SIST EN 61161:2013
(Main)Ultrasonics - Power measurement - Radiation force balances and performance requirements
Ultrasonics - Power measurement - Radiation force balances and performance requirements
This International Standard
• specifies a method of determining the total emitted acoustic power of ultrasonic transducers based on the use of a radiation force balance;
• establishes general principles for the use of radiation force balances in which an obstacle
(target) intercepts the sound field to be measured;
• establishes limitations of the radiation force method related to cavitation and temperature rise;
• establishes quantitative limitations of the radiation force method in relation to diverging and focused beams;
• provides information on estimating the acoustic power for diverging and focused beams using the radiation force method;
• provides information on assessment of overall measurement uncertainties.
This International Standard is applicable to:
• the measurement of ultrasonic power up to 1 W based on the use of a radiation force balance in the frequency range from 0,5 MHz to 25 MHz;
• the measurement of ultrasonic power up to 20 W based on the use of a radiation force balance in the frequency range 0,75 MHz to 5 MHz;
• the measurement of total ultrasonic power in well-collimated, diverging and focused ultrasonic fields;
• the use of radiation force balances of the gravimetric type or force feedback type. (See also Clause A.1)
NOTE 1 A focused beam is converging in the pre-focal range and diverging beyond focus.
NOTE 2 Ultrasonic power measurement in the high intensity therapeutic ultrasound (HITU) range, i.e. beyond 1 W or 20 W, respectively, is dealt with in the future IEC 62555.
Ultraschall - Leistungsmessung - Schallfeldkraft-Waagen und Anforderungen an ihre Funktionseigenschaften
Ultrasons - Mesurage de puissance - Balances de forces de rayonnement et exigences de fonctionnement
La CEI 61161:2013 spécifie une méthode pour déterminer la puissance acoustique totale émise par des transducteurs ultrasonores, basée sur l'usage d'une balance de forces de rayonnement; établit les principes généraux pour utiliser les balances de forces de rayonnement dans lesquelles un obstacle dénommé cible intercepte le champ acoustique à mesurer; établit des limitations de la méthode de forces de rayonnement relatives à la cavitation et à l'élévation de la température; établit des limitations quantitatives de la méthode de forces de rayonnement par rapport aux faisceaux divergents et focalisés; fournit des informations concernant l'évaluation de la puissance acoustique pour les faisceaux divergents et focalisés par la méthode de la force de rayonnement; et fournit des informations concernant l'évaluation des incertitudes de mesure globales. La présente Norme internationale est applicable au mesurage de la puissance ultrasonore jusqu'à 1 W par utilisation d'une balance de forces de rayonnement dans la plage de fréquences de 0,5 MHz à 25 MHz; au mesurage de la puissance ultrasonore jusqu'à 20 W par utilisation d'une balance de forces de rayonnement dans la plage de fréquences de 0,75 MHz à 5 MHz; au mesurage de la puissance ultrasonore totale de transducteurs dans des champs ultrasonores possédant une bonne collimation, divergents et focalisés; et à l'utilisation de balances de forces de rayonnement de type gravimétrique ou à retour de force. Cette troisième édition annule et remplace la deuxième édition publiée en 2006. Elle constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente: - alors que la deuxième édition a implicitement traité des transducteurs circulaires uniquement, la présente édition traite dans la mesure du possible des transducteurs circulaires et rectangulaires et inclut également un certain nombre de symboles destinés aux transducteurs rectangulaires; - une plus grande d'attention est accordée aux cas focalisés et l'influence du balayage a été ajoutée; - la méthode d'étalonnage de la balance de forces de rayonnement dépend désormais de l'utilisation ou non de la configuration comme outil de mesure primaire ou secondaire; - et l'Annexe B (formules fondamentales) a été actualisée et l'Annexe C fait mention de la méthode de changement de flottabilité (voir aussi la future CEI 62555).
Ultrazvok - Močnostne meritve - Ravnotežje sevalnih jakosti in tehnične zahteve
Ta mednarodni standard:
• določa metodo za določanje skupne oddane akustične moči ultrazvočnih pretvornikov glede na uporabo ravnotežja sil sevanja;
• uvaja splošna načela za uporabo ravnotežij sil sevanja, pri katerih ovira (tarča) prestreže zvočno polje, ki je predmet meritve;
• uvaja omejitve metode sil sevanja v povezavi s kavitacijo in dvigom temperature;
• uvaja kvantitativne omejitve metode sil sevanja v povezavi z razpršenimi in usmerjenimi žarki;
• ponuja informacije o oceni akustične moči za razpršene in usmerjene žarke s pomočjo metode sil sevanja;
• ponuja informacije o ocenjevanju splošnih merilnih negotovosti.
Ta mednarodni standard se uporablja za:
• merjenje ultrazvočne moči do 1 W na podlagi uporabe ravnotežja sil sevanja v frekvenčnem razponu od 0,5 MHz do 25 MHz;
• merjenje ultrazvočne moči do 20 W na podlagi uporabe ravnotežja sil sevanja v frekvenčnem razponu od 0,75 MHz do 5 MHz;
• merjenje skupne ultrazvočne moči v dobro naravnanih, razpršenih in usmerjenih ultrazvočnih poljih;
• uporabo ravnotežij sil sevanja gravimetrične vrste ali vrste ponovne uporabe sile. (Glejte tudi točko A.1).
OPOMBA 1: Usmerjeni žarek se steka v predgoriščnem območju in razprši za goriščem.
OPOMBA 2: Merjenje ultrazvočne moči v območju terapevtske ultrazvočne visoke intenzivnosti (HITU), to je nad 1 W ali 20 W, je obravnavano v nadaljnjem IEC 62555.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 61161:2013
01-julij-2013
1DGRPHãþD
SIST EN 61161:2008
8OWUD]YRN0RþQRVWQHPHULWYH5DYQRWHåMHVHYDOQLKMDNRVWLLQWHKQLþQH]DKWHYH
Ultrasonics - Power measurement - Radiation force balances and performance
requirements
Ultraschall - Leistungsmessung - Schallfeldkraft-Waagen und Anforderungen an ihre
Funktionseigenschaften
Ultrasons - Mesurage de puissance - Balances de forces de rayonnement et exigences
de fonctionnement
Ta slovenski standard je istoveten z: EN 61161:2013
ICS:
17.140.50 Elektroakustika Electroacoustics
SIST EN 61161:2013 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN 61161:2013
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SIST EN 61161:2013
EUROPEAN STANDARD
EN 61161
NORME EUROPÉENNE
April 2013
EUROPÄISCHE NORM
ICS 17.140.50 Supersedes EN 61161:2007
English version
Ultrasonics -
Power measurement -
Radiation force balances and performance requirements
(IEC 61161:2013)
Ultrasons - Mesurage de puissance - Ultraschall - Leistungsmessung -
Balances de forces de rayonnement Schallfeldkraft-Waagen
et exigences de fonctionnement und Anforderungen an ihre
(CEI 61161:2013) Funktionseigenschaften
(IEC 61161:2013)
This European Standard was approved by CENELEC on 2013-03-06. 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 CEN-CENELEC Management Centre 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 CEN-CENELEC Management Centre has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus,
the Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany,
Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Management Centre: Avenue Marnix 17, B - 1000 Brussels
© 2013 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61161:2013 E
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SIST EN 61161:2013
EN 61161:2013 - 2 -
Foreword
The text of document 87/520/FDIS, future edition 3 of IEC 61161, prepared by IEC/TC 87 "Ultrasonics"
was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as EN 61161:2013.
The following dates are fixed:
(dop) 2013-12-06
• latest date by which the document has
to be implemented at national level by
publication of an identical national
standard or by endorsement
(dow) 2016-03-06
• latest date by which the national
standards conflicting with the
document have to be withdrawn
This document supersedes EN 61161:2007.
EN 61161:2013 includes the following significant technical changes with respect to EN 61161:2007:
– whereas the second edition tacitly dealt with circular transducers only, the present edition as far
as possible deals with both circular and rectangular transducers, Including a number of symbols
for rectangular transducers;
– attention is paid to focused cases and the influence of scanning has been added;
– the method of calibrating the radiation force balance now depends on whether the set-up is used
as a primary or as secondary measurement tool;
– Annex B (basic formulae) has been updated and in Annex C the buoyancy change method is
mentioned (see also future EN 62555).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such
patent rights.
Endorsement notice
The text of the International Standard IEC 61161:2013 was approved by CENELEC as a European
Standard without any modification.
In the official version, for Bibliography, the following notes have to be added for the standards indicated:
IEC 60601-2-5 NOTE Harmonised as EN 60601-2-5.
IEC 61157 NOTE Harmonised as EN 61157.
IEC 61846:1998 NOTE Harmonised as EN 61846:1998 (not modified).
IEC 62127-1 NOTE Harmonised as EN 62127-1.
IEC 62127-2 NOTE Harmonised as EN 62127-2.
IEC 62127-3 NOTE Harmonised as EN 62127-3.
1) 1)
IEC 62555 NOTE Harmonised as EN 62555 .
1)
At draft stage.
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SIST EN 61161:2013
- 3 - EN 61161:2013
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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 61689 - Ultrasonics - Physiotherapy systems - Field EN 61689 -
specifications and methods of measurement
in the frequency range 0,5 MHz to 5 MHz
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SIST EN 61161:2013
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SIST EN 61161:2013
IEC 61161
®
Edition 3.0 2013-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Ultrasonics – Power measurement – Radiation force balances and performance
requirements
Ultrasons – Mesurage de puissance – Balances de forces de rayonnement et
exigences de fonctionnement
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX X
ICS 17.140.50 ISBN 978-2-83220-617-1
Warning! Make sure that you obtained this publication from an authorized distributor.
Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.
® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
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SIST EN 61161:2013
– 2 – 61161 © IEC:2013
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 List of symbols . 9
5 Requirements for radiation force balances . 9
5.1 General . 9
5.2 Target type . 10
5.2.1 General . 10
5.2.2 Absorbing target . 10
5.2.3 Reflecting target . 10
5.3 Target diameter . 11
5.4 Balance/force measuring system . 11
5.5 System tank . 11
5.6 Target support structures . 11
5.7 Transducer positioning . 11
5.8 Anti-streaming foils . 11
5.9 Transducer coupling . 12
5.10 Calibration . 12
6 Requirements for measuring conditions . 12
6.1 Lateral target position . 12
6.2 Transducer/target separation . 12
6.3 Water . 12
6.4 Water contact . 13
6.5 Environmental conditions . 13
6.6 Thermal drifts . 13
7 Measurement uncertainty . 13
7.1 General . 13
7.2 Balance system including target suspension . 13
7.3 Linearity and resolution of the balance system . 13
7.4 Extrapolation to the moment of switching the ultrasonic transducer . 14
7.5 Target imperfections . 14
7.6 Reflecting target geometry . 14
7.7 Lateral absorbers in the case of reflecting target measurements . 14
7.8 Target misalignment . 14
7.9 Ultrasonic transducer misalignment . 14
7.10 Water temperature . 14
7.11 Ultrasonic attenuation and acoustic streaming . 14
7.12 Foil properties . 14
7.13 Finite target size . 15
7.14 Plane-wave assumption . 15
7.15 Scanning influence . 15
7.16 Environmental influences . 15
7.17 Excitation voltage measurement . 15
7.18 Ultrasonic transducer temperature . 15
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61161 © IEC:2013 – 3 –
7.19 Nonlinearity . 15
7.20 Acceleration due to gravity . 15
7.21 Other sources . 16
Annex A (informative) Additional information on various aspects of radiation force
measurements . 17
Annex B (informative) Basic formulae . 30
Annex C (informative) Other methods of ultrasonic power measurement . 36
Annex D (informative) Propagation medium and degassing . 37
Annex E (informative) Radiation force measurement with diverging ultrasonic beams . 38
Annex F (informative) Limitations associated with the balance arrangements . 42
Bibliography . 46
Figure 1 – Section through an absorbing target . 16
Figure 2 – Linearity check: balance readout as a function of the input quantity . 16
Figure E.1 – Piston result (oscillating curve) for P/cF as a function of ka . 39
Figure E.2 – P/cF as a function of ka for four different pseudo-trapezoidal amplitude
distributions . 39
Figure E.3 – Ratio of the radiation conductance G as obtained using a convex-conical
reflecting target to an absorbing target versus the value of ka [29] . 41
Figure F.1 – Arrangement A . 42
Figure F.2 – Arrangement B, with convex-conical reflecting target . 43
Figure F.3 – Arrangement B, with absorbing target . 43
Figure F.4 – Arrangement C, with absorbing target . 43
Figure F.5 – Arrangement E, with absorbing (a) or concave-conical reflecting (b) target . 43
Figure F.6 – Arrangement F, with convex-conical reflecting target . 44
Figure F.7 – Arrangement F with absorbing target . 44
Table F.1 – Advantages and disadvantages of different arrangements . 45
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SIST EN 61161:2013
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INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ULTRASONICS – POWER MEASUREMENT –
RADIATION FORCE BALANCES AND PERFORMANCE REQUIREMENTS
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 itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
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 61161 has been prepared by IEC technical committee 87:
Ultrasonics.
This third edition cancels and replaces the second edition published in 2006. It constitutes a
technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
– whereas the second edition tacitly dealt with circular transducers only, the present edition
as far as possible deals with both circular and rectangular transducers, including a number
of symbols for rectangular transducers;
– attention is paid to focused cases and the influence of scanning has been added;
– the method of calibrating the radiation force balance now depends on whether the set-up
is used as a primary or as secondary measurement tool;
– Annex B (basic formulae) has been updated and in Annex C the buoyancy change method
is mentioned (see also future IEC 62555).
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SIST EN 61161:2013
61161 © IEC:2013 – 5 –
The text of this standard is based on the following documents:
FDIS Report on voting
87/520/FDIS 87/528/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.
NOTE The following print types are used:
• Requirements: in Arial 10 point
• Notes: in Arial 8 point
• Words in bold in the text are defined in Clause 3
• Symbols and formulae: Times New Roman + Italic.
The committee has decided that the contents of this publication will remain unchanged until
the stability 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 61161:2013
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INTRODUCTION
A number of measuring methods exist for the determination of the total emitted power of
1
ultrasonic transducers ([1], [2], [3] , see also Annex C). The purpose of this International
Standard is to establish standard methods of measurement of ultrasonic power in liquids in
the lower megahertz frequency range based on the measurement of the radiation force using
a gravimetric balance. The great advantage of radiation force measurements is that a value
for the total radiated power is obtained without the need to integrate field data over the cross-
section of the radiated sound beam. This standard identifies the sources of errors and
describes a systematic step-by-step procedure to assess overall measurement uncertainty as
well as the precautions that should be undertaken and uncertainties that should be taken into
account while performing power measurements.
Basic safety requirements for ultrasonic physiotherapy devices are identified in IEC 60601-2-5
and make reference to IEC 61689, which specifies the need for acoustic power measurements
with an uncertainty better than ± 15 % at a level of confidence of 95 %. Considering the usual
degradation of accuracy in the practical application of this standard, reference measurement
methods need to be established with uncertainties better than ± 7 %. Ultrasonic diagnostic
device declaration requirements including acoustic power are specified in other IEC standards,
as for example in IEC 61157.
The measurement of acoustic power accurately and repeatably using a radiation force
balance as defined in this standard is influenced by a number of practical problems. As a
guide to the user, additional information is provided in Annex A using the same section and
clause numbering as the main body.
—————————
1
Numbers in square brackets refer to the Bibliography.
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SIST EN 61161:2013
61161 © IEC:2013 – 7 –
ULTRASONICS – POWER MEASUREMENT –
RADIATION FORCE BALANCES AND PERFORMANCE REQUIREMENTS
1 Scope
This International Standard
• specifies a method of determining the total emitted acoustic power of ultrasonic
transducers based on the use of a radiation force balance;
• establishes general principles for the use of radiation force balances in which an obstacle
(target) intercepts the sound field to be measured;
• establishes limitations of the radiation force method related to cavitation and temperature
rise;
• establishes quantitative limitations of the radiation force method in relation to diverging
and focused beams;
• provides information on estimating the acoustic power for diverging and focused beams
using the radiation force method;
• provides information on assessment of overall measurement uncertainties.
This International Standard is applicable to:
• the measurement of ultrasonic power up to 1 W based on the use of a radiation force
balance in the frequency range from 0,5 MHz to 25 MHz;
• the measurement of ultrasonic power up to 20 W based on the use of a radiation force
balance in the frequency range 0,75 MHz to 5 MHz;
• the measurement of total ultrasonic power in well-collimated, diverging and focused
ultrasonic fields;
• the use of radiation force balances of the gravimetric type or force feedback type.
(See also Clause A.1)
NOTE 1 A focused beam is converging in the pre-focal range and diverging beyond focus.
NOTE 2 Ultrasonic power measurement in the high intensity therapeutic ultrasound (HITU) range, i.e. beyond 1 W
or 20 W, respectively, is dealt with in the future IEC 62555.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 61689, Ultrasonics – Physiotherapy systems – Field specifications and methods of
measurement in the frequency range 0,5 MHz to 5 MHz
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
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SIST EN 61161:2013
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3.1
acoustic streaming
bulk fluid motion initiated by a sound field
3.2
free field
sound field in a homogeneous isotropic medium whose boundaries exert a negligible effect on
the sound waves
[SOURCE: IEC 60050-801:1994, definition 801-23-28, modified – the term no longer contains
“sound”]
3.3
output power
P
time-average ultrasonic power emitted by an ultrasonic transducer into an approximately
free field under specified conditions in a specified medium, preferably water
Note 1 to entry: Output power is expressed in watt (W).
3.4
radiation force
acoustic radiation force
F
time-average force acting on a body in a sound field and caused by the sound field, excluding
the component due to acoustic streaming; or, more generally: time-average force (excluding
the component due to acoustic streaming) in a sound field, appearing at the boundary
surface between two media of different acoustic properties, or within a single attenuating
medium
Note 1 to entry: Radiation force, acoustic radiation force, is expressed in newton (N).
3.5
radiation pressure
acoustic radiation pressure
radiation force per unit area
Note 1 to entry: This term is widely used in the literature. However, strictly speaking, the radiation force per unit
area is a tensor quantity [4] and it should be referred to as the acoustic radiation stress tensor when a strict
scientific terminology is to be used. The integral quantity "acoustic radiation force" is generally preferred in this
International Standard. Whenever at some places, the term "acoustic radiation pressure" appears it is to be
understood as the negative value of the normal radiation stress in the direction of the field axis.
Note 2 to entry: Radiation pressure, acoustic radiation pressure, is expressed in pascal (Pa).
3.6
target
device specially designed to intercept substantially all of the ultrasonic field and to serve as
the object which is acted upon by the radiation force
3.7
ultrasonic transducer
device capable of converting electrical energy to mechanical energy within the ultrasonic
frequency range and/or reciprocally of converting mechanical energy to electrical energy
3.8
radiation conductance
G
ratio of the acoustic output power and the squared RMS transducer input voltage
Note 1 to entry: It is used to characterize the electrical to acoustical transfer of ultrasonic transducers.
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SIST EN 61161:2013
61161 © IEC:2013 – 9 –
Note 2 to entry: Radiation conductance is expressed in siemens (S).
4 List of symbols
a radius of a circular ultrasonic source transducer
b and b half-dimensions of a rectangular ultrasonic source transducer in x and y direction,
x y
respectively (so that 2 b and 2 b are the transducer's side lengths)
x y
c speed of sound (usually in water)
d and d geometrical focal lengths of a focusing ultrasonic transducer in the x-z and the
x y
y-z plane, respectively
d geometrical focal length of a focusing ultrasonic transducer in the case of
d = d = d
x y
F radiation force on a target in the direction of the incident ultrasonic wave
g acceleration due to gravity
G radiation conductance
2 2 1/2
h half the diagonal of a rectangular transducer, h = (b + b )
d d x y
h harmonic mean of b and b , h = 2 / (1/b + 1/b )
h x y h x y
k circular wavenumber, k = 2 π / λ
P output power of an ultrasonic transducer
2
s normalized distance from a circular ultrasonic transducer, s = z λ / a
z distance between an ultrasonic transducer and a target
α amplitude attenuation coefficient of plane waves in a medium (usually water)
β and β focus (half-)angles of a rectangular focusing ultrasonic transducer in the x-z
x y
and the y-z plane, respectively; β = arctan(b /d ), β = arctan(b /d ) if the
x x x y y y
transducer is planar and the focal lengths are counted from the planar
transducer surface
γ focus (half-)angle of a circular focusing ultrasonic transducer; γ = arcsin(a / d)
if the transducer is spherically curved and the focal length is counted from the
"bottom" of the "bowl"; γ = arctan(a / d) if the focal length is counted from the
plane defined by the rim of the active part of the "bowl" or if the transducer is
planar
θ angle between the direction of the incident ultrasonic wave and the normal to a
reflecting
...
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