IEC TS 62758:2012
(Main)Calibration of space charge measuring equipment based on the pulsed electro-acoustic (PEA) measurement principle
Calibration of space charge measuring equipment based on the pulsed electro-acoustic (PEA) measurement principle
IEC/TS 62758:2012(E) presents a standard method to estimate the performance of a pulsed electro-acoustic (PEA) measurement system. For this purpose, a systematic procedure is recommended for the calibration of the measurement system. Using the procedure, users can estimate whether the system works properly or not.
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Standards Content (Sample)
IEC/TS 62758 ®
Edition 1.0 2012-09
TECHNICAL
SPECIFICATION
colour
inside
Calibration of space charge measuring equipment based on the pulsed electro-
acoustic (PEA) measurement principle
IEC/TS 62758:2012(E)
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IEC/TS 62758 ®
Edition 1.0 2012-09
TECHNICAL
SPECIFICATION
colour
inside
Calibration of space charge measuring equipment based on the pulsed electro-
acoustic (PEA) measurement principle
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
V
ICS 17.220.99; 29.035.01; 29.080.30 ISBN 978-2-83220-336-1
– 2 – TS 62758 © IEC:2012(E)
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Basic theory for measurement . 8
4.1 Permittivity and induced charge density . 8
4.2 Charge in dielectrics and Poisson’s law . 8
4.3 Coulombic force of charge in electric field . 9
4.4 Reflection and transmission of pressure wave . 9
4.5 Maxwell stress . 9
4.6 Response of linear system . 10
5 Procedure to calibrate the space charge measurement . 10
5.1 Principle of calibration . 10
5.1.1 General . 10
5.1.2 Typical result of calibration measurement . 11
5.2 Sample preparation . 12
5.2.1 Sample for calibration measurement . 12
5.2.2 Sample placement . 13
5.3 Data acquisition . 13
5.3.1 Pulse voltage test . 13
5.3.2 Averaging . 13
5.3.3 Data acquisition for calibration . 14
5.3.4 Signal obtained under short circuit condition . 15
5.4 Data processing and calibration . 15
5.4.1 Deconvolution . 15
5.4.2 Calibration for horizontal axis and calculation of waveform for electric
field distribution . 16
5.4.3 Calibration for electric field and charge density distributions . 16
5.4.4 Confirmation of linearity of measurement . 17
5.4.5 Typical test results by expert members of project team . 17
Annex A (informative) Theory of PEA method . 21
Bibliography . 35
Figure 1 – Theoretical distributions for calibration measurement . 11
Figure 2 – Typical result of calibration measurement . 12
Figure 3 – Drop of silicone oil and sample placement . 13
Figure 4 – Pulse voltage application test . 13
Figure 5 – Dependence of averaging number . 14
Figure 6 – Measurement of waveform for calibration . 15
Figure 7 – Confirmation of absence of space charge accumulation during d.c. voltage
application for calibration . 15
Figure 8 – Deconvolution and calibration . 16
Figure 9 – Calibration for electric field and charge density distributions . 17
TS 62758 © IEC:2012(E) – 3 –
Figure 10 – Confirmation of linearity measurement . 17
Figure 11 – Results of calibration test by research Group A . 18
Figure 12 – Results of calibration test by research Group B . 18
Figure 13 – Results of calibration test by research Group C . 19
Figure 14 – Results of calibration test by research Group D . 19
Figure 15 – Results of calibration test by research Group E . 19
Figure A.1 – Principle of acoustic wave generation in PEA method . 22
Figure A.2 – Pressure wave propagation in PEA measurement system . 24
Figure A.3 – Response of piezo-transducer . 25
Figure A.4 – Transform from pressure to amount of charge induced on piezo-
transducer . 25
Figure A.5 – Relationship between the pulse width and thickness of piezo-transducer . 26
Figure A.6 – Adequate spatial resolution . 27
Figure A.7 – Example of two types of signal . 29
Figure A.8 – Calculation flow for deconvolution . 30
Figure A.9 – Effect of Gaussian filter . 31
Figure A.10 – PEA measurement apparatus . 32
Figure A.11 – Equivalent circuit for voltage application . 33
Figure A.12 – Equivalent circuit for signal detection . 34
Table 1 – Measurement resolution . 20
– 4 – TS 62758 © IEC:2012(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
CALIBRATION OF SPACE CHARGE MEASURING EQUIPMENT BASED ON
THE PULSED ELECTRO-ACOUSTIC (PEA) MEASUREMENT PRINCIPLE
FOREWORD
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Technical specifications are subject to review within three years of publication to decide
whether they can be transformed into International Standards.
IEC 62758, which is a technical specification, has been prepared by technical committee 112:
Evaluation and qualification of electrical insulating materials and systems.
TS 62758 © IEC:2012(E) – 5 –
The text of this technical specification is based on the following documents:
Enquiry draft Report on voting
112/206/DTS 112/219/RVC
Full information on the voting for the approval of this technical specification 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 stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• transformed into an International Standard,
• reconfirmed,
• withdrawn,
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• amended.
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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 document using a
colour printer.
– 6 – TS 62758 © IEC:2012(E)
INTRODUCTION
The pulsed electro-acoustic (PEA) method has been used to measure space charge
distribution in dielectric materials by many researchers, and it has been accepted, in general,
as a useful method to understand the electrical properties of dielectric materials. However,
since PEA measurement equipments have been developed/used independently by different
researchers over the world, there has not yet been any standard way to evaluate whether a
system works properly. The IEC has therefore established a project team to create a standard
procedure to evaluate PEA measurement equipment. This technical specification is the result.
TS 62758 © IEC:2012(E) – 7 –
CALIBRATION OF SPACE CHARGE MEASURING EQUIPMENT BASED ON
THE PULSED ELECTRO-ACOUSTIC (PEA) MEASUREMENT PRINCIPLE
1 Scope
IEC 62758, which is a technical specification, presents a standard method to estimate the
performance of a pulsed electro-acoustic (PEA) measurement system. For this purpose, a
systematic procedure is recommended for the calibration of the measurement system. Using
the procedure, users can estimate whether the system works properly or not.
2 Normative references
None.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
space charge
accumulated charge in materials
Note 1 to entry: This technical specification deals with the space charge in bulk and on surfaces of dielectric
materials.
3.2
pulsed electro-acoustic method
PEA
technique for measuring space charge density distribution in solid dielectric materials
Note 1 to entry: In this technique, the pressure wave that is generated from the charge layer in a material
specimen by applied pulse voltage to the specimen is observed using piezo-electric transducer attached behind an
electrode contacted to the specimen. Details of measurement theory are described in Clause A.1.
3.3
piezo-electric transducer
sensor to detect the intensity of the pressure wave
Note 1 to entry: By applying the pressure wave, the charge is proportionally induced on the surface of the
transducer. By connecting an adequate external circuit, the induced charge is converted to voltage signal. In the
PEA measurement, the film or plate shaped piezo-electric transducer is usually used. The pressure wave intensity
is measured as a voltage signal across the transducer when the wave propagates through the transducer. Details
of the measurement procedure are described in A.1.3.
3.4
calibration
set of operations that establish, under specified conditions, the relationship between values of
quantities indicated by measuring instrument or measuring system, or values represented by
a material measure of a reference material, and the corresponding values obtained by a
theoretical model
[SOURCE: IEC 60050-394:2007, definition 394-40-43, modified – the words "obtained by a
theoretical model" replace "realized by standards".]
Note 1 to entry: This is the standard way to estimate the performance of a PEA measurement system. In the PEA
measurement, the pressure wave generated from the charge layer in the material is measured as a voltage signal.
To obtain the charge density distribution, it is necessary to calibrate the measured voltage signal to the charge
– 8 – TS 62758 © IEC:2012(E)
density distribution. Therefore, in this technical specification, the calibration means the procedure to calculate the
charge density distribution from the measured voltage signal.
3.5
deconvolution
procedure to recover the voltage signal from the distorted one
Note 1 to entry: The measured voltage signal is usually distorted by the reflection of the pressure wave at the
interfaces between materials constituting the measurement system, the characteristic of the voltage signal
detecting circuit and the induced noise with applied pulse voltage. To recover the voltage measured signal, a so-
called de-convolution technique is usually used. The details of the deconvolution procedure are described in
Clause A.2.
4 Basic theory for measurement
4.1 Permittivity and induced charge density
When a d.c. voltage V (V) is applied to a film or sheet shaped dielectric material with
dc
thickness of d [m] through the attached electrodes, positive and negative charges with
densities of σ and –σ (C/m ) are induced at the interfaces between the material and the
0 0
electrodes. The constant average electric field E (V/m) and the charge density are ideally
dc
described by the following equations:
(1)
V
dc
E =
dc
d
σ = εE
(2)
0 dc
Where ε is the permittivity of the dielectric material described with the unit of (F/m). It is also
described using the permittivity in vacuum ε = 8,854 x 10 (F/m) as follows:
ε = ε ε
(3)
0 r
where the non-dimensional coefficient ε is called the relative permittivity.
r
4.2 Charge in dielectrics and Poisson’s law
Here, the axis z is defined in the direction of thickness of a film or a sheet shaped dielectric
material. When the charge is accumulated in the material with a volume density of ρ(z) (C/m ),
electric field distribution E(z), under static conditions, is described using the following
Poisson’s equation:
E(z) = ρ(z)dz
(4)
∫
ε ε
0 r
The electric potential distribution in the material V(z) is described as
(5)
V (z) = − E(z)dz
∫
TS 62758 © IEC:2012(E) – 9 –
4.3 Coulombic force of charge in electric field
When charge q (C) is put in the electric field E (V/m), the following Coulombic force F (N) acts
on the charge:
(6)
F = qE
When the charge q is homogeneously distributed as a perpendicular layer to z axis, the
2 2
charge density of the layer σ (C/m ]) is calculated by using the area of the material S (m ) as
σ = q/S. Therefore, the pressure wave p (Pa = N/m ]) generated from the charge layer when
the electric field E is applied to the material is
p = σE (7)
When the above electric field is generated by the pulse voltage with very short duration, the
pulse pressure wave generates from each charge layer and it propagates in the material.
4.4 Reflection and transmission of pressure wave
When a pressure wave propagates through the interfaces between different materials, it is
divided into transmitted and reflected waves. The ratio of this division is determined by so
called acoustic impedance Z (Pa s/m = N s/m ). The acoustic impedance Z is obtained by the
following equation:
Z = mu (8)
where m ( kg/m ) and u (m/s) are density and acoustic velocity in the material.
When the pressure wave propagates from material 1 to material 2, the transmission and
reflection ratios K and K are described using the acoustic impedances of the materials Z
t r 1
and Z as
2Z
K =
(9)
t
Z + Z
1 2
Z − Z
(10)
2 1
K =
r
Z + Z
1 2
When the pressure wave is generated at the interface between material 1 and 2, the ratio of
propagation towards material 2, say K is described as
g2
Z (11)
K =
g 2
Z + Z
1 2
4.5 Maxwell stress
When a voltage V is applied across electrodes attached to a sheet or a film dielectric material
with thickness of d and permittivity of ε, the following Maxwell stress F (N) is generated at the
interfaces between the material and electrodes:
– 10 – TS 62758 © IEC:2012(E)
1 V 1
dc
F = ε = E×σ (12)
2 d 2
4.6 Response of linear system
When a delta function δ(t) (impulse) as a function of time t (s) is input into a linear system, the
output of it h(t) is called “transfer function”. The relationship between h(t) and δ(t) is described
using the following convolution equation:
+∞
h(t) = δ (τ )h(t −τ )dτ
(13)
∫
−∞
When a certain function voltage v (t) inputs the linear system, the output voltage v (t) is
in out
obtained using h(t) as
+∞
v (t) = v (τ )h(t −τ )dτ
(14)
out in
∫
−∞
In the frequency domain, the above relationship is converted into the following equation:
V (f) = H(f) V (f) (15)
out in
where V (f), H(f) and V (f) are functions of frequency f (Hz) converted from v (t), h(t) and
out in out
v (t), respectively.
in
5 Procedure to calibrate the space charge measurement
5.1 Principle of calibration
5.1.1 General
A basic principle of calibration for obtaining charge density distribution from the PEA signal is
described below. Generally in calibration for measurement, we need a signal from a
measuring object which value is known absolutely. In the case of the PEA measurement for a
flat sheet sample, the induced surface charges by applied d.c. voltage at the interfaces
between the sample and electrodes are theoretically obtained when the permittivity of the
sample is known. Therefore, the following calibration process is based on the ideal
measurement of the surface charges under d.c. voltage application.
Consider a virgin (not having space charges in its bulk) dielectric (flat) sheet sample, placed
between a set of electrodes. The sample thickness and relative permittivity are d and ε ,
r
respectively. When a small d.c. voltage V is applied to the sample, positive and negative
dc
surface charges +σ and -σ are induced at interfaces between the sample and electrodes,
0 0
anode and cathode, respectively. Here, the voltage V is assumed to be relatively low so that
dc
it is not enough to generate any space charge in the bulk of sample. Since these surface
charges are located at quite thin layers, they can be treated as impulse (delta) functions on a
positional axis z along the thickness of the sample as shown in Figure 1(a). The value of
surface charge density σ can be calculated by the following equation:
σ = ε ε E = ε ε V /d (16)
0 0 r dc 0 r dc
TS 62758 © IEC:2012(E) – 11 –
where E and ε are applied average electric field and the permittivity in vacuum, respectively.
dc 0
Under the electric field E , when a pulsive voltage V (t) is superimposed on V , pulsive
dc p dc
pressure waves p (t) and p (t) are generated from the surface charges (see Annex A). In the
0 d
PEA method, the pressure wave p(t) generated from the charge distribution ρ(z) is observed
using a piezo-electric sensor which transforms the pressure to voltage signal V (t) (see A.1.3).
s
Therefore, the calibration procedure enables to transform the obtained V (t) to the charge
s
density distribution ρ(z). Since the surface charge density σ can be theoretically calculated
using Equation (1), the signal voltage of V (t) can be easily calibrated by observing σ . On the
s 0
other hand, the position z can be calculated by the following relationship:
z = u t (17)
sa
where u is acoustic velocity in the sample.
sa
However, in general, it is hard to obtain an accurate value of relative permittivity of a sample.
Therefore, the actual calibration should be carried out using some parameters that are easily
measured. As shown in Figure 1(b), the electric field distribution E(z) in the sample can be
obtained by integral calculation of charge density distribution ρ(z). It can be seen that the
electric field distribution E(z) in the sample for the calibration measurement shown in
Figure 1(b) has a simple rectangular shape with the value of flat portion, E = V /d. The
dc dc
thickness of the sample d and the applied d.c. voltage V are easy to measure. Therefore,
dc
calibration using the electric field distribution E(z) is proposed in this specification.
Anode
σ
dc
Surface
Cathode charge
a)
0 d
Surface
charge
-σ
dc
0 d
b)
Average
E
electric field
dc
V
Applied
dc
voltage
c)
0 d
IEC 1646/12
Sample thickness
Figure 1(a) – Charge density Figure 1(b) – Electric field Figure 1(c) – Electric potential
distribution distribution distribution
Figure 1 – Theoretical distributions for calibration measurement
5.1.2 Typical result of calibration measurement
Figure 2 shows a typical result of calibration measurement. In this measurement, a PMMA
(poly (methyl-methacrylate)) sheet specimen with a thickness of d = 500 µm is used.
Figure 2(a) shows charge density distribution obtained by applying a d.c. voltage of V = 2 kV
dc
to the sample. If the measurement is ideally carried out for the sample without any space
charge in its bulk, the charge density distribution should be a pair of delta functions as shown
in Figure 1(a). However, they are observed as a pair of peaks with a certain width that is
– 12 – TS 62758 © IEC:2012(E)
determined by both of the pulse widths t of the applied pulse voltage and acoustic wave
vp
traveling time t passing through the piezo-sensor (see A.1.4). The half-value width, d of the
p
r
first peak in this measurement result is defined as a positional resolution of this measurement.
An integral calculation of this peak must be equal to the surface charge density σ shown in
Figure 1(a).
a) 0
−σ = ε ε E
r
dc 0 dc
-5
-100 100 200 600
0 300 400 500
0 0
b)
-2
-5
E = 4 kV/mm
dc
-4
-10
-100 100 200 600
0 300 400 500
2,0
1,5
1,0
V = 2 kV
dc
c)
0,5
0,0
-100 100 200 600
0 300 400 500
Position z (µm)
PMMA 500 µm, V = 2 kV (E = 4 kV/mm)
DC dc
IEC 1647/12
Figure 2(a) – Charge density Figure 2(b) – Electric field Figure 2(c) – Electric potential
distribution distribution distribution
Figure 2 – Typical result of calibration measurement
5.2 Sample preparation
5.2.1 Sample for calibration measurement
A commercially available PMMA sheet with a thickness range of 0,5 mm to 1 mm may be used
for the calibration measurement. The calibration measurement shall be carried out under the
applied electric field which gives a linear relationship between calculated average electric
field and applied d.c. voltage as shown in Figure 10. It is recommended that the electric field
strength is within a range of 5 kV/mm to 30 kV/mm, providing the application time is short
enough (typically 5 min) not to accumulate space charge. Before the calibration measurement,
the thickness of the sample shall be accurately measured using a micrometer. If there are
foreign objects or dust on the surface of the sample, the interface adherence between sample
and electrodes may be lost. Since the interface adherence is important to make the signal
pressure wave smoothly propagate, the sample surfaces shall be cleaned up with soft cloth to
remove foreign objects and dusts. A sample with evaporated electrodes may also be used for
the calibration measurements.
It should be mentioned here that the PMMA sample could acquire space charges even below
30 kV/mm, above about 303 K and maintain the space charges for a long time. Therefore,
samples used for calibration shall either be not subjected to high temperatures in their history
or it must be ensured that the voltage levels are not so high as to cause accumulation of
space charges when subjected to high temperatures.
U(z) (kV)
E(z) (kV/mm) p(z) (µC/cm )
ε ε E(z) (µC/cm )
TS 62758 © IEC:2012(E) – 13 –
5.2.2 Sample placement
Prior to placing the sample between electrodes, in order to help propagation of pressure
waves signal at interfaces between electrodes and the sample, both surfaces of the sample
should be wetted with commercially available silicone oil. A semi-conductive layer should be
placed between the sample and the metal upper electrode to improve the acoustic impedance
matching (see A.1.2). Commercially available semi-conductive sheets can be used for this
purpose. Adequate force shall be applied to the sample to keep tight contact with the
electrodes using a jig mounted to the measurement system.
Upper electrode
Mechanical
Drop of silicone oil
force
Drops of
Semi-conductive
silicone oil
layer
Sample
Lower electrode
IEC 1648/12
Figure 3 – Drop of silicone oil and sample placement
5.3 Data acquisition
5.3.1 Pulse voltage test
In the PEA method, the signal is obtained by applying a pulse voltage to the sample
repeatedly. However, when only the pulse voltage is applied to the sample without any d.c.
voltage stress, a very small signal is observed (see A.1.1). Such a signal should be small
enough to be neglected in the calibration measurement. Therefore, before the calibration
measurement, the signal obtained by only the pulse voltage application shall be observed.
The signal shall be obtained with an adequate number of averaging (see 5.3.2). Figure 4
shows a typical measurement result obtained by applying the pulse voltage of 500 V with
duration of 14 ns to the PMMA sample with a thickness of 0,5 mm. It may be seen that there
is no remarkable signal in Figure 4, and such a kind of result is advisable.
0.04
0,02
0.02
0,01
Condition：
Pulse voltage 500 V
Pulse width 14 ns
-0,01 -0.02
Sample PMMA (500 µm)
No-signal
-0,02 -0 04
IEC 1649/12
Time (ns)
Figure 4 – Pulse voltage application test
5.3.2 Averaging
Generally, in the PEA method, the signal is obtained using the averaging technique that is
carried out on the data (obtained by repeatedly applying the pulse voltage to the sample). The
suitable minimum number of times for averaging depends on measurement conditions and
characteristics of equipment. A signal obtained with a deficient number of times of averaging
would be inaccurate for calibration. Figure 5 shows typical waveforms with various averaging
number. The waveforms are obtained by applying d.c. voltage of 4 kV and pulse voltage of
Voltage V (V)
– 14 – TS 62758 © IEC:2012(E)
500 V with duration of 14 ns to the PMMA sample with a thickness of 1 mm. As shown in
Figure 5(a), the waveform without averaging seems to be hidden in white noise. With the
number of times of averaging increasing, the noise level decreases as may be seen in Figures
5(b) and 5(c), and consequently the S/N (signal to noise) ratio of the waveform becomes
higher. In this example, the wave form shown in Figure 5(c) is preferable for calibration.
a)
-5
-10
PMMA 1,0 mm
-15
0 1 000
Position z (µm)
b)
-2
-4
-6
PMMA 1,0 mm
-8
0 1 000
Position z (µm)
c)
-2
-4
-6
PMMA 1,0 mm
-8
0 1 000
Position z (µm)
IEC 1650/12
Figure 5(a) – Signal without Figure 5(b) – Averaged signal Figure 5(c) – Averaged signal
averaging (100 times) (10 000 times)
Figure 5 – Dependence of averaging number
5.3.3 Data acquisition for calibration
Immediately after d.c. voltage application to the PMMA sample, the PEA signal wave form is
measured by repeatedly applying the pulse voltage with an adequate averaging number. To
confirm linearity of the results, measurements should be carried out under at least 3 levels of
d.c. electric field E below 30 kV/mm. In the obtained waveforms, time duration between
dc
peaks t must be measured and the acoustic velocity u = d/t , shall be calculated.
pp sa pp
Signal voltage V (mV) Signal voltage V (mV) Signal voltage V (mV)
s s s
TS 62758 © IEC:2012(E) – 15 –
0,02
t
pp
0,01
Condition:
V = 4 kV
dc
t = 200 ns
pp
-0,01
E = 8 kV/mm
dc
4kV
-0,02
0 200
Time (ns) IEC 1651/12
Key
t time between first and second peaks
pp
d/t = u acoustic velocity in sample
pp sa
V /d = E d.c. electric field
dc dc
Figure 6 – Measurement of waveform for calibration
5.3.4 Signal obtained under short circuit condition
After obtaining the signal under d.c. stress, as described above, the d.c. stress is removed,
and data is obtained under a short-circuit condition. If the applied d.c. voltage is so excessive
that it might cause space charge accumulation, the accumulated space charge should be
observed under a short-circuit condition immediately after removal of the d.c. voltage.
Therefore, it is necessary to observe the signal waveform under a short-circuit condition
immediately after obtaining the data for calibration. Figure 7 shows a procedure and typical
results concerning this confirmation. Figure 7(a) shows a waveform obtained under a short-
circuit condition before applying d.c. voltage for calibration. This result is the same as the
result for “pulse voltage test” mentioned in 4.3.1. Figure 7(b) is the data obtained under d.c.
voltage for calibration. Then the data under short-circuit condition shall be taken as shown in
Figure 7(c) to compare with the one under short circuit condition before the d.c. voltage
application. When the waveform (a) obtained before the d.c. voltage application is the same
as the waveform (c) obtained afterwards, it can be said that the d.c. voltage magnitude is
proper for the calibration.
0,02 0,02 0,02
0,01 0,01 0,01
0 0 0
-0,01 -0,01 -0,01
4kV
-0,02 -0,02 -0,02
0 200 0
0 200 200
Time (ns) Time (ns) Time (ns)
IEC 1652/12
Figure 7(a) – Measurement only Figure 7(b) – Measurement for Figure 7(c) – After
with pulse voltage application calibration (under d.c. voltage measurement (under
(under short circuit condition) application) short-circuit condition)
Figure 7 – Confirmation of absence of space charge accumulation
during d.c. voltage application for calibration
5.4 Data processing and calibration
5.4.1 Deconvolution
Obtained data for calibration ordinarily (or generally) includes some distortion because of the
acoustic reflection and/or due to characteristic nature of the detection circuit. Therefore, a
Voltage V (V)
Voltage V (V)
Voltage V (V)
Voltage V (V)
– 16 – TS 62758 © IEC:2012(E)
deconvolution technique is usually applied to the obtained data (see Clause A.2). When the
deconvolution technique is carried out, the high frequency noise is increased. Therefore, a
low pass filter is also applied in addition to the deconvolution technique. By applying
adequate deconvolution and filtering procedure, the waveform with two peaks is obtained as
shown in Figure 8(a).
d
d
r
Width at half
V
dc
height: d
r
d
4kV 4kV 4kV 4kV 4kV 4kV
0 525
0 200 0 525
Time t (ns) Position z (m) Position z (m)
z
z = u t z' dz'
sa
IEC 1653/12
Figure 8(a) – Deconvoluted Figure 8(b) – Waveform for Figure 8(c) – Waveform for
waveform positional charge density electric field distribution
distribution
Figure 8 – Deconvolution and calibration
5.4.2 Calibration for horizontal axis and calculation of waveform for electric field
distribution
Using Equation (17), the horizontal axis in “time” shown in Figure 8(a) is converted to
st
“position” as shown in Figure 8(b). In this case, the width at half height of the 1 peak “d ”
r
shall be measured. The ratio k of d to the sample thickness d (k = d /d x 100 /%)) is defined as
r r
spatial resolution of this measurement. The spatial resolution between 2 % to 10 % is
preferable (see A.1.4). To calibrate the vertical axis in charge density distribution, a waveform
for the electric field distribution is calculated. By integrating positional charge distribution
shown in Figure 8(b), the waveform for electric field distribution is obtained as shown in
Figure 8(c).
5.4.3 Calibration for electric field and charge density distributions
As shown in Figure 9(a), the waveform for electric field distribution shall have a flat shape. As
shown in Figure 9(b), the vertical axis of the waveform for electric field is decided as the value
of flat part is equal to the electric field E (= V /d). Then the charge density distribution is
dc dc
calculated by differentiation using a nominal value of relative permittivity , as shown in
r
Figure 9(c). Since the value of the vertical axis in charge density distribution depends on , it
r
is necessary to specify the numerical value used for the calibration.
Arbitrary unit
Arbitrary unit
Arbitrary unit
TS 62758 © IEC:2012(E) – 17 –
20 6
V /d
dc
00 0
0 0
-10 -3
4kV 4kV 4kV 4kV
4kV
22 -20 -6 6
0 525 0 525
0 525
Position z (m) Position z (m)
Position z (m)
E(z)
(z)
E = V /d IEC 1654/12
dc dc 0 r
z
Figure 9(a) – Waveform for Figure 9(b) – Calibration of electric Figure 9(c) – Calculated charge
electric field distribution field distribution using measured distribution from calibrated
average electric field electric field distribution
Figure 9 – Calibration for electric field and charge density distributions
5.4.4 Confirmation of linearity of measurement
When a calibration, as described in 4.4.3, is successfully achieved, the other measurements
should be carried out under different electric fields E using the same procedure mentioned
dc
above in order to confirm linearity of such a calibration. Observations of signals under a short-
circuit condition before and after the measurement with d.c. stress are also required to check
whether the adequate d.c. stress is applied to the sample. When the data processing and
electric field calibration are carried out, the same parameters obtained by the first calibration
process have to be used. An additional two or three results should be obtained. When the
values of electric fields being proportional to the applied voltages are obtained in all cases,
the calibration procedure is considered valid.
4 kV
8 kV
12 kV
-200
-400
0 500 Applied d.c. voltage V (V)
dc
Position z (m)
IEC 1655/12
Figure 10 – Confirmation of linearity measurement
5.4.5 Typical test results by expert members of project team
Figures 11 to 16 show typical calibration test results obtained by various research groups of
expert members in this project. Table 1 shows sample thickness, permittivity and resolution of
measurements. Judging from the results, the calibrated space charge distributions are
different because of the usage of different system with different resolutions or permittivities.
For example, in the case of measurement results obtained using high resolution system, the
first peaks are larger than those obtained using lower resolution system. However, the
obtained electric field distributions are mostly the same. It means that the space charge
distributions shall be shown with the description of the measurement resolution and the
permittivity. Anyway, the electric fields in all results seem to be proportional to the applied
average electric fields. Therefore, the calibrations must be fairly carried out in all results.
Electric field E(z) (kV/mm)
Electric field E(z) (kV/mm)
Calculated electric field E (kV/mm)
dc
Charge density (z) (C/m )
– 18 – TS 62758 © IEC:2012(E)
4 kV
8 kV
12 kV
7,55 kV/mm 10
15,10 kV/mm
22,65 kV/mm
-10
-20
0 200 400 600
Position z (µm) Position z (µm) IEC 1656/12
Figure 11(a) – Electric field distribution Figure 11(b) – Charge density distribution
Figure 11 – Results of calibration test by research Group A
0,4 20
4 kV
4 kV
8 kV
8 kV
12 kV
12 kV
0,2 10
0 0
-0,2 -10
-0,4 -20
0 500 0 500
Position z (µm) Position z (µm)
IEC 1657/12
Figure 12(a) – Electric field distribution Figure 12(b) – Charge density distribution
Figure 12 – Results of calibration test by research Group B
Electric field E(z) (kV/mm)
Electric field E(z) (MV/cm)
Charge density ρ(z) (C/m )
Charge density ρ(z) (C/m )
TS 62758 © IEC:2012(E) – 19 –
Applied field:
4 kV/mm
8 kV/mm
12 kV/mm
16 kV/mm
-4
-5
Applied field:
-8
-4 kV/mm
-10
-8 kV/mm
-12
-12 kV/mm
-15 kV/mm
-15
-16 -16 kV/mm
-18 kV/mm
-20
-20
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
Position z (µm) Position z (µm)
IEC 1658/12
Figure 13(a) – Electric field distribution Figure 13(b) – Charge density distribution
Figure 13 – Results of calibration test by research Group C
00,4.4
4,0 kV
4.0kV 4,0 kV
No. 1 No. 1
4kV
No.1
No.1
88,.00 kkVV
8,0 kV
8kV
12kV
12 kV
112 k2kVV
0.2
0,2 1100
0.0
0,0 0
-10
--00,.22 -10
-20
-0.4
-0,4 -20
0 520
0 520
0 520
0 520
IEC 1659/12
Position z (µm)
Position z (µm)
Figure 14(a) – Electric field distribution Figure 14(b) – Charge density distribution
Figure 14 – Results of calibration test by research Group D
0,4 30
Q-4
...
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