Saku Levikari
DETECTION OF CRACKS - ACOUSTIC EXPERIMENTS
ON MULTILAYER CERAMIC CAPACITORS
Master’s thesis
LUT School of Energy Systems
Electrical Engineering June 28, 2018
Abstract
Lappeenranta University of Technology
LUT School of Energy Systems
Electricl engineering
Saku Levikari
Detection of Cracks - Acoustic Experiments
on Multilayer Ceramic Capacitors
2016
Master’s thesis
48 pages
Examiners: Prof. Pertti Silventoinen and Dr. Tommi Ka¨rkka¨inen
In this thesis, it is shown that damaged Multilayer Ceramic Capacitors (MLCCs)
can be acoustically identified in a non-destructive manner. This is done by utilizing
the piezoelectric behavior of the ceramic dielectric, which causes the capacitor to
physically deform when voltage is applied. An acoustic response is obtained by driv-
ing an MLCC with pulse wave sweep over a wide frequency range, and measuring
mechanical vibrations directly from the capacitor using a piezoelectric point contact
sensor. Structural damage in the MLCC causes characteristic changes in the acous-
tic response, which can be algorithmically detected. An algorithm is introduced, in
which an acoustic envelope is obtained from an MLCC and compared with a statis-
tical reference envelope obtained from a sample of intact MLCCs. The results show
that a damaged MLCC can be identified based on its acoustic emission.
Tiivistelma¨
Lappeenranta University of Technology
LUT School of Energy Systems
Electricl engineering
Saku Levikari
Detection of Cracks - Acoustic Experiments
on Multilayer Ceramic Capacitors
2016
Diplomityo¨
48 sivua
Tarkastajat: Prof. Pertti Silventoinen ja TkT Tommi Ka¨rkka¨inen
Ta¨ssa¨ tyo¨ssa¨ osoitetaan, etta¨ vialliset monikerroksiset keraamiset kondensaattorit
(Multilayer Ceramic Capacitor, MLCC) voidaan tunnistaa akustisesti kondensaat-
toria vahingoittamatta. Ta¨ma¨ tapahtuu hyo¨dynta¨ma¨lla¨ kondensaattorin keraamisen
va¨liaineen pietsosa¨hko¨isyytta¨, joka aiheuttaa kondensaattorin rungon deformoitu-
misen kun ja¨nnite kytketa¨a¨n komponentin yli. Kondensaattorista mitataan akusti-
nen vaste syo¨tta¨ma¨lla¨ komponenttiin pulssimuotoista ja¨nnitetta¨. Ja¨nnitteen taa-
juutta nostetaan lineaarisesti laajan taajuusalueen yli, mitaten samalla konden-
saattorin rungon mekaanisia va¨ra¨htelyja¨ pietsosa¨hko¨isella¨ pintakontaktianturilla.
Kondensaattorissa olevat mekaaniset vauriot aiheuttavat komponentin akustiseen
vasteeseen muutoksia, jotka voidaan havaita tarkoitukseen kehitetylla¨ algortmilla.
Tyo¨ssa¨ esitella¨a¨n algoritmi, joka laskee kondensaattorin akustisesta vasteesta ver-
hoka¨yta¨n, ja vertaa sita¨ ehjien kondensaattorien vasteista muodostettuun refer-
enssiverhoka¨yra¨a¨n. Tulokset osoittavat, etta¨ vikaantunut kondensaattori voidaan
tunnistaa akustisien emissioiden perusteella.
Acknowledgements
This study was carried out in the Laboratory of Applied Electronics at Lappeenranta
University of Technology, Finland, between 2016 and 2017. The research was made
in close collaboration with ABB Drives, Helsinki, and ABB Corporate Research,
Switzerland.
I would like to express my gratitude to my supervisors Prof. Pertti Silventoinen
and Dr. Tommi J. Ka¨rkka¨inen at LUT for providing guidance throughout the
making of this thesis. I would also like to offer my special thanks for my supervisor
Dr. Caroline Andersson at ABB Corporate Research, Switzerland, for her valuable
technical advice and comments.
Special thanks goes to Kjell Ingmann, Juha Tamminen and Martti Mattila at ABB
Drives Helsinki for their technical advisory during this project.
Furthermore, I would like to thank Assoc. Prof. Mikko Kuisma and everyone at
6405 for providing technical, theoretical and comical insight throughout the making
of this thesis.
I wish to thank my family and friends for their support through this project.
Finally, I would like to thank my dear wife, Milla, for everything.
Saku Levikari
June 2018
Lappeenranta, Finland
Contents
Abstract
Tiivistelma¨
Acknowledgments
Contents
Nomenclature 7
1 Introduction 9
1.1 Goal of this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Research questions and contributions . . . . . . . . . . . . . . . . . . 12
2 Physics of multilayer ceramic capacitors 13
2.1 Dynamics of MLCCs . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Piezoelectric behaviour of MLCCs . . . . . . . . . . . . . . . . 13
2.2 Acoustic emissions from PCB . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Mechanical force transfer . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Vibrational dynamics of Printed Circuit Boards . . . . . . . . 16
3 Experiments 17
3.1 Measuring Acoustic Emissions from MLCCs . . . . . . . . . . . . . . 17
3.2 Instrumentation and equipment . . . . . . . . . . . . . . . . . . . . . 17
3.3 MLCC measurement procedure . . . . . . . . . . . . . . . . . . . . . 19
3.4 Test board setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Analysis methods for the acoustic data . . . . . . . . . . . . . . . . . 24
3.5.1 Observation model for the envelope signal . . . . . . . . . . . 25
3.5.2 Analysis methods . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Results 28
4.1 Acoustic emission characteristics of damaged MLCCs . . . . . . . . . 28
4.2 Statistical analysis of MLCCs before and after bending . . . . . . . . 29
4.2.1 1206-case MLCCs . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.2 1210-case MLCCs . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.3 1812-case capacitors . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.4 2220-case capacitors . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Comparison of observed acoustic emission amplitudes . . . . . . . . . 38
4.4 Repeatability of the measurements . . . . . . . . . . . . . . . . . . . 39
4.4.1 Error propagation in LGLS-values . . . . . . . . . . . . . . . . 39
4.4.2 Errors in measured voltages and LGLS-values . . . . . . . . . . 40
4.5 Effects of PCB vibrations . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Discussion 42
5.1 Signs of mechanical damage in MLCCs . . . . . . . . . . . . . . . . . 42
5.2 LGLS-values and statistical observations . . . . . . . . . . . . . . . . . 42
5.3 Ability to recognize defects . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4 Consistence of measurements . . . . . . . . . . . . . . . . . . . . . . . 43
6 Conclusions 45
References 46
7Nomenclature
Latin alphabet
A Area
a Length of a plate
b Width of a plate
C Capacitance
D Duty cycle
D Flexural rigidity
dpk Piezoelectric constant tensor
~E Electric field
E Electric field strength
F Force, temporal component of deflection field of a plate
f Frequency
H(·) Hilbert transform
H Observation matrix
h Half-thickness of a plate
LGLS Difference value of two curves, one GLS-fitted into another
N Number of observations
NDS Downsampling factor
~P Polarization field
P polarization
Q Total electric charge
q Electric charge
S, Sij Strain
S Surface
sEpq Electric compliance tensor
Tq Stress
U Voltage
v Error vector
W Weighting matrix
w Deflection field of a plate
Wx1,x2 Spatial component of deflection field of a plate
Greek alphabet
 dielectric constant
γE Young’s modulus
ν Poisson’s ratio
ω Angular frequency
ωmn Resonance frequencies of a plate
σ Surface charge density
8θ Observation model parameter for LS-fitting
Subscripts
DS Downsampling
GLS Generalized Least Squares
i, j, p, q Tensor components
x1, x2 Location on a plate surface
Abbreviations
AC Alternating Current
BaTiO3 Barium Titanate
DC Direct Current
FFT Fast Fourier Transform
lpf Low-pass filter
MLCC Multilayer Ceramic Capacitor
Std Standard deviation
TiO3 Titanium Oxide
91 Introduction
Multilayer Ceramic Capacitors (MLCCs) are widely used in industry because of their
high capacitance per volume and favorable electrical characteristics (Ko et al., 2014).
Approximately 80% of all currently manufactured capacitors are chip-type MLCCs
(TDK Corporation, 2016). MLCCs are, however, prone to mechanical damage and
subsequent failure because of fragility of the ceramic dielectric. Typical mechanical
defects in MLCCs include cracks, voids and delaminations. Voids typically do not
expand over time, but they may cause cracks and delaminations to expand (Adams,
2014).
Figure 1.1 shows a cross-section of an MLCC with a typical crack within the di-
electric near the end termination, cutting a portion of the inner electrodes. Such a
defect is often caused in the production, or as a result of mishandling or bending of
the Printed Circuit Board (PCB) the MLCC is attached to (Krieger et al., 2006).
Thermal stresses during manufacturing or soldering process are also associated with
the emergence of these defects (Huang et al., 2015). If a defect is sufficiently large,
it may shorten the operational life of the capacitor, lower the capacitance value or
cause the capacitor to short circuit. (Kahn and Checkaneck, 1983). Water getting
inside the MLCC trough a crack may also cause degradation of the ceramic dielec-
tric. The degradation results from electrolysis within the dielectric material when
voltage is applied to the capacitor (Wang et al., 2003).
Dielectric materialInternal electrodesTermination
CrackSolder
Circuit board
Figure 1.1: Structure of a typical Multilayer Ceramic Capacitor with a crack in the
dielectric material cutting a part of the inner electrodes
The aforementioned defects are often not recognized in production, but start af-
fecting the performance of the capacitor in operational use (Kahn and Checkaneck,
1983). Hence, there is a need for detecting such defects before the final product is
sold.
10 1 Introduction
Microsectioning is a commonly used destructive method for detecting and localizing
mechanical defects in MLCCs. Multiple non-destructive methods have also been
developed:
Kahn and Checkaneck (1983) introduced a method in which an MLCC is placed
under a mechanical ram with increasing downward force on the MLCC. Acous-
tic signals emitted by the cracks in the dielectric are counted using a transducer
mounted on the ram. The authors suggested that the method could be used for
statistical screening of a sample of MLCCs taken from a production line.
Acoustic microscopy and opto-acoustic microscopy, i.e. measurement of laser-induced
acoustic emissions, have been studied for defect detection purposes in the form
of scanning laser acoustic microscopy and C-mode scanning acoustic microscopy.
(Commare, 1993)
Bechou et al. (1996) introduced a method for defect detection and localization based
on electromechanical resonances of an MLCC. The method consisted of impedance
analysis of the MLCC under DC bias voltage. The same method was used by
Krieger et al. (2006). This method relies on the piezoelectric deformation of the
MLCC under DC bias voltage. The impedance of the MLCC is analyzed over a
wide frequency range, covering the mechanical resonance frequencies of the MLCC.
Mechanical resonances and possible defects cause peaks in the impedance curve,
from which they can be detected.
Chan et al. (1995) presented a method of defect detection, which is based on laser
speckle pattern analysis. A local short circuit between electrodes in an MLCC causes
the temperature to rise at the location of the defect, leading to thermal deformation.
This deformation can be detected by comparing laser speckle images of the MLCC
under voltage and under no voltage. This method requires a more complicated test
setup than the one presented in this thesis, but according to authors, is suitable
for in situ measurements. This method requires voltage applied to the capacitor.
Erdahl and Ume (2004) demonstrated a method for MLCC quality inspection, in
which the MLCC was excited into vibration using a pulsed laser, and the vibration
was measured using laser interferometry. This method is very similar to the method
presented in this thesis in such way that the physical vibration of the top side of
the MLCC is measured. The laser interferometry is capable of measuring higher
frequencies than other methods, including the one presented in this thesis, but
requires more complicated measurement setup. This method requires no voltage
application to the MLCC.
Krieger et al. (2006) used audio range microphone to obtain acoustic emissions from
an MLCC attached to a PCB. Similar method was tested out in this thesis. Accord-
ing to study by Ko et al. (2014), the audio range frequencies are, however, mainly
result of the vibration of the circuit board. Thus, the audio-range acoustic emissions
are mainly dictated by the properties of the PCB, although the the structural condi-
tion of the capacitor probably also has some contribution to the acoustic emissions
1.1 Goal of this study 11
obtained.
Other non-destructive methods for measuring vibrations and structural condition of
an MLCC are scanning laser Doppler vibrometer (Ko et al., 2014), computer tomog-
raphy using ultrasound, and X-ray imaging. The usability of neutron radiography
has also been studied (Kieran, 1981).
This thesis presents a nondestructive method of characterizing soldered multilayer
ceramic capacitors acoustically. First, an MLCC is subjected to frequency-swept
pulse wave. During the frequency sweep, MLCC generates acoustic emissions, which
are observed using a piezoelectric point contact sensor placed on top of the capacitor.
The acoustic response of the MLCC is then analyzed for anomalies which might
indicate damage in the capacitor. The advantages of the method presented in this
thesis are:
Simplicity
The measurement equipment required for this method only requires a point
contact sensor and an amplifier alongside a signal generator and an oscillo-
scope.
Speed
Measuring one MLCC takes less than a minute. The measurement speed
is limited mainly by manual placement of the point contact sensor and the
oscilloscope’s data transfer rate.
Ability to recognize different types of defects
This method is capable of recognizing mechanical defects in both the dielectric
medium and near the solder joints.
The disadvantages of this method are sensitivity to Electromagnetic Interference
(EMI) and variations in the physical contact between the point contact sensor and
the MLCC. Both of these cause bias when comparing the responses of MLCCs.
Thus far this method is only suitable for offline measurements, because a measured
capacitor has to be driven with sufficiently high voltage.
The acoustic approach presented in this thesis has been a subject for further study. It
has been shown that damage in MLCCs indeed correlates with the acoustic emission
metrics presented in this thesis (Levikari et al., 2018a). A Support Vector Machine
classifier has been succcessfully demonstrated for classification of MLCC acoustic
emissions (Levikari et al., 2017). The acoustic method presented in this thesis has
also been used to construct an open MLCC acoustic data set (Levikari et al., 2018b).
1.1 Goal of this study
The aim of this study is to find a method for detecting defects in multilayer ceramic
capacitors based on acoustic emissions. This study focuses on MLCCs of type II, i.e.
12 1 Introduction
high-permittivity capacitors in which barium titanate (BaTiO3) is typically used as
the dielectric material. Different methods for obtaining acoustic data from MLCCs
are compared, and analysis methods for acoustic data are developed and compared
with each other.
An MLCC itself cannot generate significant acoustic response within audio frequency
range; instead, the vibrating PCB is the main source of MLCC-related audible noise
(Ko et al., 2014). Obtaining acoustic emissions using a microphone typically limits
the frequency range to audible frequencies, and the properties of the PCB are likely
to dominate the acoustic response. In order to bypass the contribution of the PCB,
a method for obtaining acoustic emissions directly from the MLCC is presented.
1.2 Research questions and contributions
The contributions and associated research questions of this thesis are:
Verification of acoustic method
Is it possible to obtain information on the structural condition of an MLCC
capacitor based on acoustic response?
Development of methods and instrumentation
What kind of methods and instrumentation are needed to yield measurements
that are repeatable, reliable and sensitive enough for the acoustic monitoring
of MLCCs?
Development of method of analysis
What kind of method of analysis is able to discriminate between valid and
cracked MLCCs?
13
2 Physics of multilayer ceramic capacitors
Ceramic capacitors are classified under three types, shown in Table 2.1. The method
presented in this thesis is based on measuring the mechanical motion of Type II
Multilayer Ceramic Capacitors. This motion is caused by piezoelectric behavior
of barium titanate (BaTiO3) used as dielectric in Type II MLCCs. There are no
notable piezoelectric effects in capacitors of Type I (Prymak, 2006). Because SrTiO3
also exhibits piezoelectric behavior (Furuta and Miura, 2010), this method might
also be applicable in some form to Type III capacitors.
2.1 Dynamics of MLCCs
Structure of a typical MLCC is presented in fig. 1.1 (see page 9). An MLCC can
be expected to have multiple mechanical resonant frequencies, which depend on the
structure, material properties and physical dimensions of the capacitor and its end
terminations. Because of the relatively complex structure of an MLCC, obtaining
closed-form solutions for the mechanical resonances is infeasible. The mechanical
behavior and resonances of MLCCs have been studied previously by Ahmar and
Wiese (2015) and Ko et al. (2014) using finite element method. The fundamen-
tal mechanical resonance frequencies of the MLCC in that particular study are in
MHz-range. Previous studies suggest that the absence of audio-range mechanical
resonances, in conjunction with the small physical size of MLCCs, means that the
capacitor itself creates no significant audible noise. (Ko et al., 2014)
2.1.1 Piezoelectric behaviour of MLCCs
The mechanical deformation of an MLCC arises from the piezoelectric properties
of barium titanate (BaTiO3) used as dielectric in MLCCs. In room temperature,
barium titanate has tetragonal crystalline structure which consists of grains less
than a micrometer in size. The grains are divided into domains, in each of which
the crystals share the same polarization, known as the spontaneous polarization.
The dielectric constant  relates to the polarization P of a medium as (Lee and
Table 2.1: Classification of ceramic capacitors by dielectric material. Based on TDK
Corporation (2016)
Type Dielectric material
I (Low permittivity) TiO2 etc.
II (High permittivity) BaTiO3 etc.
III (Semiconductor) BaTiO3, SrTiO3 etc.
14 2 Physics of multilayer ceramic capacitors
Aksay, 2001)
 ≈ P
0 + E
. (2.1)
Below Curie-point and under no external electric field E, the grain domains of the
BaTiO3 are spontaneously polarized. Under weak electric field, the polarization of
the domains is easily reversed. The polarization reversal by the electric field yields
higher  and thus, higher capacitance. (Skelly and Waugh, 2009).
Applying voltage bias over an MLCC causes net polarization over the domains of the
dielectric, resulting in deformation of the dielectric (Yang, 2005). This phenomenon
is called the inverse piezoelectric effect (Ousten et al., 1998). When high electric
field is applied to the material, the reversal of the polarization in the grains becomes
more difficult, and the net polarization essentially reaches its saturation. This causes
decrease in capacitance in MLCCs under DC bias voltage. (Skelly and Waugh, 2009).
Figure 2.1 shows the directions of the electric fields and strains inside a capacitor. If
a surface S that encloses one electrode with charge qenclosed is formed (Figure 2.1),
then according to Gauss’s law
‹
S
~E · d~S =qenclosed

(2.2)
⇒ E =qenclosed
S
(2.3)
on surfaces where ~E ‖ d~S, and E = 0 elsewhere. In an MLCC with n layers of an
area A, each electrode has an approximate charge of qenclosed =
Q
n/2
, where Q is the
total charge of a terminal. The electric field inside the dielectric is then
E =
2Q
nA
. (2.4)
The total capacitance of an MLCC is
C =
Q
U
. (2.5)
From Equations (2.4) and (2.5) is found that
E =
2CU
nA
. (2.6)
When piezoelectric material is subjected to external electric field ~E = (E1, E2, E3),
the material experiences deformation. The strain S = Sij in the material is described
in tensor notation as
Sp = s
E
pqTq + dpkEk (2.7)
(Dahiya, 2013), where sEpq is the electric compliance tensor at constant electric field,
Tq is the stress the material is subjected to, and dpk is the piezoelectric constant
2.1 Dynamics of MLCCs 15
tensor (IEE, 1987). The values of sEpq and dpk for barium titanate are well known
(Zgonik et al., 1994).
The electric field between the internal electrodes of a multilayer capacitor can be
assumed to be homogeneous and perpendicular to the electrode plates. Assuming
~E = (0, 0, E3) and no external stress applied, the strain in the direction of the
electric field becomes
S3 = d333E3 (2.8)
(IRE, 1949). According to (2.8), the strain and subsequent motion of the MLCC
occurs mainly in the direction of the surface normal of the PCB, facilitating the
measurement from the top cover of the capacitor.
From Eqs. (2.8) and (2.6) is obtained that the strain inside the dielectric material
is
S3 = d333
CU
A
. (2.9)
Thus, the strain inside a ceramic capacitor is higher if the capacitance or voltage is
increased, or if the electrode surface area is decreased. A more detailed study on the
strains inside an MLCC with closed-form solutions has been made by Hsueh and
Ferber (2002).
d
+
E
+Q -Q
-V+V
+ P
- P
P
Electrode
BaTiO3 EP
S
S
+
- P
-
-
+ P
-
-(1)
(3)
(2)
Figure 2.1: Electric fields inside an MLCC. When voltage is applied to end terminations,
surface charge densities σ are formed on the electrode plates, creating electric field ~E
between the plates. The electric field causes BaTiO3 to polarize, creating polarization
field ~P antiparallel to the field ~E. As BaTiO3 polarizes, its crystalline structure is
altered, creating strain ~S. The dashed line around the center electrode represents a
Gauss surface, enclosing a total charge of qenclosed.
16 2 Physics of multilayer ceramic capacitors
2.2 Acoustic emissions from PCB
2.2.1 Mechanical force transfer
The kinetic energy of an MLCC is translated into the PCB via solder joints of the
MLCC. The reverse piezoelectric effect creates strain and mechanical displacement
along the poling axis. This movement is translated into transverse motion of the
MLCC, which in turn creates torque on the PCB. (Ko et al., 2014)
2.2.2 Vibrational dynamics of Printed Circuit Boards
The vibrational motion of a plate can be described using Kirchoff-Love plate equa-
tions (Love, 1888), which are a commonly used model for small-amplitude vibrations
of thin plates. Because the thickness of a PCB is typically very small compared to
its other dimensions, the PCB is assumed to behave like a rectangular Kirchoff-Love
plate with width a = 39.0 cm, length b = 30.4 cm and thickness 2h = 1.55 mm. The
deflection field w of the plate, separated into spatial and temporal components W
and F , is then
w(x1, x2, t) = W (x1, x2)F (t) (2.10)
where the force acting on the plate is of the form
F (t) = Aeiωt +Be−iωt. (2.11)
If a PCB is approximated with a Kirchoff-Love-plate with isotropic material prop-
erties and simply supported on all sides, the harmonic modes ωmn are obtained by
(Reddy, 2007)
ωmn =
pi2
b2
√
D
ρh
(
m2
b2
a2
+ n2
)
. (2.12)
Using Young’s modulus γE as an average of the lengthwise value 24 · 109 Pa and
cross-wise value 21 · 109 Pa, and Poisson’s ratio ν as an average of lengthwise 0.136
and cross-wise 0.118, the flexural rigidity of FR-4 is approximately D = γEh
3
12(1−ν2) ≈
7.8. From eq. (2.12), it is obtained that the PCB has a fundamental mode ω11
at a frequency of 278.8 Hz. It is also seen that the PCB has its first 10 modes
at frequencies below 2.5 kHz. These frequencies are well below of the resonance
frequencies of the MLCCs, which are in the MHz-range.
17
3 Experiments
3.1 Measuring Acoustic Emissions from MLCCs
The main goal of the experiments was to obtain acoustic information from the
MLCCs. Initially, two ways of measuring acoustic emissions were taken into consid-
eration:
The indirect method
In this method, acoustic emissions are measured from the PCB the MLCC
is attached to. Driving the MLCC with AC voltage causes the MLCC to
create mechanical vibrations. These vibrations are transmitted to the PCB,
from which they can be measured, for example, with a microphone (Ko et al.,
2014), or a point contact sensor.
The direct method
In this method, the MLCC is driven with AC voltage, causing the MLCC
to vibrate mechanically. These vibrations are measured directly from the
capacitor using a point contact sensor.
The feasibility of obtaining acoustic information via the indirect method was stud-
ied at the beginning of this project. It was observed that with this method, the
characteristics of the acoustic signal are heavily dependent on the location and dis-
tance of the sensor or microphone from the PCB. The mass, physical dimensions
and material properties of the PCB determine the possible vibrational modes, as
described in eq. (2.12).
To remove the effects of sensor placement and the vibration of the PCB, the direct
method was selected for this thesis. Preliminary experiments show that the me-
chanical vibration amplitude of the PCB is very small on frequencies above 50 kHz
(Fig. 4.12) and thus, the PCB has practically no contribution to the acoustic data
obtained directly from the MLCC.
To minimize the effect of any external vibrations which could affect the measure-
ments (such as background acoustic noise), the measurements were performed in an
anechoic room. The main source of disturbances in the measurement data is EMI,
for which the main cause is the measurement equipment.
3.2 Instrumentation and equipment
To generate acoustic response over a wide range of frequencies, the MLCCs were
driven with pulse wave frequency sweeps, or chirps, using an Agilent 33250A signal
generator. The chirps were 100 ms in duration, with frequency linearly increasing
from 100 Hz to 2 MHz and with voltage of ±10 Vpeak. Duty cycle was set to signal
18 3 Experiments
generator’s maximum of D = 80%, as this was observed to maximize the ampli-
tude of the acoustic response. Figure 3.1 shows the frequency content of an ideal
pulse wave, which has power distributed over a wide range of harmonic frequencies.
Driving an MLCC with a pulse wave was observed to create significantly higher
acoustic response than a sine wave. Because a pulse wave consists of a high number
of harmonics, the obtained acoustic response also contains resonance peaks caused
by higher harmonics of the pulse wave signal.
0 50 100 150
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Po
w
er
 (a
rbi
tra
ry 
un
its
)
Figure 3.1: A 1024-point FFT of a pulse wave with frequency of 10 Hz and duty cycle of
80 %
The acoustic response of the MLCC was picked up using a KRN point contact sensor
placed on top of the MLCC. The signal from the point contact sensor was amplified
using a KRN preamplifier. Specifications of the point contact sensor and preamplifier
are shown in Table 3.1. The output of the preamplifier was connected to a Keysight
InfiniiVision MSO-X 4104A Mixed Signal Oscilloscope. The measurement data was
the processed in Matlab.
The sensor was placed in a 3D-printed fixture (Fig. 3.2) to provide repeatable weight
and contact on MLCCs under examination. The tip of the sensor was covered with
Kapton-tape to prevent shorting the MLCC via its end terminations. The sensor
was used because it had the widest frequency range of the sensors readily available.
The measurement setup assembled in the anechoic room is shown in figures 3.3 and
3.4. An acoustic wall seen in figure 3.3 was assembled between the test board setup
and the rest of the measurement equipment to block the acoustic noise caused by
the oscilloscope and the signal generator.
3.3 MLCC measurement procedure 19
Table 3.1: Specifications of the point contact sensor and preamplifier
Point contact sensor
Model: KRNBB-PC Broadband point contact sensor
Manufacturer: KRN Services
Design: Conical piezoelectric crystal, built-in JFET (Mhamdi et al., 2015).
Sensitivity: 15mV/nm ± 4dB over a frequency range 20 kHz – 1 MHz
Maximum frequency: 2.5 MHz
(KRN, 2015)
Preamplifier
Model: AMP-1BB-J single channel broadband preamplifier
Manufacturer: KRN Services
Bandwidth: 3 dB over a frequency range 18.2 kHz – 2.0 MHz
Gain: 28.1 dB at a frequency of 300 kHz
(KRN, 2014)
3.3 MLCC measurement procedure
Acoustic measurements were performed on each MLCC individually. The test boards
were characterized by measuring voltage chirp response of each MLCC on the board.
Each board was characterized twice:
1. Characterization of intact board
Each individual MLCC on the intact board was characterized to obtain refer-
ence data
2. Bending of the board
The boards were bent using different strain levels. One pair of Boards 1 and
2 was subjected to strain of 6000 µstr, and another to strain of 4300µstr for
Board 1 and 5800µstr for Board 2.
3. Characterization of the bent board
Each MLCC on the board was characterized after the bending in order to find
defective capacitors.
Pre-bending data was used as a statistical reference for each type of capacitors.
Reference response curve with standard deviation intervals was created for each
capacitor column by taking the average of the measured acoustic responses. This
approach was chosen partly because it provides information on how a certain kind of
an intact MLCC typically behaves acoustically, and partly because the measurement
setup caused some uncertainties on the measurement data. After the bending, each
capacitor on a column was compared to the statistical reference of that capacitor
type. One-to-one–comparisons were also made for single capacitors, comparing the
acoustic responses of one capacitor before and after bending.
20 3 Experiments
Figure 3.2: KRN point contact sensor with 3D-printed fixture on top of an MLCC
3.4 Test board setup
Several test boards with specifications shown in Table 3.2 were used in the mea-
surements. Labeled as Board 1’s and Board 2’s, the test boards were structurally
identical, with only difference being the capacitor population. The four main vari-
ables within the capacitor populations were:
Case size
1206, 1210, 1812 and 2220 size MLCCs
Orientation
Angle and location of an MLCC
Termination type
Standard vs. flex type capacitors
Suppliers
TDK, AVX and Kemet
An overview of the MLCCs assembled on the test boards is shown in tab 3.3. The
MLCCs were assembled on the boards in such way that each column of capacitors
has 10 MLCCs of the same case size, type and orientation (figure 3.5). The capacitor
populations of the Boards 1 and 2 are shown in Tables 3.4 and 3.5 respectively.
3.4 Test board setup 21
Figure 3.3: Overview of the
measurement setup
Figure 3.4: Point contact sensor
and PCB
Table 3.2: Test board specifications
Board material FR-4
Board dimensions 39.0 cm by 30.4 cm
Board thickness 1.55 mm
Number of traces 2
Coatings none
Type of solder SAC: 96.5Sn-3.0Ag-0.5Cu
Table 3.3: Overview of the MLCCs assembled on the test boards
Size Type Producer Code number Series V rating C
1206 Normal TDK C2316X7R1E475K160AC C-series 24 V 4.7 µF
1206 Flex Kemet C1206X475K3RACAUTO FT caps 24 V 4.7 µF
1210 Normal TDK C3225X7R1E106M250AC C-series 24 V 10 µF
1210 Flex AVX 12103C106M4Z2A Flexiterm 24 V 10 µF
1210 Flex Kemet C1210X106M3RACTU FT caps 24 V 10 µF
1812 Normal TDK C5432X7R1E226M250KC C-series 24 V 22 µF
2220 Normal TDK C5750X7R1E226M250KA C-series 24 V 22 µF
2220 Flex Kemet C2220X226K3RACAUTO FT caps 24 V 22 µF
22 3 Experiments
Connectors for the MLCCs
Columns
a b c d e f g h i j k l
CXX1
CX10
CXX2
Figure 3.5: Illustration of the placement of the MLCCs on a test board.
Table 3.4: Details about the MLCCs on Board 1
MLCC nr col Size Orientation Type Producer V rating C
C1-C10 a 1206 0◦ Normal TDK 24 V 4.7 µF
C11-C20 b 1206 0◦ Flex Kemet 24 V 4.7 µF
C21-C30 c 1206 45◦ Normal TDK 24 V 4.7 µF
C31-C40 d 1206 45◦ Flex Kemet 24 V 4.7 µF
C41-C50 e 1206 90◦ Normal TDK 24 V 4.7 µF
C51-C60 f 1206 90◦ Flex Kemet 24 V 4.7 µF
C61-C70 g 1210 0◦ Normal TDK 24 V 10 µF
C71-C80 h 1210 0◦ Flex Kemet 24 V 10 µF
C81-C90 i 1210 45◦ Normal TDK 24 V 10 µF
C91-C100 j 1210 45◦ Flex Kemet 24 V 10 µF
C101-C110 k 1210 90◦ Normal TDK 24 V 10 µF
C111-C120 l 1210 90◦ Flex Kemet 24 V 10 µF
3.4 Test board setup 23
Table 3.5: Details about the MLCCs on Board 2
MLCC nr col Size Orientation Type Producer V rating C
C121-C130 a 1812 0◦ Normal TDK 24 V 22 µF
C131-C140 b 1210 0◦ Flex AVX 24 V 10 µF
C141-C150 c 1812 45◦ Normal TDK 24 V 22 µF
C151-C160 d 1210 45◦ Flex AVX 24 V 10 µF
C161-C170 e 1812 90◦ Normal TDK 24 V 22 µF
C171-C180 f 1210 90◦ Flex AVX 24 V 10 µF
C181-C190 g 2220 0◦ Normal TDK 24 V 22 µF
C191-C200 h 2220 0◦ Flex Kemet 24 V 22 µF
C201-C210 i 2220 45◦ Normal TDK 24 V 22 µF
C211-C220 j 2220 45◦ Flex Kemet 24 V 22 µF
C221-C230 k 2220 90◦ Normal TDK 24 V 22 µF
C231-C240 l 2220 90◦ Flex Kemet 24 V 22 µF
24 3 Experiments
3.5 Analysis methods for the acoustic data
The number of measured capacitors has to be sufficiently large (dozens or hundreds)
to have statistical meaning. The measurement files are also large in size, because
the sampling rate of data acquisition must be at least 10 times the highest frequency
fed to the capacitor in order to detect these frequencies. Therefore, there is a need
for an automatic analysis method which can statistically compare a single measured
capacitor to a reference model of this particular type of capacitor.
A method for analyzing MLCC acoustic data was developed. The method is based
on obtaining an envelope curve of the measured acoustic response. The use of
acoustic envelope provides a smooth curve which neglects phase-differences between
measurements whilst maintaining the amplitude information. The envelope curves
can be used for one-to-one–comparison and statistical comparison between several
envelopes by taking the mean ± standard deviation of multiple envelopes.
A small number of intact and defective capacitors were examined as a preliminary
study. By observing the raw measurement data visually, it was noted that a de-
fective MLCC has several characteristic differences compared to an intact MLCC.
Such characteristics can be algorithmically detected and include changes in number,
location and height of the characteristic peaks of the acoustic response.
The first 1/50th of the measured signal, corresponding to a frequency range of
100 Hz−40 kHz, was cut off from the measurement files because of a high-amplitude
burst that occurred in the lower frequencies of the chirp with nearly all of the
capacitors. An envelope was then calculated for the signal u = u(t).
Mathematically, the envelope e(t) of a signal u(t) is the modulus of the analytic
signal:
e(t) =
√(
u(t)
)2
+Re
{H(u(t))}2. (3.1)
These signals were numerically calculated, and then filtered with 2nd order Butter-
worth-type lowpass filter with cutoff frequency of 8 kHz. The result was then down-
sampled with downsampling factor NDS = 80, such that
e(t) = DownsampleNDS
{
lpf
[√(
u(t)
)2
+Re
{H(u(t))}2]} (3.2)
where H(·) is the Hilbert transform, and Re{H(u(t))}2 is the so-called analytic
signal. The obtained envelope signals e(t) are presented as corresponding frequency
domain signals e(f) by scaling the timescale of the measurements with the generator
sweep frequency and timespan. It was assumed that the MLCC reacts to changes in
the input frequency nearly instantaneously, so the vibration frequency of the MLCC
is equal to the signal generator frequency.
Reference envelopes were formed for each capacitor column by calculating the mean
3.5 Analysis methods for the acoustic data 25
of the acoustic response envelopes of ten intact MLCCs on a column:
eref (f) =
∑10
n=1 en
10
. (3.3)
3.5.1 Observation model for the envelope signal
During the experiments, it was observed that the amplitude of the point contact
sensor output voltage is slightly dependent on the position, angle and downward
force of the point contact sensor. To decrease the effect of these variations, a method
of fitting one envelope into another in Least Squares (LS) sense was used. A model
where an envelope is fitted into another by multiplying with a scalar is sufficient by
following deduction:
Small variations within the mechanical coupling between the sensor and an MLCC
are assumed to scale the amplitude of the observed signal by some constant A > 0.
If u1(t) and u2(t) are signals measured from the same MLCC with different levels of
mechanical coupling, it holds that
u2(t) = Au1(t). (3.4)
Envelope curves e1(t) and e2(t) are calculated for the signals u1(t) and u2(t) as
described in Eq. (3.1). Because Hilbert transform is a linear, it holds that for the
envelopes
e2(t) =
∣∣∣∣∣∣H{u2(t)} ∣∣∣∣∣∣ = ∣∣∣∣∣∣H{Au1(t)} ∣∣∣∣∣∣ = ∣∣∣∣∣∣AH{u1(t)} ∣∣∣∣∣∣ = Ae1(t). (3.5)
In addition to the variation of the mechanical contact between the sensor and the
MLCC, the electromagnetic interference from the frequency sweep caused distortion
in the measurement data. The effect of the EMI is clearly seen in Fig. 4.12 as a
somewhat sinusoidal component in the envelopes at frequencies past 1 MHz. This
disturbance was observed to be partially caused by the leads that were attached
to the connectors of the PCB and the wires on the PCB surface. The noise was
also observed to increase in amplitude as the point contact sensor was taken close
(∼ 1 cm) to the MLCC. An attempt of canceling out the EMI component was made
by LS-fitting an envelope of measured EMI into the acoustic response envelopes.
This method yielded no successful results, because the EMI component is slightly
different at each location and MLCC on a test board. The EMI component is,
however, similar with both intact and damaged MLCCs, so it causes no substantial
differences between envelopes. Small EMI-related differences between envelopes are
partially canceled in calculations by using a method of weighted LS-fitting, shown
in (3.6) - (3.13).
26 3 Experiments
3.5.2 Analysis methods
The obtained acoustic response envelopes were inspected both visually and algorith-
mically for defects:
Visual observations
Visual inspection of the measurement data for changes in the acoustic en-
velopes between pre- and post-bending measurements. This method was
mainly used during the measurements and to verify the calculated values for
those capacitors that appeared defective.
GLS-fit and comparison
Perform a generalized least squares fit into the envelope data being examined
to compensate for the variation in measurement data amplitude induced by
the variations in the measurement setup. Based on eq. (3.5), the fitted model
is the reference envelope multiplied with scalar, eref = Hθ + v, or in matrix
form, e1...
eN
 =
 eref,1...
eref,N
(θ1)+
v1...
vN
 (3.6)
where v is error vector that is assumed to have zero mean (Gaussian distribu-
tion), H is the observation matrix and θ is the parameter vector. The fit is
calculated with weighting matrix W ,
W = diag
(
1
σ21
, · · · , 1
σ2N
)
(3.7)
where the diagonal elements are the inverse variances of the reference curve.
The GLS solution of the parameter vector θˆ is then obtained by
θˆGLS =
(
HTWH
)−1
HTWe. (3.8)
LGLS-difference value is calculated for an envelope e by calculating squared
distances li between points ei and eref,i, scaled with pointwise variances of the
reference data:
li =
1
σ2ref,i
(ei − eˆi)2 (3.9)
or in matrix form
l = W (e− eˆ)T (e− eˆ) (3.10)
The total difference LGLS is obtained by taking the sum of li over the mea-
3.5 Analysis methods for the acoustic data 27
surement sample of N data points and scaling the sum with N∑N
i=1
1
σ2ref
(ei − eˆi)2
N
. (3.11)
The result is then divided with the mean of fit difference sums µLGLS ,ref calcu-
lated from the individual reference envelopes:
LGLS =
∑N
i=1
1
σ2ref
(ei − eˆi)2
NµLGLS ,ref
. (3.12)
where µLGLS ,ref is
µLGLS ,ref =
∑nref
k=1
(∑N
i=1
1
σref,i(erefk,i−eˆrefk,i)
N
)
nref
(3.13)
Thus, the value of LGLS = 1 corresponds to the reference envelope itself.
Spectrogram analysis
Spectrograms were calculated for certain capacitors to identify the frequency
content of observed resonance peaks. Because the input pulse waveform con-
tains a high number of harmonics, the resonance frequencies of an MLCC are
excited several times during a frequency sweep. The spectrograms were used
to identify the true number of resonant peaks in pre- and post-bending mea-
surements. The spectrograms were calculated using Matlab’s spectrogram()-
function.
28 4 Results
4 Results
Comparison of acoustic envelopes before and after bending was made both visually
and using the LGLS - algorithm presented in (3.6) - (3.13).
It was observed that nearly all of the MLCCs on bent boards show at least small
increase in LGLS-values when compared to those of pre-bending data. Small changes
between the pre- and post-bending LGLS-values are likely measurement method-
related, whereas significant changes in these values may indicate structural damage
in the MLCC.
4.1 Acoustic emission characteristics of damaged MLCCs
A small sample of MLCCs was initially selected for identifying the characteristic
changes in the acoustic envelope of a damaged capacitor. The capacitors were se-
lected from two Board 2s, such that one of the boards had been bent, and some
MLCCs on it had been identified as defective by electrical analysis. These MLCCs
were characterized alongside the corresponding MLCCs on the non-bent board. Fig-
ure 4.1 shows an example of typical changes in acoustic envelope of an MLCC that
has been structurally damaged. In both pre- and post-bending figures, the obtained
data is from the same individual MLCC.
Comparing the measured signal before and after bending in Figs. 4.1a and 4.1b
show the typical differences between an intact and a damaged MLCC. With all the
MLCCs, regardless the case size and termination type, the most prominent signs of
mechanical damage seen in the envelope graphs are
1. Increase in the amplitude of the characteristic peaks
2. Introduction of new peaks, especially at frequencies above 1 MHz
The corresponding numbers 1 and 2 are also marked on figures 4.1a and 4.1b. Ad-
ditionally, small changes in the resonant frequencies and relative heights of the
characteristic peaks were observed in some damaged capacitors. Spectrograms in
figures 4.1c and 4.1d show, that the four highest peaks in Fig. 4.1a are actually one
resonant frequency at about 0.7 MHz which is also excited by the second, third and
fourth harmonic of the pulse wave (see Fig. 3.1 in page 18). In Fig. 4.1b, the peak
at 1 MHz is excited by the fundamental frequency of the pulse wave, while the peak
at 0.5 MHz appears to consist of both the fundamental frequency and the second
harmonic of the pulse wave. The small peak in 4.1b at about 0.65 MHz is excited
by the fundamental frequency of the pulse wave.
Based on figures 4.1a - 4.1d, three new resonant frequencies can be detected in
the post-bending measurements. This suggests that the MLCC might have suffered
multiple different mechanisms of damage. This is also supported by Fig. 4.2. In
Fig. 4.2a, a horizontal crack can be seen propagating through the dielectric of the
4.2 Statistical analysis of MLCCs before and after bending 29
0 0.5 1 1.5 2
Signal generator frequency (MHz)
0
0.05
0.1
0.15
0.2
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 (V
)
1
1
1
(a) Envelope of acoustic response of an
intact capacitor C146
0 0.5 1 1.5 2
Signal generator frequency (MHz)
0
0.05
0.1
0.15
0.2
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 (V
)
1
1
1
2
2
2
(b) Envelope of acoustic response of the
capacitor C146 after bending
(c) Spectrogram of acoustic response of
C146 before bending
(d) Spectrogram of acoustic response of
C146 after bending
Figure 4.1: Envelopes and spectrograms of acoustic responses of capacitor C146 (1812
size) before and after bending. The numbers 1 and 2 in (a) and (b) indicate the typical
changes in the acoustic response of a damaged capacitor: 1 - amplitude increase in the
highest peaks; 2 - emergence of new peaks
MLCC, whereas in both figures 4.2a and 4.2b fractures can be seen in the MLCC
close to the end terminations, near the soldering pads. Not all defective MLCCs
showed dielectric fractures in X-ray-images, but only near end terminations.
4.2 Statistical analysis of MLCCs before and after bending
Figures 4.3 and 4.4 show the pre- and post-bending histograms of the LGLS values
for test boards subjected to 6000 µstr, 5800 µstr and 4300 µstr bending strains.
It is clearly seen that the PCB bending procedure affects the obtained acoustic
emissions. It is also seen that the range of post-bending LGLS values is significantly
30 4 Results
(a) One end termination of C146 (b) Another end termination of C146
Figure 4.2: X-ray images of a damaged MLCC C146 (1812 size). Courtesy of ABB
Switzerland Ltd.
different for each case size. Calculated LGLS-values for capacitors on Boards 1 and 2
before and after 4300/5800µstr bending are visualized in Figures 4.5a and 4.5b, and
Figures 4.6a and 4.6b show the corresponding values for the boards before and after
6000µstr bending. Figure 4.7 shows the box plots of the LGLS-values for Boards 1
and 2.
Table 4.1: MLCCs identified as defective by X-ray analysis
Case size 4300 µstr 5800 µstr 6000 µstr
1206 – 1/60 1/60
1210 0/30 1/60 2/90
1812 15/30 – 20/30
2220 6/60 – 5/60
4.2 Statistical analysis of MLCCs before and after bending 31
0 2 4 6 8 10
0 
20
40
60
Before bending
0 2 4 6 8 10
GLS-fit difference value
0 
20
40
After bending
%
 o
f M
LC
Cs
(a) 1206-size case
0 2 4 6 8 10 12 14
0 
20
40
60
Before bending
0 2 4 6 8 10 12 14
GLS-fit difference value
0 
20
40
After bending
%
 o
f M
LC
Cs
(b) 1210-size case
0 20 40 60 80 100 120
0  
50 
100
Before bending
0 20 40 60 80 100 120
GLS-fit difference value
0 
10
20
30
After bending
%
 o
f M
LC
Cs
(c) 1812-size case
0 20 40 60 80 100 120
0  
50 
100
Before bending
0 20 40 60 80 100 120
GLS-fit difference value
0 
10
20
30
After bending
%
 o
f M
LC
Cs
(d) 2220-size case
Figure 4.3: Histograms of LGLS-values for different case size capacitors before and after
6000 µstr bending.
32 4 Results
0 10 20 30 40 50 60
0  
50 
100
Before bending
0 10 20 30 40 50 60
GLS-fit difference value
0 
20
40
After bending
%
 o
f M
LC
Cs
(a) 1206-size case, 5800 µstr bending
0 5 10 15
0  
50 
100
Before bending
0 5 10 15
GLS-fit difference value
0 
20
40
After bending
4300 µstr
5800 µstr
%
 o
f M
LC
Cs
(b) 1210-size case, 5800 and 4300 µstr
bending
0 20 40 60 80 100
0  
50 
100
Before bending
0 20 40 60 80 100
GLS-fit difference value
0 
10
20
After bending
%
 o
f M
LC
Cs
(c) 1812-size case, 4300 µstr bending
0 20 40 60 80 100 120 140
0  
50 
100
Before bending
0 20 40 60 80 100 120 140
GLS-fit difference value
0 
20
40
After bending
%
 o
f M
LC
Cs
(d) 2220-size case, 4300 µstr bending
Figure 4.4: Histograms of LGLS-values for different case size capacitors before and after
5800/4300 µstr bending.
4.2 Statistical analysis of MLCCs before and after bending 33
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
5
10
15
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
5
10
15
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 Intact
Defective
(a) Board 1
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
20
40
60
80
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
20
40
60
80
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 Intact
Defective
(b) Board 2
Figure 4.5: From top to bottom: Calculated LGLS-values before bending, after
4300/5800 µstr bending, and X-ray analysis results for MLCCs on Boards 1 and 2.
34 4 Results
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
5
10
15
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
5
10
15
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 Intact
Defective
(a) Board 1
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
20
40
60
80
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 0
20
40
60
80
a b c d e f g h i j k l
1
2
3
4
5
6
7
8
9
10 Intact
Defective
(b) Board 2
Figure 4.6: From top to bottom: Calculated LGLS-values before bending, after 6000 µstr
bending (mean of two measurement runs), and X-ray analysis results for MLCCs on
Boards 1 and 2.
4.2 Statistical analysis of MLCCs before and after bending 35
a b c d e f g h i j k l
0
10
20
30
40
50
60
L G
LS
(a) Board 1 after 4300 µstr bending
a b c d e f g h i j k l
0
20
40
60
80
100
120
L G
LS
(b) Board 2 after 5800 µstr bending
a b c d e f g h i j k l
0
2
4
6
8
10
12
L G
LS
(c) Board 1 after 6000 µstr bending
a b c d e f g h i j k l
0
10
20
30
40
50
60
70
80
90
L G
LS
(d) Board 2 after 6000 µstr bending
Figure 4.7: Box plots of LGLS-values per column on Boards 1 and 2. The boxes denote
second and third quartile of the data, with red line being the median. The whiskers
indicate the range of data. Maximum length of the whiskers is two times the
interquartile range. Red ”+”–markers outside the whiskers denote outliers.
36 4 Results
4.2.1 1206-case MLCCs
Out of the 60 1206-case MLCCs, seen in columns a-f in Fig. 4.6a, only C021 showed
signs of damage in the post-bending X-ray analysis. C021 was damaged in both of
the boards subjected to 6000 µstr and 5800 µstr bending strain. In Fig. (4.3a),
a slight increase in LGLS-values can be seen for 1206-case capacitors, with highest
values obtained from C021.
However, the acoustic response of C021 in Fig. 4.8a shows a shift in the resonant
frequency of the highest resonance peak from 1.1 MHz to about 1.2 MHz in all
pre-and post bending measurements, suggesting that the capacitor might from an-
other manufacturing batch, or already defective during the reference measurements.
Spectrogram of C021 in Fig. 4.8b shows that the observed resonance peak is excited
by the fundamental frequency of the input signal, not harmonics. Capacitor C001
on another PCB showed similar characteristics to C021 before and after bending.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency (MHz)
0
0.05
0.1
0.15
0.2
0.25
0.3
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
Mean of reference spectra
Std of reference spectra
C021 before bending
C021 after bending
(a) Mean ± std of acoustic envelopes of
capacitors C021-C030 alongside pre- and
post-bending acoustic spectrum of C021
(b) Spectrogram of C021 after bending
Figure 4.8: Acoustic response and spectrogram of C021 after 6000 µstr bending
All 1206-case capacitors yielded good acoustic response and signal-to-noise ratio.
For flex-termination capacitors, there was a notable differences in resonance peak
heights between capacitors both before and after bending. This makes the compar-
ison against averaged envelope more unreliable than with the normal-termination
capacitors.
4.2.2 1210-case MLCCs
Table 4.1 shows that no capacitors were damaged on the test board subjected to
4300 µstr bending, and only individual MLCCs were damaged by the higher bending
strains, as seen in figures 4.6a (columns g-l) and 4.6b (columns b, d and f).
4.2 Statistical analysis of MLCCs before and after bending 37
Damaged capacitor C081 does not show increase in LGLS-values in Fig. 4.6a. Figure
4.9a shows that the envelopes of the MLCC in the pre- and post-bending measure-
ments are almost identical. Similarly, the defective C101 showed very little difference
in pre- and post-bending measurements. In Fig. 4.9b, the high standard deviation
values in the reference data at 0.65 MHz is caused by acoustic response of C090
which differs from the other reference capacitors on the column.
With all of the 1210-case MLCCs there was variation in the resonant peak heights
along a column, both before and after bending. An example of this variation is seen
in Fig. 4.10, where all the capacitors on the column could be divided into two sets,
one having the highest resonant peak at 0.75 MHz as with C175, and the other at
0.6 MHz as with C175.
0 0.5 1 1.5 2
Signal generator frequency (MHz)
-0.05
0
0.05
0.1
0.15
0.2
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
Mean of reference data
Std of reference data
C081 before bending
C081 after bending
(a) C081
0 0.5 1 1.5 2
Signal generator frequency (MHz)
-0.05
0
0.05
0.1
0.15
0.2
0.25
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
Mean of reference data
Std of reference data
C090 before bending
C090 after bending
(b) C090
Figure 4.9: Mean ± std of acoustic envelopes of capacitors C081-C090 alongside pre- and
post-bending acoustic responses of damaged C081 and non-damaged C90
4.2.3 1812-case capacitors
Majority of the 1812-size MLCCs was damaged by bending, as seen in table 4.1.
In the post-6000µstr-measurements, all the defective MLCCs on col. e are clearly
seen in Fig. 4.6b, showing the 1812-case capacitors on columns a, c and e. Col. c
yields also distinguishable LGLS-values, although smaller in value than those on col.
e. Bending strain of 4300 µstr yielded fewer damaged 1812-case capacitors, with
C144, C145 and C149 left intact on column e. These non-damaged MLCCs can be
distinguished from the damaged ones in Fig. 4.5b.
The 1812-size capacitors yielded high acoustic response, and the typical changes in
the acoustic response can easily be seen in Figs. 4.1a and 4.1b.
38 4 Results
0 0.5 1 1.5 2
Signal generator frequency (MHz)
0
0.05
0.1
0.15
0.2
0.25
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
C131, C132, C135, C138, C139
C133, C134, C136, C137, C140
Figure 4.10: Pre-bending acoustic envelopes of all MLCCs on Board 2 column b.
4.2.4 2220-case capacitors
Figure 4.11 shows two damaged 2220-size MLCCs. The highest resonance peak of
C201 in Fig. 4.11a shows a small frequency shift in post-bending measurements, but
the amplitude does not deviate far from the ±Std-limits. The post-bending acoustic
envelope of C221 in Fig. 4.11b shows significant increase in both number and height
of the resonant peaks.
The 2220-sized MLCCs yielded the lowest acoustic response of the four case sizes,
as shown in table 4.2. Figure 4.11a shows that the noise level at the 2 MHz is ap-
proximately the same as the reference envelope’s resonant peak voltage at 0.5 MHz.
4.3 Comparison of observed acoustic emission amplitudes
The Mean±Std of acoustic emission peak voltages per case size are shown table
4.2. The voltage values are for intact capacitors. Because the amplitude of ob-
served acoustic emission is likely related to the strain (deformation) of the dielectric
material in (2.9), the ratios C/A are also provided in the table 4.2.
4.4 Repeatability of the measurements 39
0 0.5 1 1.5 2
Signal generator frequency (MHz)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
Mean of reference data
Std of reference data
C201 before bending
C201 after bending
(a) C201
0 0.5 1 1.5 2
Signal generator frequency (MHz)
0
0.02
0.04
0.06
0.08
0.1
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(V
)
Mean of reference data
Std of reference data
C221 before bending
C221 after bending
(b) C221
Figure 4.11: Mean ± std of acoustic responses of C201-210 and C221-C230 alongside
damaged MLCCs C201 and C221 before and after bending
Table 4.2: Capacitances C, surface areas A (Bergenthal, 2016), ratios C/A and
Mean±Std for acoustic emission peak voltages for intact MLCCs of different case sizes
Case size A (mm2) C (µF) C
A
(
µF
mm2
)
Mean(max {e})(V) Std(max {e})(V)
1206 5.12 4.7 0.92 0.0874 0.0247
1210 8.00 10 1.25 0.1588 0.0447
1812 14.40 22 1.52 0.1230 0.0237
2220 28.00 22 0.79 0.0284 0.0052
4.4 Repeatability of the measurements
Repeatability of the measurement method was tested on three columns of intact
capacitors and three columns of damaged capacitors. The measured columns were
a, b and e on an intact Board 2 and on a Board 2 bent to 4300 µstr. The mea-
sured columns were chosen according to results obtained from characterization of the
entire Board: column e showed multiple defective MLCCs in the post-bending mea-
surements, whereas capacitors on column b yielded two different types of acoustic
response. Column a was chosen as a reference column. Each MLCC was measured
five times, detaching the point contact sensor between the measurements.
4.4.1 Error propagation in LGLS-values
The LGLS-values are of the form (3.12), where
eˆ = Hθˆ =
(
HTH
)−1
HTe.
40 4 Results
If the error of e is at highest δ, then the maximum value of θˆ including error is(
HTH
)−1
HT(1 + δ)e = (1 + δ)θˆ.
Then the difference (e− eˆ)2 in (3.12) becomes
((1 + δ)e− eˆ)2 =
(
(1 + δ)e− (1 + δ)Hθˆ
)2
= (1 + δ)2
(
e−Hθˆ
)2
= (1 + δ)2 (e− eˆ)2
= (e− eˆ) + (δ2 + 2δ) (e− eˆ)
Thus, the amplitude error δe in e becomes error(
δ2 + 2δ
)
LGLS
in the corresponding LGLS-value.
4.4.2 Errors in measured voltages and LGLS-values
The acoustic response envelope e is assumed to behave as in (3.6), such that the
error in measured voltage is of the form δe, δ ∈ R. In successive measurements, the
δ is assumed to be caused by the inconsistence of the mechanical contact between
the sensor and capacitor. Voltage measured at the highest peak of acoustic response
was used as a measure of repeatability. Because the acoustic response differs from
capacitor to capacitor, Table 4.3 shows the maximum Std:s of mean peak voltages
alongside the corresponding relative standard deviations, mean of peak voltages and
corresponding δ in LGLS for columns a, b and e on the intact and bent Board 2s.
The relative Std:s were used as δ:s when calculating δLGLS:s.
4.5 Effects of PCB vibrations
The possible contribution of the PCB on the capacitor AE measurements was studied
by taking reference measurements of the PCB at various distances from the certain
MLCC, while driving the capacitor with AC pulse wave sweep (Fig. 4.12). The
results show that the PCB vibrates with highest amplitudes in audible frequencies;
at a frequency of 50 kHz the measured amplitudes have dropped below the noise
floor.
The frequency range of the first resonance modes of the PCB from (2.12), alongside
the results in Fig. 4.12, suggest that the board has little to no contribution to
the observed acoustic data of the MLCCs near the resonance frequencies of the
capacitors.
4.5 Effects of PCB vibrations 41
Table 4.3: Minimum and maximum acoustic response voltages of single MLCCs
measured from columns a, b and e on intact and bent Board 2s
Col max
i=1,...,10
{Std (ei)} Mean (max {ei}) (V) Relative Std δLGLS
Intact Board 2
a 0.0171 0.1683 10.2 % 121.4 %
b 0.0238 0.2221 10.8 % 122.8 %
e 0.0242 0.1560 15.6 % 133.7 %
Bent Board 2
a 0.0211 0.2089 10.2 % 121.5 %
b 0.0279 0.2798 10.0 % 121.0 %
c 0.0345 0.3072 11.3 % 123.9 %
0 20 40 60 80 100
1
2
3
4
5
6
7
8
9
10
11
Signal generator frequency (kHz)
Po
in
t c
on
ta
ct
 s
en
so
r v
ol
ta
ge
 e
nv
el
op
e 
(m
V)
Calculated envelopes for measured acoustic emissions at various distances from an MLCC
 
 
 10 mm above the MLCC, off from the PCB
 PCB, 10 mm away from the MLCC
 PCB, 30 mm away from the MLCC
 Center of the PCB
Figure 4.12: Vibrations measured at various distances away from the MLCC C142 whilst
driving the capacitor with AC pulse sweep.
42 5 Discussion
5 Discussion
5.1 Signs of mechanical damage in MLCCs
The results show that subjecting an MLCC to mechanical damage can cause several
characteristic changes in its acoustic envelope. Several new resonant peaks in the
acoustic response of an MLCC might imply that the capacitor has suffered damage in
multiple different locations, and the failure mechanisms may be different. However,
it is unclear how the characteristic differences in caused by a termination crack,
delamination or crack within the active region of an MLCC differ from one another.
The X-ray images of 1812-sized MLCCs in Figs. 4.2a and 4.2b show cracks both
near the end termination and inside the dielectric. It is possible that the solder
contacts set conditions for the mechanical vibration amplitude of an MLCC to some
degree, and cracks in these locations lead to increased amplitude. Likewise, cracks
propagating through the active region of an MLCC might be responsible for new
resonant peaks. These are, however, only hypotheses, and would have to be validated
by a dedicated study.
5.2 LGLS-values and statistical observations
According to the histograms in Figs. 4.3 and 4.4, most of the MLCCs saw an increase
in the calculated LGLS-values. Because the LGLS-calculation compares a single data
point to a mean, a small increase in LGLS-values is very likely when the LGLS-
values are calculated for data points which are not included in the reference data.
The variations within observed acoustic emission amplitudes also cause increase in
LGLS-values. Another cause of inaccuracies for LGLS-method is the variation within
the reference data, which is mean±std of a set of intact MLCCs. These capacitors
should be selected such that all variables, such as manufacturer, batch, capacitance,
termination type and case size are the same. However, with some MLCCs, there
was two or more different types of acoustic responses found in the reference data.
This causes high variation to the reference data, so comparing individual signals
with the reference curve becomes more inaccurate.
EMI from the measurement setup causes inaccuracies in the LGLS-values. Typi-
cally during a single MLCC column characterization run, the EMI-component in
the measured data caused little variance to the acoustic response curves. When
the measurement setup is altered, as for example when swapping the test board
being inspected, the geometry of the instrument wiring changes, which may cause
differences in the observed acoustic response.
5.3 Ability to recognize defects 43
5.3 Ability to recognize defects
On Board 1, which housed MLCCs of smaller case sizes, the post-bending LGLS-
values were typically between 1 and 4. Columns i and k yielded higher values with
higher variance, as seen in Fig. 4.6a. In Fig. 4.6a, the defective 1206-sized C021
is clearly distinguishable from other MLCCs on column c. 1210-sized MLCCs C081
and C101 on columns i and k yield relatively low LGLS-values, and thus cannot be
identified as detective by LGLS-values.
On Board 2, defective MLCCs of 1812 size on column e can be clearly seen in
Fig. 4.6b. Defective 1812-sized MLCCs on column c yield LGLS-values similar
to the 1812-size MLCCs on column a, although no capacitors on column a were
identified as defective in the X-ray analysis. Defective 2220-sized capacitors C101
and C109 on column i are not highlighted by the LGLS-values, which likely results
from poor acoustic response obtained from the 2220-size capacitors on columns g-
j. Columns k and l yielded better acoustic response, which is indicated by higher
LGLS-values in Figs. 4.6b and 4.7d. Defective MLCCs C221 and C229 on column
k show significantly increased LGLS-values in Fig. 4.6b, whereas C235 on column
l yields one of the lowest LGLS-values on the column, and cannot be identified as
defective by its LGLS-value.
5.4 Consistence of measurements
The 1812- and 1210-sized MLCCs yielded the strongest acoustic response. The pre-
and post-bending response of 1812-sized capacitors was more consistent than 1210-
sized capacitors’, making the LGLS-comparison more precise for 1812-sized MLCCs.
1210-sized capacitors yielded slightly lower voltages, but the acoustic responses of
the 1812-sized capacitors were more consistent, making the algorithmic comparison
more accurate. For many of the 1210-sized capacitors, the acoustic envelopes were
significantly different from each other, even when comparing capacitors on a single
column. Such behavior was observed in both pre- and post-bending measurements,
and might be related to capacitors originating from different manufacturing batches.
The 1206-sized MLCCs yielded weaker acoustic response than 1210- and 1812-sized
ones, but the obtained acoustic envelopes were more consistent than with the 1210-
sized ones. Few 1206-sized MLCCs yielded acoustic envelopes different from others,
akin to the 1210-sized ones.
The 2220-case MLCCs proved to be the most difficult case size to measure because
of their low acoustic response. In addition, providing sufficient mechanical coupling
between sensor and capacitor proved difficult with some of the capacitors, because
the top surface of these MLCCs was slightly concave. This case size yielded rela-
tively consistent acoustic envelopes, with no significant difference between capacitors
within one column.
44 5 Discussion
The overall acoustic emission amplitudes for different case sizes in table 4.2 appear
to somewhat agree with (2.9), which states that the strain in vertical direction in
is proportional to capacitance and inversely proportional to capacitor surface area.
A high C/A-ratio might explain why the 1210- and 1812-sized MLCCs yield the
highest acoustic response. Based solely on (2.9), the 1812-sized capacitors should
yield higher acoustic response than 1210-sized MLCCs, but other factors, such as di-
mensions, mass, material properties and solder joints also contribute to the acoustic
response.
45
6 Conclusions
It was shown that mechanical defects in an MLCC alter the acoustic response of
the MLCC, and such defects can be detected using a piezoelectric point contact
sensor. The algorithm for defect detection presented in this thesis partially succeeds
in recognizing defects in multilayer ceramic capacitors. The biggest challenges of
the method are in providing good and repeatable mechanical contact between the
point contact sensor and MLCC, and the variation within the reference sample of
capacitors.
The mechanical contact issue could be improved by using a point contact sensor
with the protective collar removed from surrounding the contact point. The contact
point could also be placed on the MLCC more accurately by using a servo-controlled
frame for the sensor, for example.
It appears that another kind of data-analysis method would be needed for reliable
defect detection method. Although the defect-related changes can often be visually
observed from the acoustic response envelope, the LGLS-method often yields ”false
alarms”, because either
(1) The overall amplitudes of the envelopes differ because of variations in the
mechanical contact between the sensor and MLCC, or because of the EMI-
related component in the measurement data, or
(2) The reference sample contains capacitors with significantly different acoustic
responses, resulting in an inaccurate reference envelope with high variance.
Issue (1) could be alleviated by improving the measurement setup as suggested.
The contribution of the EMI-component could be reduced by taking a measurement
run approximately mm above each MLCC, LS-fitting the observed EMI-component
into the acoustic response envelope, and then subtracting the fit. Multiple measure-
ment runs could also be preformed on a single MLCC to obtain an average acoustic
response.
Issue (2) would be more difficult to address, because in ideal situation, the reference
data would be obtained from the capacitor itself before physical damage occurs.
In a production-line application, an acoustic response envelope could be compared
with several different reference envelopes, obtained from different batches etc. of a
certain type of capacitor.
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