plane-wave couplers .27
Figure C.2 – Mechanical configuration of large-volume couplers .29
Figure D.1 – Examples of static pressure coefficient of LS1P and LS2P microphones
relative to the low-frequency value as a function of relative frequency f/f .32
o
Figure D.2 – General frequency dependence of that part of the temperature coefficient
for LS1P and LS2P microphones caused by the variation in the impedance of the
enclosed air .33

Table 1 – Uncertainty components .19
Table A.1 – Values for E .21
V
3
Table B.1 – Real part of Z in gigapascal-seconds per cubic metre (GPa⋅s/m ).24
a,C
3
Table B.2 – Imaginary part of Z in gigapascal-seconds per cubic metre (GPa⋅s/m ).25
a,C
Table C.1 – Nominal dimensions for plane-wave couplers.28
Table C.2 – Nominal dimensions and tolerances for large-volume couplers .29
Table C.3 – Experimentally determined wave-motion corrections for the air-filled large-
30
volume coupler used with type LS1P microphones.
Table F.1 – Calculated values of the quantities in Clauses F.1 to F.5 for two sets of
environmental conditions .40
Table F.2 – Coefficients used in the equations for humid air properties.41

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SIST EN 61094-2:2009
– 4 – 61094-2 © IEC:2009
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

ELECTROACOUSTICS –
MEASUREMENT MICROPHONES –

Part 2: Primary method for pressure calibration of laboratory
standard microphones by the reciprocity technique


FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61094-2 has been prepared by IEC technical committee 29:
Electroacoustics.
This second edition cancels and replaces the first edition published in 1992. This second
edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
• an update of Clause 6 to fulfil the requirements of ISO/IEC Guide 98-3;
• an improvement of the heat conduction theory in Annex A;
• a revision of Annex F: Physical properties of humid air.

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SIST EN 61094-2:2009
61094-2 © IEC:2009 – 5 –
The text of this standard is based on the following documents:
FDIS Report on voting
29/671/FDIS 29/676/RVD

Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts of the IEC 61094 series, published under the general title Electroacoustics –
Measurement microphones, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in
the data related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

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SIST EN 61094-2:2009
– 6 – 61094-2 © IEC:2009
ELECTROACOUSTICS –
MEASUREMENT MICROPHONES –

Part 2: Primary method for pressure calibration of laboratory
standard microphones by the reciprocity technique



1 Scope
This part of International Standard IEC 61094
– is applicable to laboratory standard microphones meeting the requirements of
IEC 61094-1 and other types of condenser microphone having the same mechanical
dimensions;
– specifies a primary method of determining the complex pressure sensitivity so as to
establish a reproducible and accurate basis for the measurement of sound pressure.
All quantities are expressed in SI units.
2 Normative references
The following referenced documents are indispensable for the application of this document.
For dated references, only the edition cited applies. For undated references, the latest edition
of the referenced document (including any amendments) applies.
IEC 61094-1:2000, Measurement microphones – Part 1: Specifications for laboratory standard
microphones
ISO/IEC Guide 98-3, Uncertainty of measurement – Part 3: Guide to the expression of
1
uncertainty in measurement (GUM:1995)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 61094-1 and
ISO/IEC Guide 98-3 as well as the following apply.
3.1
reciprocal microphone
linear passive microphone for which the open circuit reverse and forward transfer impedances
are equal in magnitude
3.2
phase angle of pressure sensitivity of a microphone
for a given frequency, the phase angle between the open-circuit voltage and a uniform sound
pressure acting on the diaphragm
NOTE Phase angle is expressed in degrees or radians (° or rad).
___________
1
 ISO/IEC Guide 98-3:2008 is published as a reissue of the Guide to the expression of uncertainty in
measurement (GUM), 1995.

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SIST EN 61094-2:2009
61094-2 © IEC:2009 – 7 –
3.3
electrical transfer impedance
for a system of two acoustically coupled microphones the quotient of the open-circuit voltage
of the microphone used as a receiver by the input current through the electrical terminals of
the microphone used as a transmitter
NOTE 1 Electrical transfer impedance is expressed in ohms (Ω).
NOTE 2 This impedance is defined for the ground-shield configuration given in 7.2 of IEC 61094-1:2000.
3.4
acoustic transfer impedance
for a system of two acoustically coupled microphones the quotient of the sound pressure
acting on the diaphragm of the microphone used as a receiver by the short-circuit volume
velocity produced by the microphone used as a transmitter
3
NOTE Acoustic transfer impedance is expressed in pascal-seconds per cubic metre (Pa⋅s/m ).
3.5
coupler
device which, when fitted with microphones, forms a cavity of predetermined shape and
dimensions acting as an acoustic coupling element between the microphones
4 Reference environmental conditions
The reference environmental conditions are:
− temperature 23,0 °C
− static pressure 101,325 kPa
− relative humidity 50 %
5 Principles of pressure calibration by reciprocity
5.1 General principles
5.1.1 General
A reciprocity calibration of microphones may be carried out by means of three microphones,
two of which shall be reciprocal, or by means of an auxiliary sound source and two
microphones, of which one shall be reciprocal.
NOTE If one of the microphones is not reciprocal it can only be used as a sound receiver.
5.1.2 General principles using three microphones
Let two of the microphones be connected acoustically by a coupler. Using one of them as a
sound source and the other as a sound receiver, the electrical transfer impedance is
measured. When the acoustic transfer impedance of the system is known, the product of the
pressure sensitivities of the two coupled microphones can be determined. Using pair-wise
combinations of three microphones marked (1), (2) and (3), three such mutually independent
products are available, from which an expression for the pressure sensitivity of each of the
three microphones can be derived.
5.1.3 General principles using two microphones and an auxiliary sound source
First, let the two microphones be connected acoustically by a coupler, and the product of the
pressure sensitivities of the two microphones be determined (see 5.1.2). Next, let the two
microphones be presented to the same sound pressure, set up by the auxiliary sound source.
The ratio of the two output voltages will then equal the ratio of the two pressure sensitivities.

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SIST EN 61094-2:2009
– 8 – 61094-2 © IEC:2009
Thus, from the product and the ratio of the pressure sensitivities of the two microphones, an
expression for the pressure sensitivity of each of the two microphones can be derived.
NOTE In order to obtain the ratio of pressure sensitivities, a direct comparison method may be used, and the
auxiliary sound source may be a third microphone having mechanical or acoustical characteristics which differ from
those of the microphones being calibrated.
5.2 Basic expressions
Laboratory standard microphones and similar microphones are considered reciprocal and thus
the two-port equations of the microphones can be written as:
z i + z q = U
11 12
 (1)
z i + z q = p
21 22
where
p is the sound pressure, uniformly applied, at the acoustical terminals
(diaphragm) of the microphone in pascals (Pa);
U is the signal voltage at the electrical terminals of the microphone in volts
(V);
q is the volume velocity through the acoustical terminals (diaphragm) of the
3
microphone in cubic metres per second (m /s);
i is the current through the electrical terminals of the microphone in
amperes (A);
z = Z is the electrical impedance of the microphone when the diaphragm is
11 e
blocked in ohms (Ω);
z = Z is the acoustic impedance of the microphone when the electrical
22 a
–3
terminals are unloaded in pascal-seconds per cubic metre (Pa⋅s⋅m ),
z = z = M Z is equal to the reverse and forward transfer impedances in volt-seconds
12 21 p a
–3
per cubic metre (V⋅s⋅m ), M being the pressure sensitivity of the
p
–1
microphone in volts per pascal (V⋅Pa ).
NOTE Underlined symbols represent complex quantities.
Equations (1) may then be rewritten as:
Z i + M Z q = U
e p a
 (1a)
M Z i + Z q = p
p a a
which constitute the equations of reciprocity for the microphone.
Let microphones (1) and (2) with the pressure sensitivities M and M be connected
p,1 p,2
acoustically by a coupler. From Equations (1a) it is seen that a current i through the
1
electrical terminals of microphone (1) will produce a short-circuit volume velocity (p = 0 at the
diaphragm) of M i and thus a sound pressure p = Z M i at the acoustical
p,1 1
a,12 p,1 1
2
terminals of microphone (2), where Z is the acoustic transfer impedance of the system.
a,12
The open-circuit voltage of microphone (2) will then be:
U = M ⋅ p = M M Z i
2 p,2 p,1 p,2 a,12 1
2

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SIST EN 61094-2:2009
61094-2 © IEC:2009 – 9 –
Thus the product of the pressure sensitivities is given by:
U
1
2
M M = (2)
p,1 p,2
Z i
a,12 1
5.3 Insert voltage technique
The insert voltage technique is used to determine the open-circuit voltage of a microphone
when it is electrically loaded.
Let a microphone having a certain open-circuit voltage and internal impedance be connected
to a load impedance. To measure the open-circuit voltage, an impedance, small compared to
the load impedance, is connected in series with the microphone and a calibrating voltage
applied across it.
Let a sound pressure and a calibrating voltage of the same frequency be applied alternately.
When the calibrating voltage is adjusted until it gives the same voltage drop across the load
impedance as results from the sound pressure on the microphone, the open-circuit voltage
will be equal in magnitude to the calibrating voltage.
5.4 Evaluation of the acoustic transfer impedance
The acoustic transfer impedance Z = p /(M i ) can be evaluated from the equivalent
a,12 p,1 1
2
circuit in Figure 1, where Z and Z are the acoustic impedances of microphones (1) and
a,1 a,2
(2) respectively.

M i
p,1 1
1
Z Z p
a,1 a,2 2
IEC  260/09

Key
1 Coupler
Figure 1 – Equivalent circuit for evaluating the acoustic transfer impedance Z
a,12
In several cases, Z can be evaluated theoretically. Assume the sound pressure to be the
a,12
same at any point inside the coupler (this will take place when the physical dimensions of the
coupler are very small compared to the wavelength). The gas in the coupler then behaves as
a pure compliance and, from the equivalent circuit in Figure 2, Z is given by Z'
a,12 a,12
(assuming adiabatic compression and expansion of the gas):

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SIST EN 61094-2:2009
– 10 – 61094-2 © IEC:2009

M i
p,1 1
Z Z Z p
a,1 a,V a,2 2
IEC  261/09

Figure 2 – Equivalent circuit for evaluating Z’ when coupler
a,12
dimensions are small compared with wavelength
V V
⎛ ⎞
1 1 1 1 V
e,1 e,2
⎜ ⎟
= + + = jω + + (3)
'
⎜ ⎟
Z Z Z κ p κ p κ p
Z s r s,r r s,r
a,V a,1 a,2
⎝ ⎠
a,12
where
3
V is the total geometrical volume of the coupler in cubic metres (m );
3
V is the equivalent volume of microphone (1) in cubic metres (m );
e,1
3
V is the equivalent volume of microphone (2) in cubic metres (m );
e,2
κ p
s
Z = is the acoustic impedance of the gas enclosed in the coupler in pascal-seconds
a,V
jωV
3
per cubic metre (Pa⋅s/m );
ω is the angular frequency in radians per second (rad/s);
p is the static pressure in pascals (Pa);
s
p is the static pressure at reference conditions in pascals (Pa);
s,r
κ is the ratio of the specific heat capacities at measurement conditions;
κ is κ at reference conditions.
r
Values for κ and κ in humid air can be derived from equations given in Annex F.
r
At higher frequencies, when the dimensions are not sufficiently small compared with the
wavelength, the evaluation of Z generally becomes complicated. However, if the shape of
a,12
the coupler is cylindrical and the diameter the same as that of the microphone diaphragms,
then, at frequencies where plane-wave transmission can be assumed, the whole system can
be considered as a homogeneous transmission line (see Figure 3).

M i
p,1 1
Z , y , l
Z Z p
a,0 0
a,1 a,2 2
IEC  262/09

’ when plane wave
Figure 3 – Equivalent circuit for evaluating Z
a,12
transmission in the coupler can be assumed
Z is then given by Z' (assuming adiabatic compression and expansion of the gas):
a,12 a,12

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