SIST EN 50324-3:2004

SLOVENSKI SIST EN 50324-3:2004

STANDARD
julij 2004
Piezoelectric properties of ceramic materials and components - Part 3: Methods of
measurement - High power
ICS 31.140 Referenčna številka
SIST EN 50324-3:2004(en)
©  Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

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EUROPEAN STANDARD EN 50324-3
NORME EUROPÉENNE
EUROPÄISCHE NORM May 2002
ICS 31.140
English version
Piezoelectric properties of ceramic materials and components
Part 3: Methods of measurement -
High power
Propriétés piézo-électriques des Piezoelektrische Eigenschaften von
matériaux et composants céramiques keramischen Werkstoffen
Partie 3: Méthodes de mesure - und Komponenten
Grande puissance Teil 3: Meßverfahren -
Großsignal
This European Standard was approved by CENELEC on 2001-12-01. 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, Czech Republic,
Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands,
Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels
© 2002 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 50324-3:2002 E

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EN 50324-3:2002 - 2 -
Foreword
This European Standard was prepared by the CENELEC BTTF 63-2, Advanced technical
ceramics.
The text of the draft was submitted to the formal vote and was approved by CENELEC as
EN 50324-3 on 2001-01-12.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2002-12-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2004-12-01
This part 3 is to be read in conjunction with EN 50324-1 and EN 50324-2.
__________

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- 3 - EN 50324-3:2002
Contents
Page
1 Scope. 4
2 Specification of material. 4
2.1 Power applications criteria. 4
2.2 Materials for electromechanical conversion. 4
2.2.1 Figure of Merit M. 4
2.2.2 Methodology for the composition selection . 6
2.3 Materials for mechanoelectrical conversion. 7
2.3.1 Figure of Merit. 7
2.3.2 Methodology for the composition selection . 7
3 Boundary conditions and methods of measurements for the large signal
parameters of piezoceramic materials and components. 7
3.1 Dielectric large signal properties - Methods of measurement . 8
3.2 Mechanical large signal properties - Limits. 9
3.2.1 Methods of measurement . 9
3.2.2 Mechanical losses as a function of the dynamic strain . 10
Annex A (informative) Methods and calculations .14
A.1 Mechanical large signal properties in longitudinal length mode.14
A.2 Mechanical large signal properties in transverse length mode -
Methods and calculations.15

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EN 50324-3:2002 - 4 -
1 Scope
This European Standard relates to piezoelectric transducer ceramics for power application
over a wide frequency range both as electromechanical or mechanoelectrical converters.
This standard covers the large signal characterization of piezoelectric ceramics material
only, and not the characterization of a complete assembled transducer.
The selection of a material for a given power application is difficult and the advice given in
clause 2 is mainly indicative.
2 Specification of material
2.1 Power applications criteria
Most mechanical, electrical and piezoelectric coefficients defined in EN 50324-2 exhibit a
non-linear behaviour when the piezoelectric material is subjected to large electrical and/or
mechanical signals.
However, the difference in non-linear behaviour of the various ceramic compositions is not
the only criterion to decide which is the most suited for a given power application. In general,
the material factors which limit the available acoustic power capacity of a piezoceramic
based transducer are mainly
- the dynamic mechanical strength of the ceramic,
- the reduction in efficiency due to dielectric and mechanical ceramic internal losses,
- depolarization due to temperature rise.
2.2 Materials for electromechanical conversion
2.2.1 Figure of Merit M
The figure of Merit characterizes the ability of the material to convert the electrical energy
into mechanical energy. It may be represented by the appropriate electromechanical
coupling factor measured under high power conditions. A more suited figure of Merit for
power applications is M , derived from the electromechanical transformer ratio N of the
ij
Mason equivalent electric circuit (see Figure 1). This figure of Merit is measured at low signal
level and it is assumed that it is constant at high level.

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- 5 - EN 50324-3:2002
'
The power, P, supplied to the load resistance R is:
L
2 2
V A
P = M
ij
'
2
R
L
�
A
N = M
ij
�
N
A = electrode area
� = length for longitudinal and transverse length modes, thickness t for
   thickness extensional and thickness shear modes
R' = mechanical or acoustical load resistance
L
C = clamped capacitance of the sample
o
i = motional current
m
V = applied voltage
N = electromechanical transformer ratio
Figure 1 - Equivalent circuit of a purely capacitative
piezoelectric element at the series resonance
Table 1 lists the electromechanical coupling coefficients kij and the Mij corresponding to the
main resonant modes.
Table 1 - Figures of Merit for the main modes of vibration of piezoelectric elements
Mode
k M
ij ij
2 -4
C m
2
Parallel expander bar
k E
33
()d / s
33 33
2
Transverse expander bar
k E
31
()d / s
31 11
2
Thickness extensional plate
k e
t
33
2
Thickness shear plate
k
15
e
15
NOTE  The piezoelectric, dielectric and elastic coefficients depend on the electric field and on the uniaxial
stress.
So the k and M values should be determined under high power conditions in order to take into account the
ij ij
non-linearities of these coefficients. However, to a first approximation the low signal values may be used.

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EN 50324-3:2002 - 6 -
2.2.2 Methodology for the composition selection
The power radiated in a medium with specific acoustic impedance Z is:
a
2 2 2 2
P = 4 π R (Z ) A f u
a
e
where
R (Z ) is the real part of Z , u is the RMS mechanical displacement, f the frequency and A
e a a
the radiating area.
The losses of the transducer depend on the dielectric, mechanical and piezoelectric non-
linear coefficients. When the device is at the resonance frequency, for a low quality Q factor
the mechanical displacement u is low, for a high electric field. Therefore, the dielectric losses
will be a limiting factor in this case. When the device has a high Q, factor the mechanical
displacement u will be very high at the resonance frequency and the mechanical losses will
be a limiting factor.
In all cases, it is necessary to use the mechanical Q factor of the device, not of the material.
Because the power losses of the device also depend on the frequency, both factors, device
Q factor and frequency, modify the composition selection.
2.2.2.1 Materials for very low frequency transducers or low Q factor (high E)
�
At frequencies lower than 10 kHz or Q < 50, the velocity u = 2πfu is very small and the
mechanical losses are not a limiting factor.
The acoustic load reflected at the "material – medium" interface can be very high as well as
the applied electric field is high in order to maintain a high mechanical displacement. In such
transducers, the dielectric losses are the limiting factor. Type 300 materials are required with
a low large signal dielectric loss tangent:
tan δ ≤ 0,01 at E = 400 kV/m
d
2.2.2.2 Materials for medium frequency transducers or medium Q factor
In such transducers, the working conditions of the piezoelectric materials are the most
severe. Both the dielectric and mechanical losses are limiting factors. Type 300 materials
are required with reduced large signal mechanical and dielectric loss tangents:
tan δ   ≤ 0,01  at E = 400 kV/m
d
4
tan δ ≤ 0,0015 and α ≤ 8 10  (see definition of α and tan δ in 3.2.2)
0m 0m
2.2.2.3 Materials for high frequency transducers or high Q factor (high u)
At frequencies higher than 50 kHz or Q < 500, a high power per unit area is delivered due to
the high velocities. The limiting factor is the mechanical losses. Type 300 materials may be
used but type 100 materials can also be used because of their higher electromechanical
activity.

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- 7 - EN 50324-3:2002
2.2.2.4 Materials for pulsed transducers
These transducers work with high pulsed voltages at a very low duty cycle. As a
consequence, the losses are not important, and the material dielectric breakdown strength is
the limiting factor. Type 100 materials with high piezoelectric coefficients, may be used as
well as some type 200 materials.
2.3 Materials for mechanoelectrical conversion
2.3.1 Figure of Merit
The figure of Merit characterizes the ability of the material to convert the mechanical energy
into electrical energy. Figure 2 shows the mechanoelectrical energy cycle for a piezoceramic
used in a gas fire igniter. During the spark, the strain of the material rapidly changes at
constant stress (A-M). The electrical power delivered per unit volume may be expressed as
follows:
1
2
W = M T
E
m
2
where
M = d.g is the figure of Merit for mechanoelectrical conversion.
T = stress during the spark
m
Area OAM = W
d
1
E D 2
W = (s - s ) T
d 33 33 m
2
E D 2 E
s - s = k s = d g
33 33 33 33 33 33
Figure 2 - Strain-stress diagram for mechanoelectrical energy conversion
(longitudinal stress along direction 3)
2.3.2 Methodology for the composition selection
For spark transducers, M = d.g must be large up to the maximum stress reached during the
conversion. Application of repetitive and high level stresses must not lead to depolarization.
Modified materials of group 100 may be used in quasi-static compression type generators
and modified materials of group 200 may be used in dynamic compression type generators.
3 Boundary conditions and methods of measurement for the large signal
parameters of piezoceramic materials and components
Non-linear behaviour in ferroelectric materials arises from the influence of the mechanical
and electrical stresses on domains. The limits on linear behaviour vary for the different
ceramic compositions, and are related to the coercive force.
Non-linearities of displacement with respect to applied field (D = f(E), S = f(T)) give rise to
dissipation, lower the efficiencies and generate heat.

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EN 50324-3:2002 - 8 -
The non-linearities between fields (E = f(T)), or displacements (D = f(S)), or crossed field and
displacements (D = f (T), S = f(E)), produce harmonic distortion.
3.1 Dielectric large signal properties - Methods of measurement
The dissipated power per unit volume due to the dielectric losses is given by the following
relation
2
T
P = ωE ε tan δ
D 3 33 d
The dielec
...