Electroacoustics - Measurement microphones - Part 10: Absolute pressure calibration of microphones at low frequencies using calculable pistonphones

IEC TR 61904-10:2022
- is applicable to laboratory standard microphones meeting the requirements of IEC 61094-1 and other types of measurement microphones,
- describes one possible absolute method for determining the complex pressure sensitivity, based on a device capable of generating a known sound pressure, especially at low frequencies, and
- provides a reproducible and accurate basis for the measurement of sound pressure at low frequencies.
All quantities are expressed in SI units.

General Information

Status
Published
Publication Date
03-Aug-2022
Technical Committee
Current Stage
PPUB - Publication issued
Completion Date
04-Aug-2022
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IEC TR 61094-10
Edition 1.0 2022-08
TECHNICAL
REPORT
colour
inside
Electroacoustics – Measurement microphones –
Part 10: Absolute pressure calibration of microphones at low frequencies using
calculable pistonphones
IEC TR 61094-10:2022-08(en)
---------------------- Page: 1 ----------------------
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---------------------- Page: 2 ----------------------
IEC TR 61094-10
Edition 1.0 2022-08
TECHNICAL
REPORT
colour
inside
Electroacoustics – Measurement microphones –
Part 10: Absolute pressure calibration of microphones at low frequencies using
calculable pistonphones
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 17.140.50 ISBN 978-2-8322-4374-9

Warning! Make sure that you obtained this publication from an authorized distributor.

® Registered trademark of the International Electrotechnical Commission
---------------------- Page: 3 ----------------------
– 2 – IEC TR 61904-10:2022 © IEC 2022
CONTENTS

FOREWORD ........................................................................................................................... 4

1 Scope .............................................................................................................................. 6

2 Normative references ...................................................................................................... 6

3 Terms and definitions ...................................................................................................... 6

4 Reference environmental conditions ................................................................................ 7

5 Principles of absolute pressure calibration of microphones using a calculable

pistonphone ..................................................................................................................... 7

5.1 General principle .................................................................................................... 7

5.2 Basic expressions ................................................................................................... 7

5.3 Heat conduction correction ..................................................................................... 9

5.4 Operating frequency range ...................................................................................... 9

6 General characteristics .................................................................................................... 9

6.1 The pistonphone ..................................................................................................... 9

6.2 Measuring the piston volume velocity .................................................................... 10

6.3 Test signals .......................................................................................................... 10

6.4 Mounting the microphone and pressure-equalizing tube ........................................ 10

6.5 Measuring the output voltages of the microphones ................................................ 10

7 Factors influencing the pressure sensitivity.................................................................... 10

7.1 General ................................................................................................................. 10

7.2 Polarizing voltage ................................................................................................. 11

7.3 Shield configuration .............................................................................................. 11

7.4 Dependence on environmental conditions ............................................................. 11

7.4.1 General ......................................................................................................... 11

7.4.2 Static pressure .............................................................................................. 11

7.4.3 Temperature .................................................................................................. 11

7.4.4 Humidity ........................................................................................................ 12

7.5 Vibration ............................................................................................................... 12

7.6 Distortion .............................................................................................................. 12

8 Calibration uncertainty components ............................................................................... 12

8.1 General ................................................................................................................. 12

8.2 Measurements of microphone output voltage ........................................................ 12

8.3 Piston ................................................................................................................... 12

8.3.1 Frequency ..................................................................................................... 12

8.3.2 Measurement of the volume velocity .............................................................. 12

8.4 Acoustic transfer impedance ................................................................................. 13

8.4.1 Cavity properties ........................................................................................... 13

8.4.2 Physical quantities ......................................................................................... 13

8.5 Microphone parameters ........................................................................................ 13

8.5.1 Front cavity.................................................................................................... 13

8.5.2 Acoustic impedance ....................................................................................... 13

8.5.3 Polarizing voltage .......................................................................................... 14

8.6 Uncertainty on pressure sensitivity level ............................................................... 14

Annex A (informative) Example designs of pistonphones using laser interferometry ............. 16

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IEC TR 61904-10:2022 © IEC 2022 – 3 –

Annex B (informative) Measurement uncertainties ............................................................... 18

B.1 General ................................................................................................................. 18

B.2 Example of a typical uncertainty analysis .............................................................. 18

B.2.1 General ......................................................................................................... 18

B.2.2 Uncertainty budget ........................................................................................ 18

B.2.3 Combined and expanded uncertainties .......................................................... 19

Bibliography .......................................................................................................................... 20

Figure 1 – Equivalent circuit for evaluating the sound pressure over the exposed

surface of the diaphragm of the microphone ........................................................................... 8

Figure A.1 – Schematic cross-section of a laser pistonphone ................................................ 16

Figure A.2 – Example of laser pistonphone ........................................................................... 17

Figure A.3 – Example of laser pistonphone ........................................................................... 17

Table 1 – Uncertainty components ........................................................................................ 14

Table B.1 – Example of uncertainty budget at 1 Hz ............................................................... 19

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– 4 – IEC TR 61904-10:2022 © IEC 2022
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTROACOUSTICS –
MEASUREMENT MICROPHONES –
Part 10: Absolute pressure calibration of microphones
at low frequencies using calculable pistonphones
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

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Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.

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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.

IEC TR 61094-10 has been prepared by IEC technical committee 29: Electroacoustics. It is a

Technical Report.
The text of this Technical Report is based on the following documents:
Draft Report on voting
29/1113/DTR 29/1124/RVDTR

Full information on the voting for its approval can be found in the report on voting indicated in

the above table.
The language used for the development of this Technical Report is English.
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IEC TR 61904-10:2022 © IEC 2022 – 5 –

This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in

accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available

at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are

described in greater detail at www.iec.ch/publications.

A list of all parts in the IEC 61094 series, published under the general title Electroacoustics –

Measurement microphones, can be found on the IEC website.

Future documents in this series will carry the new general title as cited above. Titles of existing

documents in this series will be updated at the time of the next edition.

The committee has decided that the contents of this document will remain unchanged until the

stability date indicated on the IEC website under webstore.iec.ch in the data related to the

specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

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of its contents. Users should therefore print this document using a colour printer.

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– 6 – IEC TR 61904-10:2022 © IEC 2022
ELECTROACOUSTICS –
MEASUREMENT MICROPHONES –
Part 10: Absolute pressure calibration of microphones
at low frequencies using calculable pistonphones
1 Scope
This part of IEC 61094

• is applicable to laboratory standard microphones meeting the requirements of IEC 61094-1

and other types of measurement microphones,

• describes one possible absolute method for determining the complex pressure sensitivity,

based on a device capable of generating a known sound pressure, especially at low

frequencies, and

• provides a reproducible and accurate basis for the measurement of sound pressure at low

frequencies.
All quantities are expressed in SI units.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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

IEC 61094-2:2009, Electroacoustics – Measurement microphones – Part 2: Primary method for

pressure calibration of laboratory standard microphones by the reciprocity technique

IEC 61094-2:2009/AMD1:2022
3 Terms and definitions

For the purposes of this document, the terms and definitions given in IEC 61094-1 and

IEC 61094-2 and the following apply.

ISO and IEC maintain terminology databases for use in standardization at the following

addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.1
pistonphone

device in which sound pressure is generated in a fixed sealed volume of air, by the motion of

one or more pistons creating a well-defined volume velocity
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IEC TR 61904-10:2022 © IEC 2022 – 7 –
3.2
calculable pistonphone

pistonphone where the generated sound pressure can be calculated from physical principles

4 Reference environmental conditions
The reference environmental conditions are the following:
• temperature 23,0 °C;
• static pressure 101,325 kPa;
• relative humidity 50 %.
5 Principles of absolute pressure calibration of microphones using a
calculable pistonphone
5.1 General principle

The microphone to be calibrated is exposed to a known or calculable sound pressure produced

within the sealed cavity (or coupler) of a pistonphone, without the need for a prior measurement

with another microphone. The dimensions of the cavity are constrained to allow the assumption

to be made that the sound pressure is uniformly distributed within.

A sound generator consisting of a sealed cavity (or coupler) of known volume that is driven by

a piston or similar mechanism capable of producing a known volume velocity (e.g. an

electrodynamic loudspeaker) has the potential to generate a known sound pressure. If the

piston is assumed to be rigid and of known frontal area, laser interferometry or other

displacement measurement techniques can be used to determine the piston displacement and

thereby derive the volume displacement.

The pressure sensitivity M of the microphone is then determined directly from its open-circuit

output voltage U and the applied sound pressure p .
m,0 m
m0,
M =
(1)

Alternatively, a microphone system comprising of a microphone, a preamplifier and optionally

and amplifier stage, can be calibrated by the same principle, except that the system output

voltage replaces the open-circuit output voltage of the microphone in Formula (1).

5.2 Basic expressions

The generated sound pressure p that is applied to the diaphragm of the microphone is

calculated from an evaluation of the acoustic transfer impedance Z of the cavity and a

measurement of the piston displacement 𝛿𝛿𝛿𝛿.

The acoustic transfer impedance is the constant of proportionality between the sound pressure

at the microphone diaphragm and the volume velocity driving the cavity. In the case of a

sinusoidally driven rigid piston, the volume velocity is given by the product of the piston area

S , the piston displacement and a factor jω, where ω is the angular frequency:
pjω Sδx⋅Z
(2)
m pT
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– 8 – IEC TR 61904-10:2022 © IEC 2022

If the piston is not rigid, calculation of the volume velocity requires the surface integral of

displacement to be determined, for example with scanning interferometry.

The acoustic transfer impedance can be calculated when the cavity has a simple geometry

enabling its volume, V to be determined. When the characteristic cavity dimensions are

significantly smaller than the acoustic wavelength, λ (typically when V λ ), then the sound

pressure can be assumed to be uniformly distributed within the cavity. Then, assuming adiabatic

compression and expansion of the gas and that the cavity is perfectly sealed, the acoustic

impedance of the cavity Z is κ P /(jωV), where κ is the ratio of specific heats for air and P is

c s s

the static pressure inside the cavity. From the equivalent circuit in Figure 1, Z is then given by:

1 11 V
e,m
= += jω +
 (3)
Z ZZ κP κP
T C m S r S,r
where
V is the equivalent volume of microphone to be calibrated;
e,m

κ and κ are the ratio of the specific heats at measurement conditions and at reference

conditions respectively;
P is the reference static pressure.
s,r

Values for κ and κ in humid air can be determined from formulas given in IEC 61094-2:2009,

Annex F.
Key
𝜔𝜔 angular frequency
S piston surface area
δx piston displacement
q and q volume velocities
Z and Z acoustic impedances of the cavity and microphone respectively
c m
p sound pressure acting on the microphone
Figure 1 – Equivalent circuit for evaluating the sound pressure over
the exposed surface of the diaphragm of the microphone

At higher frequencies, where the wavelength can no longer be considered sufficiently large

compared to the cavity dimensions, the evaluation of Z generally becomes more complicated

and requires the specific geometry of the cavity to be accounted for. The onset of such

behaviour is generally considered to be the upper frequency limit for the operation of the

pistonphone within the scope of this document.
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IEC TR 61904-10:2022 © IEC 2022 – 9 –
5.3 Heat conduction correction

The evaluation of Z in Formula (3) assumes adiabatic conditions in the cavity. However, in

practice, the influence of heat conduction at the walls of the cavity causes increasing departure

from purely adiabatic conditions as the frequency is reduced, especially for small cavities.

At frequencies where the sound pressure can be considered to be uniformly distributed within

the cavity and under the assumption that the walls remain at a constant temperature, the

influence of the heat conduction losses can be calculated and expressed in terms of a complex

correction factor ΔH to the geometrical volume V in Formula (3). The formulation for the

influence of the heat conduction losses and expressions for a correction factor ΔH, when the

cavity shape is a perfect right circular cylinder, are given in IEC 61094-2:2009 and

IEC 61094-2:2009/AMD1:2022.
5.4 Operating frequency range

The upper frequency limit of operation is likely to be determined by the onset of sound pressure

non-uniformity. This is normally assessed by modelling the sound field within the pistonphone

cavity. The model can be used to determine a correction to account for the non-uniform sound

pressure distribution for the specific cavity geometry, but a point will be reached where the

magnitude of this correction, and therefore the associated uncertainty, becomes unacceptable.

Each cavity geometry will require individual treatment, but an upper frequency limit of around

200 Hz is typically possible when characteristic dimensions are no greater than 60 mm.

It is also possible that the volume velocity source determines the upper frequency of operation.

As the frequency increases, a greater amount of force is necessary to drive the piston. The

frequency at which this capability is exceeded could also set a practical operational limit.

The low frequency limit can be governed by the uncertainty associated with the heat conduction

correction, or by pressure leakage from the cavity. The limits that can be achieved are strongly

related to the specific design of the pistonphone but there are reports of devices operating at

frequencies of 0,01 Hz [1] [2] .
6 General characteristics
6.1 The pistonphone

A convenient pistonphone cavity geometry is a right circular cylinder as this allow direct

application of the heat conduction model presented in IEC 61094-2:2009 and
IEC 61094-2:2009/AMD1:2022.

The estimation of the sound pressure generated within the pistonphone is strongly dependent

on the internal volume. When the cavity and the volume velocity source are made from a hard,

dimensionally stable, non-porous materials, the influences of time, temperature, humidity and

other physical parameters can be expected to have no adverse effect on performance.

Since the pistonphone is typically activated by a vibrating mechanism, care can be needed to

ensure the microphone under test is not subjected to extraneous vibration signals capable of

contributing to the measured output voltage.

There are no constraints on the size of the cavity, but note that the generated sound pressure

is proportional to the ratio of the induced volume velocity to the overall volume of the cavity.

Therefore, a larger cavity requires a more powerful volume velocity source.
___________
Numbers in square brackets refer to the Bibliography.
---------------------- Page: 11 ----------------------
– 10 – IEC TR 61904-10:2022 © IEC 2022

Conversely, the effects of heat conduction generally become less significant at a given

frequency as the size of the cavity increases. Heat conduction effects can also be minimised

for a given cavity volume, with a dimensional aspect ratio (length-to-diameter ratio for a

cylindrical cavity) close to unity.

A unit aspect ratio also maximises the upper frequency limit of operation for a given volume,

when the limit is dictated by the onset of sound pressure non-uniformity within the cavity.

Example pistonphone designs can be found in Annex A.
6.2 Measuring the piston volume velocity

If the piston is assumed to be rigid, a technique based on laser interferometry (for example see

ISO 16063-11) or other displacement measurement techniques can be used to determine the

piston displacement and derive the volume displacement when the piston area is known.

6.3 Test signals

Calibration can be achieved with sinusoidal or broadband stimuli where the signals within

frequency bands or at discrete frequencies can be extracted.
6.4 Mounting the microphone and pressure-equalizing tube

The normal construction of a laboratory standard or working standard microphone has the cavity

behind the diaphragm fitted with a narrow pressure-equalization tube to permit the static

pressure to be the same on both sides of the diaphragm. Consequently, at very low frequencies,

this tube also partially equalizes the sound pressure. During the calibration, if sound which is

coherent with that acting on the diaphragm also reaches the pressure-equalizing tube, the

sensitivity will be altered as a result. This tendency increases as the frequency is reduced.

Therefore, the configuration of the pressure-equalizing tube during a calibration strongly

influences the frequency response obtained for the microphone under test.

Given this dependency, there are advantages in the pistonphone being capable of coupling the

microphone in different ways. For example, some applications can require the microphone

sensitivity to be determined with the pressure-equalization tube completely within the sound

field (pseudo-free-field response) while others might require the pressure-equalization tube to

be isolated from the sound field (pressure-field response).
6.5 Measuring the output voltages of the microphones

The open-circuit output voltage of the microphone can be determined with the insert voltage

technique (for example, see IEC 61094-2:2009, 5.3) or by using a measuring system consisting

of a high input impedance microphone preamplifier and a voltmeter (for example, see

IEC 61094-5:2016, Annex C).
7 Factors influencing the pressure sensitivity
7.1 General

The pressure sensitivity of a microphone under test can depend on several external factors

depending on the transduction mechanism of the microphone. The following parameters are

considerations for laboratory standard microphones operating on an electrostatic principle with

an externally applied polarizing voltage, and other measurement microphones operating in a

similar way.
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IEC TR 61904-10:2022 © IEC 2022 – 11 –
7.2 Polarizing voltage

The basic mode of operation of a polarized condenser microphone assumes a constant

electrical charge on the microphone. The product of the microphone capacitance, and the

electrical resistance through which the polarizing voltage is applied, determines the time

constant for charging the microphone. At sufficiently high frequency (typically above 2 Hz), the

time constant is much longer than the acoustic period, and the constant charge condition can

be maintained. However, a constant charge cannot be maintained at very low frequencies.

While the open-circuit sensitivity of the microphone, as obtained using the insert-voltage

technique, will be determined correctly, the absolute output from the preamplifier associated

with the microphone will decrease at low frequencies in accordance with this time constant.

The sensitivity of a laboratory standard or working standard microphone is approximately

proportional to the polarizing voltage
...

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