IEC 62458:2010

IEC 62458 ®
Edition 1.0 2010-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Sound system equipment – Electroacoustical transducers – Measurement of
large signal parameters
Équipements pour systèmes électroacoustiques – Transducteurs
électroacoustiques – Mesurage des paramètres de signaux forts

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IEC 62458 ®
Edition 1.0 2010-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Sound system equipment – Electroacoustical transducers – Measurement of

large signal parameters
Équipements pour systèmes électroacoustiques – Transducteurs

électroacoustiques – Mesurage des paramètres de signaux forts

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.160.50 ISBN 978-2-8322-1080-3

– 2 – IEC 62458:2010  IEC 2010
CONTENTS
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Test signals . 9
4.1 General . 9
4.2 Large d.c. signal . 9
4.3 Large d.c. signal and small a.c. signal . 9
4.4 Broadband noise signal . 9
4.5 Music . 9
5 Mounting condition . 10
5.1 Drive units . 10
5.2 Loudspeaker systems . 10
6 Climatic conditions . 10
7 Acoustical environment . 10
8 Preconditioning . 10
9 Time-varying properties of the loudspeaker . 11
10 Methods of measurement . 11
10.1 General . 11
10.2 Static or quasi-static method . 11
10.3 Point-by-point dynamic method . 12
10.4 Full dynamic method . 14
11 Nonlinear force factor . 15
11.1 Force factor curve Bl(x) . 15
11.2 Force-factor limited displacement, X . 16
Bl
11.3 Symmetry point, x (x ) . 17
sym ac
11.4 Voice coil offset, x . 18
offset
12 Nonlinear stiffness . 18
12.1 Nonlinear stiffness curve K (x) . 18
ms
12.2 Compliance-limited displacement xC . 19
12.3 Stiffness asymmetry A (x ) . 19
K peak
13 Displacement-dependent inductance, L (x) . 20
e
13.1 Inductance curve L (x) . 20
e
13.2 Inductance-limited displacement, x . 21
L
14 Current -dependent inductance, L (i) . 21
e
14.1 Characteristic to be specified . 21
14.2 Method of measurement . 21
15 Parameters derived from geometry and performance . 22
15.1 Maximal peak displacement, x . 22
MAXd
15.2 Method of measurement . 22

Figure 1 – Electro-dynamical transducer . 7
Figure 2 –Static and quasi-static measurement setup . 12
Figure 3 – Setup for measurement of large signal parameters by using the point-by-
point dynamic method . 13
Figure 4 – Setup for dynamic measurement of large signal parameters . 14

Figure 5 – Reading the maximal peak displacement x limited by force factor only . 16
B
Figure 6 – Reading the voice coil offset from the symmetry point x (x ) curve . 17
sym ac
Figure 7 – Definition of the symmetry point x in the nonlinear force factor
sym
characteristic Bl(x) . 18
Figure 8 – Reading the stiffness asymmetry from the K (x) curve. 20
ms
– 4 – IEC 62458:2010  IEC 2010
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SOUND SYSTEM EQUIPMENT –
ELECTROACOUSTICAL TRANSDUCERS –
MEASUREMENT OF LARGE SIGNAL PARAMETERS

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-
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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.
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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.
International Standard IEC 62458 has been prepared by IEC technical committee 100: Audio,
video and multimedia systems and equipment.
This first edition cancels and replaces IEC/PAS 62458 published in 2006. It constitutes a
technical revision. The main changes are listed below:
– descriptions of the methods of measurement are adjusted to the state of the technology;
– addition of Clauses 4 to 15;
– integration of Annex A in the main body of the standard;
– overall textual review.
The text of this standard is based on the following documents:
FDIS Report on voting
100/1624/FDIS 100/1647/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.
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.
IMPORTANT – The “colour inside” logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this publication using a colour printer.

– 6 – IEC 62458:2010  IEC 2010
INTRODUCTION
Electro-mechanical-acoustical transducers such as loudspeaker drive units, loudspeaker
systems, headphones, micro-speakers, shakers, and other actuators behave in a nonlinear
manner at higher amplitudes. This limits the acoustical output and generates nonlinear signal
distortion. Linear models fail in describing the large signal behaviour of such transducers and
extended models have been developed which consider dominant nonlinearities in the motor
and suspension. The free parameters of the large signal model have to be measured on the
particular transducer by using static or dynamic methods. The large signal parameters show
the physical cause of the signal distortion directly and are very important for the objective
assessment of sound quality and failure diagnostics in development and manufacturing.
Furthermore, the model and parameters identified for a particular transducer are the basis for
predicting the maximum output and signal distortion for any input signal. The close
relationship between causes and symptoms simplifies the interpretation of the harmonic and
intermodulation distortion measured according to IEC 60268-5. Large signal parameters are
valuable input data for the synthesis of loudspeaker systems and the development of
electrical control systems dedicated to loudspeakers.

SOUND SYSTEM EQUIPMENT –
ELECTROACOUSTICAL TRANSDUCERS –
MEASUREMENT OF LARGE SIGNAL PARAMETERS

1 Scope
This International Standard applies to transducers such as loudspeaker drive units,
loudspeaker systems, headphones, micro-speakers, shakers and other actuators using either
an electro-dynamical or electro-magnetic motor coupled with a mechanical suspension. The
large signal behaviour of the transducer is modelled by a lumped parameter model
considering dominant nonlinearities such as force factor, stiffness and inductance as shown in
Figure 1. The standard defines the basic terms and parameters of the model, the methods of
measurements and the way the results should be reported.
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 60268-1, Sound system equipment – Part 1: General
IEC 60268-5:2003, Sound system equipment – Part 5: Loudspeakers
Amendment 1 (2007)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
electro-mechanical equivalent circuit
electrical circuit of an electro-dynamical transducer, as shown in Figure 1
L (x, i )
2 3
i
R (T ) L (x, i)
F C (x) M R
e V e m ms
ms ms
v
i
i
R (x, i )
2 2
Z
load
u Bl(x) v Bl(x) Bl(x) i
IEC  2511/09
NOTE 1 This Figure shows an example of a lumped parameter model of an electro-dynamical transducer
considering the dominant nonlinearities.
NOTE 2 Other equivalent circuits can be applied. Contrary to the results of linear modelling some parameters of
the lumped elements are not constant but depend on instantaneous state variables (such as displacement x,
velocity v, current i).
Figure 1 – Electro-dynamical transducer

– 8 – IEC 62458:2010  IEC 2010
3.2
input current and voltage
i, u
electrical state variables at the terminals of the transducer
3.3 displacement
x
deflection of the voice coil from the rest position
3.4
velocity
v
time derivative of displacement x
3.5
d.c. resistance
R
e
electrical impedance Z (s) at very low frequencies where the effect of the back EMF can be
e
neglected
NOTE 1 Electrical impedance can be used for measuring the d.c. resistance R of the voice coil. The d.c.
e
resistance R depends on the mean voice coil temperature T
e V.
3.6
nonlinear inductance and losses
nonlinear elements to model the effect of the magnetic a.c. field, the losses in the magnetic
material, and the losses caused by eddy currents where the equivalent circuit in Figure 1 uses
the LR-2 model comprising the inductance L (x, i), the inductance L (x, i ) and additional
e 2 2
resistance R (x, i )
2 3
3.7
nonlinear force factor
Bl(x)
dependency of instantaneous force factor Bl(x) on voice coil displacement x defined by the
integral of magnetic flux density B versus the voice-coil conductor of length l
NOTE 1 The product of force factor Bl(x) and velocity v is the back EMF generated on the electrical side in an
equivalent circuit as shown in Figure 1. The product of force factor Bl(x) and input current i gives the electro-
dynamical driving force of the mechanical system.
3.8
reluctance force
F
m
additional electro-magnetic driving force caused by the displacement varying inductances
L (x, i) and L (x, i )
e 2 2
3.9
stiffness, K (x), of the suspension
ms
ratio between the instantaneous restoring force F(x) and the displacement x as given by
F(x)
K (x)= (1)
ms
x
NOTE 1 The nonlinear compliance C (x) = 1/K (x) is the reciprocal quantity of the mechanical stiffness.
ms ms
3.10
mechanical mass
M
ms
total moving mass including the mass of the moving assembly and the reactive part of the air
load on both sides of the diaphragm
3.11
mechanical resistance
R
ms
non-electrical losses of the driver, due to suspension, turbulences and radiation
3.12
mechanical impedance
Z
load
mechanical impedance which may represent any additional load caused by mechanical
elements (cone, panel) or acoustical elements (such as a vented enclosure or horn)
4 Test signals
4.1 General
The measurement of the large signal parameters requires an electrical, mechanical or
acoustical stimulus. Depending on the method used for the measurement of the large signal
parameters different kind of test signals are used as stimulus for the excitation of the
transducer. Since the loudspeaker behaves as a time-varying system the stimulus may cause
a permanent or temporary change of the loudspeaker properties. Thus, the properties of the
stimulus (spectral bandwidth, crest factor, proability density function) shall be statet. The
same stimulus should be used if the numerical values of the results should be compared from
two measurements.
4.2 Large d.c. signal
A constant d.c. voltage or d.c current of defined magnitude and sufficient duration is supplied
to the electrical terminals to measure the steady-state response of the transducer. If the
transducer is mounted in a sealed enclosure a difference between the static air pressures
inside and outside the enclosure may be used as d.c. stimulus.
4.3 Large d.c. signal and small a.c. signal
A constant d.c. signal of defined magnitude and sufficient duration (see 4.2) superimposed
with a small a.c. signal is used as stimulus. The a.c. signal (such as noise, sinusoidal sweep,
impulsive test signals) should have sufficient bandwidth to identify all parameters of the
loudspeaker model.
4.4 Broadband noise signal
One of the noise signals defined in IEC 60268-1 or any other noise having sufficient
bandwidth and amplitude may be used as stimulus. The crest factor of the noise should be
less than 4 to reduce clipping in the amplifier.
4.5 Music
Ordinary music, speech of sufficient bandwidth and amplitude may be used as a stimulus.
NOTE The dynamic methods need a stimulus which provides persistent excitation of the loudspeaker to identify
the parameters correctly. The stimulus should have enough spectral components at least one octave below
resonance frequency f and one decade above f .
s s
– 10 – IEC 62458:2010  IEC 2010
5 Mounting condition
5.1 Drive units
The driver unit may be mounted
a) in free air without a baffle or enclosure,
b) in a standard baffle according to 11.1 of IEC 60268-5,
c) in half-space free field according to 5.2 of IEC 60268-5,
d) in the standard measuring enclosure (type A or type B) according to 11.2 of
IEC 60268-5, or another, specified enclosure,
e) in vacuum,
f) other configuration defined in the presentation of the results.
The acoustic loading depends upon the mounting arrangement, which shall be clearly
described in the presentation of the results.
During the measurement the transducer should be firmly clamped to suppress additional
mechanical resonances close to the resonance frequency f . A vertical position of the
s
transducer (cone displacement in horizontal direction) is recommended to avoid any bias due
the weight of the moving assembly.
Drive units for horn loaded loudspeakers, headphones, micro-speakers and microphones
should preferably be measured in a vacuum to reduce the acoustic load, suppress additional
acoustic resonances, and to avoid nonlinear damping due to turbulent air flow.
5.2 Loudspeaker systems
Loudspeaker systems are measured under conditions which correspond with the intended use.
6 Climatic conditions
The measurements should be made at an ambient temperature 15°C to 35°C, preferably at
20°C, relative humidity 25 % to 75 %, air pressure 86 kPa to 106 kPa as specified in
IEC 60268-1 to avoid any influence of temperature and humidity that may affect the properties
of the drive unit suspensions.
7 Acoustical environment
The measurement room shall be large enough that the influence of the acoustical environment
on the mechanical vibration of the transducer is negligible.
If the measurement of the large signal parameters is based on sound pressure output it is
recommended to place the measuring microphone in the near field of the transducer. It is
recommended to use a method that measures electrical or mechanical signals only, which is
thus immune to unwanted acoustic noise.
8 Preconditioning
The loudspeaker should be preconditioned according to Clause 12 of IEC 60268-5. A
temporary voice coil offset caused by storing the transducer for some time in the horizontal
position can be removed by operating the transducer for at least 5 min in the vertical position
before performing the regular measurement.

9 Time-varying properties of the loudspeaker
The stimulus provided to the electrical input of the loudspeaker may cause a heating of the
voice coil and may also change the properties of the suspension during measurement. Thus,
the electrical resistance of the coil should be measured during measurement and considered
in the calculation of the loudspeaker parameters (e.g. electrical loss factor Q ).
es
10 Methods of measurement
10.1 General
The following methods may be used for the measurement of the large signal parameters. The
method used should be stated together with the results.
10.2 Static or quasi-static method
10.2.1 General
This technique determines the non-linear parameters of the transducer by using a d.c. signal
with magnitude u (usually voltage) as stimulus. After reaching steady state relevant state
i
variables (d.c. displacement x , d.c. force F ) are measured and the parameter value (such as
i i
K(x ) = F /x ) is calculated. After changing the magnitude of the d.c. signal the measurement is
i i i
repeated at further working points x with i = 1, …, N to measure the non-linear parameters
i
within the working range –x < x < x with sufficient resolution.
peak i peak
Due to the visco-elastic behaviour of the suspension material, the settling time required to
reach steady state may exceed several seconds and a static method is very time consuming.
In a quasi-static method the state variables are measured before steady state is reached and
the settling time used should be stated.
Creep and other visco-elastic properties of the suspension cause significant discrepancies
between the stiffness K(x) measured statically by using a d.c. signal and the stiffness K (x)
ms
measured dynamically by using an broadband noise signal.
The d.c. signal of the static and quasi-static methods cannot be used for the measurement of
the nonlinear voice coil inductance L (x, i). Figure 2 shows a setup for static and quasi-static
e
measurement of large signal parameters.

– 12 – IEC 62458:2010  IEC 2010
Transducer Sensor
DC signal
generator
u
i
Parameter Measured
signal
calculation
Input
signal
Parameter value
at working point u
i
Selection of working
point
Large signal
parameters
IEC  2512/09
Figure 2 –Static and quasi-static measurement setup
10.2.2 Procedure
Proceed as follows.
a) According to the limits of working range –x < x < x investigated and the resolution
peak i peak
required, the number of measurements N is determined, a starting voltage u is
start
selected and the incremental voltage u is defined.
step
b) The first working point i = 1 is initialized.
c) The transducer is excited by a d.c. signal voltage u = u + i u .
×
start step
i
d) At the working point, i, the displacement, x , and other relevant state variables (such as
i
force F ) are measured after the transducer has reached steady state or a defined settling
i
time T has passed.
e) The nonlinear parameter (for example, K(x ) = F /x ) is calculated.
i i i
f) The next working point i = i + 1 is selected and previous steps 1 to 5 are repeated until
i > N.
g) The parameter values are interpolated between the working points x with i = 1, …, N or
i
the coefficients of the power series expansion (such as Equation (3)) are calculated.
10.3 Point-by-point dynamic method
10.3.1 General
This technique determines the non-linear parameters of the transducer with a d.c. signal, u
i
(such as d.c. voltage or a constant air pressure), superimposed with a small a.c. signal, u ,
ac
as stimulus. After reaching the steady state, the relevant state variables (d.c. displacement x
i
and the amplitudes of the a.c. force F and a.c. displacement x ) are measured and the
ac ac
parameter value (such as the incremental stiffness K (x ) = F /x ) is calculated. After
inc i ac ac
changing the magnitude of the d.c. part of the stimulus the measurement is repeated at
further working points x with i = 1, …, N, to measure the non-linear parameters within the
i
working range –x < x < x with sufficient resolution.
peak i peak
The amplitude u of the a.c. stimulus is sufficiently small to ensure that the transducer
ac
behaves linearly (K(x + x ) ≈ constant, Bl(x + x ) ≈ constant and L (x + x ) ≈ constant)
i ac i ac e i ac
and a linear loudspeaker model can be applied.
Whereas some small signal parameters (force factor Bl(x ) and inductance L (x )) are identical
i i
e
to the large signal parameters measured by other methods, this technique provides the
incremental stiffness, K (x ), which can only be transformed into the regular stiffness by
inc i
integration
x
K(x)= K (x)dx (2)
inc
∫
x
Due to the visco-elastic behaviour of the suspension material, there are significant differences
between the stiffness K(x) measured by the point-by-point method using a d.c. signal and the
stiffness Kms(x) measured dynamically with a program like an a.c. signal. Figure 3 shows a
setup for point-by-point dynamic measurement of large signal parameters.
10.3.2 Test equipment
The stimulus comprising a d.c part and an a.c. part can be produced by using a generator
with a d.c. offset and a d.c.-coupled power amplifier. However, providing the d.c. part via the
electrical input produces significant heating of the voice coil at high amplitudes. Alternatively,
the transducer may be mounted in a sealed box, and the voice coil position may be varied by
changing the d.c. air pressure inside the box.
AC signal
Measured
generator
signal
u
ac
Transducer Sensor
Error
i (t)
signal
u (t)
e (t)
i′ (t)
Optimal
u Linear
i
DC signal
parameter
model
generator
Estimated
Input fitting
signal
signal
Smal signal parameters
at working point u
i
Selection of working
point
Large signal
parameters
IEC  2513/09
Figure 3 – Setup for measurement of large signal parameters
by using the point-by-point dynamic method

– 14 – IEC 62458:2010  IEC 2010
10.3.3 Procedure
According to the limits of working range –x < x < x investigated and the resolution
peak i peak
required, the number of measurements N, starting voltage u and incremental voltage u
start step
is defined. The first working point i = 1 is selected.
Proceed as follows.
a) The transducer is excited by a stimulus u + u = u + i × u + u .
i ac start step ac
b) At working point, i, the d.c. displacement, x , and a.c. state variables (such as a.c force
i
F and a.c. displacement x ) are measured after the transducer has reached steady
ac ac
state or a defined settling time T has passed.
c) The small signal parameters (such as K (x ) = F /x ) are calculated at the particular
inc i ac ac
working point x by using a linear model which is optimally fitted to the measured signal.
i
d) The next working point i = i + 1 is selected and steps 1 to 5 are repeated until i > N.
e) The parameter values are interpolated between the working points x with i = 1, …, N or
i
the coefficients of the power series expansion (such as Equation (3)) are calculated.
10.4 Full dynamic method
10.4.1 General
The full dynamic method uses an a.c. stimulus of sufficient amplitude and bandwidth such as
music or an audio-like signal (noise). Usually, there is no d.c. component in the stimulus.
Measured state variables (voltage, current, displacement) are the basis for the identification
of free parameters of the non-linear model (such as the lumped model in Figure 1). Based on
identified state variables (such as voice coil temperature) and transducer nonlinearities
(stiffness K ) the amplitude of the stimulus is adjusted automatically to operate the
ms
transducer at maximal amplitudes –x < x < x safely and to avoid any damage of the
peak peak
i
transducer. Figure 4 shows the setup for dynamic measurement of large signal parameters.

Measured
signal
Gain
Transducer Sensor
Power
control
Error
i (t)
amplifier
signal
AC signal
u (t)
generator
e (t)
i′ (t)
Optimal
Nonlinear
parameter
model
Estimated
Input
fitting
signal
signal
Selection of working
range
Large signal
parameters
IEC  2514/09
Figure 4 – Setup for dynamic measurement of large signal parameters

10.4.2 Requirements
A signal source is required providing an audio-like signal which is provided via a power
amplifier to the loudspeaker terminals. A sensor is required to monitor at least one state
variable (such as current) of the loudspeaker. A signal processing system is required to model
the relationship between input signal (such as voltage) and monitored state variable (such as
current) and to calculate the optimal parameters by using a fitting technique.
10.4.3 Procedure
Proceed as follows.
a) A broadband noise signal of small amplitude is supplied via a power amplifier to the
terminals of the speaker (voltage supply).
b) The electrical input current i at the terminals or other state signals (displacement or sound
pressure) is measured using a mechanical or acoustical sensor.
c) The input current i’(t) is predicted using the nonlinear transducer model (such as lumped
model in Figure 1). The error signal e(t) = i(t) – i’(t) is calculated and the free parameters
are estimated by minimizing the error signal e(t).
d) The displacement limits x and x are derived from Equations (4) and (7). The increase of
Bl C
the voice coil temperature ∆T is estimated by monitoring the d.c. resistance R of the coil.
e
V
exceeds
e) The amplitude of the stimulus is increased until the peak displacement x
peak
either the force factor limited displacement, x or the compliance limited displacement, x
Bl,
C
or the increase of the voice coil temperature ∆T exceeds the permissible limits.
V
f) Adequacy of the modeling and optimal parameter fitting shall be checked by calculating
the mean squared error between measured and modeled response (such as current,
velocity, displacement).
11 Nonlinear force factor
11.1 Force factor curve Bl(x)
11.1.1 Characteristic to be specified
The non-linear force factor, Bl(x), is preferably reported as a graphical representation showing
the parameter as a function of displacement, x, within the measured range –x < x < x
peak peak
Positive displacement, x, corresponds to a deflection of the coil away from the back-plate. It is
recommended that the displacement axis is labelled with verbal comments to support the
orientation of the coil-in and coil-out position.
11.1.2 Method of measurement
11.1.2.1 General
The force factor characteristic may be measured by the static, point-by-point dynamic or the
full dynamic method as defined in Clause 10. The method used shall be reported.
11.1.2.2 Coefficients of force factor expansion
The coefficients b with j = 0, 1, …, N in the power series expansion of the force factor curve
j
N
j
Bl(x)= b x (3)
j
∑
j=0
shall be reported with peak displacement x describing the limits of the fitting range
peak
−x < x < x .
peak peak
– 16 – IEC 62458:2010  IEC 2010
11.2 Force-factor limited displacement, X
Bl
11.2.1 Characteristic to be specified
The decrease of the Bl-value caused by a movement of the coil away from the rest position
x = 0 limits the maximal peak displacement. The force-factor limited peak displacement x is
Bl
implicitly defined by the condition that the minimal force factor ratio
 
Bl(x)
  100 % = Bl (4)
min min
 
Bl(0)
−x < x< x
 
Bl Bl
equals a defined threshold Bl .
min
It is recommended to use a threshold of Bl = 82 % which corresponds with 10 %
min
modulation distortion according to Clause 24 of IEC 60268-5 for a two-tone signal comprising
a tone at resonance frequency f = f and a second tone at f = 8,5 f .
s s
1 2
The peak value x shall be reported with the minimal force factor ratio, Bl used, for
min
B
example:
x = 3 mm with Bl = 82 %
min
Bl
11.2.2 Method of measurement
The nonlinear force factor curve shall be measured according to 11.1.2.
The value Bl(x = 0) at the rest position is determined and this value is multiplied by the
threshold of the minimal force factor ratio (such as Bl = 82 %).
min
The smallest displacement x for which Bl(x ) = Bl(x = 0)*Bl gives x . See Figure 5.
min
Bl Bl
Bl(x = 0)
Bl
Bl (x = 82 %)
min
N/A
Bl(x )
B
x
B
0,0
–x
peak +x
peak
0,0
x
<< coil in mm coil out >>
IEC  2515/09
Figure 5 – Reading the maximal peak displacement x limited by force factor only
B
11.3 Symmetry point, x (x )
sym ac
11.3.1 Characteristic to be specified
The symmetry point in the Bl-curve describes the centre point between two points on the Bl-
curve producing the same Bl-value
Bl(x (x ) − x ) = Bl(x (x ) + x ) (5)
sym ac ac sym ac ac
which are separated by 2 x . The dependency of the symmetry point x (x ) versus
ac sym ac
displacement x shall be reported as a curve as shown in Figure 6.
ac
[mm]
Reset position
x
offset
x
sym
0,0 x
ac
[mm]
IEC  2516/09
Figure 6 – Reading the voice coil offset from the symmetry point x (x ) curve
sym ac
– 18 – IEC 62458:2010  IEC 2010
11.3.2 Method of measurement
As illustrated in Figure 7, a Bl-value is selected which is smaller than Bl and the
max
corresponding displacement values x and x are read on both sides of the Bl maximum giving
1 2
Bl(x ) = Bl(x ). The symmetry point x = (x + x )/2 and the displacement x = |x – x |/2
1 2 sym 1 2 ac 2 1
are calculated. The procedure is repeated for smaller Bl-values.
Bl
max
x x
ac ac
Bl
N/A
x
sym
0,0
x x
1 2
–x
peak +x
peak
0,0
x
<< coil in mm coil out >>
IEC  2517/09
Figure 7 – Definition of the symmetry point x in the nonlinear
sym
force factor characteristic Bl(x)

11.4 Voice coil offset, x
offset
The voice coil offset x is the symmetry point x (x ) for a high value of x (x > x ) to
offset sym ac ac ac Bl
assess the symmetry at the steep slopes of the Bl-curve. The voice coil offset x is
offset
reported together with the amplitude x , for example:
ac
x = 0,4 mm at x = 5,2 mm
offset ac
NOTE If the symmetry point varies significantly with the displacement (x (x ) ≠ constant), the asymmetry of
sym ac
the Bl-curve is caused by the magnetic field geometry and cannot be compensated by a coil shift.
12 Nonlinear stiffness
12.1 Nonlinear stiffness curve K (x)
ms
12.1.1 Characteristic to be specified
The non-linearity of the suspension is preferably reported as a graphical representation of the
stiffness showing the parameter K (x) as a function of displacement, x, within the measured
ms
range –x < x < x as shown in Figure 8. Positive displacement, x, corresponds to a
peak peak
deflection of the coil away from the back-plate. It is recommended that the displacement axis
be labeled with verbal comments to support the orientation of the coil-in and coil-out position.

NOTE The graphical representation of the nonlinear compliance C (x) which is the reciprocal of the nonlinear
ms
stiffness K (x) makes the interpretation of nonlinearity more difficult at higher displacements, where the impact of
ms
the nonlinearity on the restoring force is dominant.
12.1.2 Method of measurement
12.1.2.1 General
The stiffness characteristic shall preferably be measured by using the full dynamic method as
defined in Clause 10, because it describes the behavior of the suspension for an audio-like
stimulus best. The d.c. component in the stimulus used in static, quasi-static and point-by-
point dynamic techniques causes significant differences in the measured stiffness due to
visco-elastic behavior.
12.1.2.2 Coefficients of stiffness expansion
The coefficients k with j = 0, 1, …, N in the power series expansion of the stiffness curve
i
defined by
N
j
K (x)= k x (6)
ms ∑ j
j=0
shall be reported together with peak displacement x describing the limits of the fitting
peak
range –x < x < x .
peak peak
12.2 Compliance-limited displacement xC
12.2.1 Characteristic to be specified
-value of the suspension caused by a movement of the
The decrease of the compliance C
MS
coil away from the rest position x = 0 limits the maximal peak displacement. The compliance
limited displacement x is implicitly defined by the condition that the minimal compliance ratio
C
 
C (x)
MS
 
100 % = C (7)
min
min
 
C (0)
−x < x< x
MS
C C 
equals a defined threshold C .
min
It is recommended to use a threshold of C = 75 % which corresponds with 10 % harmonic
min
distortion for a sinusoidal excitation tone at resonance frequency f . The limit used shall be
s
reported with the displacement x , for example:
C
x = 2 mm at C = 75 %
C min
12.2.2 Method of measurement
The nonlinear stiffness curve is measured according to 12.1. The c
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