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New function for representing IEC 61000-4-2 standard electrostatic discharge current
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New function for representing electrostatic discharge (ESD) currents according to the IEC 61000-4-2 Standard current is proposed in this paper. Good agreement with the Standard defined parameters is obtained. This function is compared to other functions from literature. Its first derivative needed for field calculations is analyzed in the paper. Main advantages are simplified choice of parameters, possibility to obtain discontinuities in the decaying part, and zero value of the function first derivative at t=0 +. Parameters of the function are obtained by using Least-squares method (LSQM).
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FACTA UNIVERSITATIS
Series: Electronics and Energetics Vol. 27, No 4, December 2014, pp. 509 - 520
DOI: 10.2298/FUEE1404509J
NEW FUNCTION FOR REPRESENTING IEC 61000-4-2
STANDARD ELECTROSTATIC DISCHARGE CURRENT
Vesna Javor
University of Niš, Faculty of Electronic Engineering of Ni š, Serbia
Abstract. New function for representing electrostatic discharge (ESD) current s
according to the IEC 61000-4-2 Standard current is proposed in this paper. Good
agreement with the Standard defined parameters is obtained. This function is compared
to other functions from literature. Its first derivative needed for field calculations is
analyzed in the paper. Main advantages are simplified choice of parameters, possibility
to obtain discontinuities in the decaying part, and zero value of the function first
derivative at t=0+. Parameters of the function are obtained by using Least-squares
method (LSQM).
Key words: Analytically extended function, electromagnetic compatibility, electrostatic
discharge current, IEC 61000-4-2, least -squares method
1. INTRODUCTION
Nowadays, electromagnetic compatibility (EMC) gains in its importance with the
development and global marketing of electronic components, electric al devices and systems,
so as with public concern for electromagnetic pollution. Electrical engineers and industrial
professionals, dealing with the design and manufacture of such products, have to take into
account many aspects of EMC in order to obtain and market a product which complies
with EMC standards and directives. Besides utility and functionality, better appearance
but lower costs as possible, any device, equipment or system has to comply with its
electromagnetic environment and to function satisfactorily - without introducing intolerable
electromagnetic disturbances (EMDs) to other in its environment or being disturbed by an
external influence from the environment [1].
Electrostatic discharges (ESDs) are common phenomena and among very important
EMC aspects of concern. Lightning discharges are discharges of static electricity, although
their processes are in fact transient, and far from being "static" phenomena. These discharges
produce the most powerful EMDs for electrical systems. In general, electrostatic discharges
are dangerous in many technological processes: in textile industry, petrol industry, powder
production, food industry, chemical industry, manipulating with various substances and
transporting them, etc. However, there are also useful applications of ESDs: in medical
Received July 1, 2014
Corresponding author: Vesna Javor
Faculty of Electronic Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia
(e-mail: vesna.javor@elfak.ni.ac.rs)
510 V. JAVOR
devices as defibrillators, in photocopiers , spray painting, electrostatic precipitators, electrostatic
dusters, some technological processes in producing fabrics, etc.
An ESD occurs between two objects at a distance close enough for the sufficient
difference of their electrostatic potentials to produce breakdown. Static electricity may
appear not only on parts of machines and after separating different materials in contact, but
also on humans. In every day's life, human body may discharge through fingers or other
body parts via skin or small metal pieces, such as keys, to some objects. This may happen at
working places which is dangerous in production of electronic components. It is well
known that integrated circuits and fast complementary metal oxide semiconductor
components, so as digital devices in general, are more sensitive than analog, although ESD
may have influence on any kind of electrical devices and systems.
The Standard IEC 61000-4-2 [2], [3], and European standard EN 61000-4-2 (issued
by CENELEC) deal with the typical waveform of electrostatic discharge current, range of
test levels, test equipment, test set-up and procedures related to electrostatic discharge
immunity requirements for the equipment under test (EUT). Scientific Committee
SC77B, WG 10, is also ma intaining the Standard 61000-4-3 on radiated radio-frequency
electromagnetic field immunity test, ([4],[5]). Recent status of these standards and the
elements of maintenance are discussed in [6].
Test generators current waveform is defined in IEC/EN 61000-4-2 standards for contact
ESD testing: its initial peak current, current level at 30ns, current level at 60ns, so as rise
time from 10% to 90% of the initial peak current. In order to improve the repeatability of
tests, tolerance of the rise time of electrostatic discharge current waveform was expanded in
the Ed.2 of the standard [3]. The oscilloscope bandwidth was increased beyond 1GHz, so to
measure rise time more accurately [7]. Minimum 2GHZ oscilloscope bandwidth is needed
according to the IEC 61000-4-2, Ed.2 . ESD generators simulate real discharges thus enabling
repetitive test procedures for EUT. However, ESD test generator current waveshape depends
on various conditions, as discussed in [8], and these are: charging voltages, approach
speeds, types of electrodes, relative arc length, humidity, etc. Parameters of the real ESD
testers are also discussed in [9], and the influence of various conditions on current
waveshape is investigated using simulation with PSpice in [10]. A modified test generator
with a reference waveshape close to the standard one and the corresponding equation for
that waveshape are discussed in [11]. Another equation was proposed already in [12] in order
to study ESD in coaxial cable shields . A mathematical function accurately representing
standard ESD current is necessary for computer simulation of such phenomena, for
verification of test generators and for better modeling of ESDs.
Mathematical functions for modeling lightning discharge currents are used in literature
to approximate currents of ESD testing waveforms, but they have some disadvantages
along with their complexity, as described in [13]. New function which may represent both
typical ESD and lightning currents, as given in corresponding standards, is proposed in this
paper in order to make further steps in research and use advantages of computer simulations
of the problem. Any function is more useful for such purposes if simple as possible,
whereas still capable to satisfactorily approximate experimentally measured characteristics.
Channel-base current function (CBC) is proposed in [14] for typical and experimental
lightning stroke currents, and two-peaked function in [15]. For representing ESD currents
an analytically extended function (A EF) , as the sum of two or three CBC expressions, is
used in this paper.
New Function for Representing Electrostatic Discharge Current 511
The procedure of choosing function parameters has to be further investigated in order to
make it simple for any user. The se parameters may be estimated applying different procedures
such as Genetic algorithm (GA) as in [17], or Marquardt least-squares method (MLSM) as
done in [18] for the lightning currents. In this paper Least-squares method (LSQM) is used.
Firstly, the analysis of usually used functions is given, and after that the comparison of the
proposed function to the IEC 61000-4- 2 Standard one, so as the choice of its parameters and
the analysis of the first derivative.
2. FUNCTIONS FOR APPROXIMATING E LECTROSTATIC DISCHARGE C URRENTS
In IEC 61000-4-2 standard, ESD current peak is described with 3.75A/kV, current value
at 30ns with 2A/kV,
at 60ns with 1A/kV. The tolerance for ESD contact mode
currents is
10% for I peak in Ed.1,
15% in Ed.2,
30% for
and
(in both
Ed.1 and Ed.2). Rise time
in the range 0.7
1ns is defined in Ed.1 for a typical contact
mode discharge, and 0.6
1ns in Ed.2 of the Standard. Parameters of ESD currents are
given in Table 1, for the defined discharge test voltages. Discharges may be contact or air
ESDs. According to the standard, application of contact discharges is preferably used for
testing, whereas air discharge only if not available otherwise. Test level voltages range
between 2 and 8kV for contact discharges, but between 2 and 15kV for air discharges. The
arc lengths about 0.85mm are common for ESD test generators and for 5kV as discussed in
[11], but level and rise time of ESD currents are less reproducible in the case of air
discharge and depend significantly on humidity, shape of the tip, speed of the tip approach,
etc. ESD of a human through a small piece of metal is simulated with ESD generators for
testing robustness of sensitive electronics toward ESD. Current waveform parameters are
given in Table 1 for 2, 4, 6 and 8kV discharge voltages.
Human-body model (HBM) discharge current may be approximately obtained with a
simple electrical circuit having the charging resistor
, energy-storage capacitor
150pF
10%, and the discharge resistor of
value representing skin, as in Fig.1.
The produced waveshape differs from the test generator ESD currents, so as from the
Standard one. More complex circuits are also suggested in literature.
Table 1 Standard 61000 -4- 2 ESD Current Waveform Parameters
Rise time of the
first peak
Rise time of the
first peak
512 V. JAVOR
Fig. 1 Simple circuit for obtaining typical HBM current waveform [2]
Fig. 2 ESD current waveform given in IEC 61000-4-2
HBM and contact mode discharges are used for verification of ESD test generators,
and the standard ESD current pulse is given in Fig. 2. Some functions from literature are
compared for 4kV ESD and the proposed function is compared to the best fit function of
those and the Standard waveshape.
The following expression is proposed in [19], using four exponential functions
1 1 2 2 3 4
( ) [exp( / ) exp( / )] [exp( / ) exp( / )] i t i t t i t t
, (1)
for i 1 = 498A, i 2 = 148.5A,
1 = 1.4ns,
2 = 1.3ns,
3 = 23.37ns,
4 = 20ns as function
parameters. This function is presented in Figs. 3 and 4 with the dash-dot line.
An expression using two Gaussian functions is proposed for ESD currents in [12] as
the following:
22
22
1 1 2 2
( ) exp[ ( ) /σ ] exp[ ( ) /σ ] i t A t t B t t t
, (2)
for A = 13A, B = 0.4A/ns, t 1 = 5ns, t 2 = 10ns, 1 = 1.414ns, 2 = 35.35ns. This function is
presented in Figs. 3 and 4 with the dash-dot-dot line for A = 13.25A, B = 391A/ns,
t1 = 2ns, t2 = 300ns, 1 = 0.6ns, 2 = 122.2ns, as given in [13]. For the experimental
ESD current described in [16] parameters of (2) are determined by using GA and
minimizing relative error of the current as the following: A = 4.95A, B = 0.27A/ns,
New Function for Representing Electrostatic Discharge Current 513
t1 = 5.18ns, t 2 = 1.62ns, 1 = 9.78ns, 2 = 54.72ns. Using GA method and minimizing
relative error of the current, parameters of (2) in [21] are determined as: A = 5.29A,
B = 0.33A/ns, t1 = 6.07ns, t2 = 9.48ns, 1 = 4.31ns, 2 = 52.03ns.
The pulse function [23] is given with the following expression
0 1 2
( ) [1 exp( / )] exp( / )
p
i t I t t
, (3)
and its binomial expression with
0 1 2 1 3 4
( ) [1 exp( / )] exp( / ) [1 exp( / )] exp( / )
pq
i t I t t I t t
. (4)
For 4kV ESD and the binomial expression (4) of pulse functions, for parameters:
I0 = 106.5A, I1 = 60.5A,
1 = 0.62ns,
2 = 1.1ns,
3 = 55ns,
4 = 26ns, [13], the waveshape
is presented in Figs. 3 and 4 with the long-dash lines.
The trinomial expression of pulse functions is given with
0 1 2 1 3 4
2 5 6
( ) [1 exp( / )] exp( / ) [1 exp( / )] exp( / )
[1 exp( / )] exp( / ),
pq
r
i t I t t I t t
I t t
(5)
and the quadrinomial expression with
0 1 2 1 3 4
2 5 6 3 7 8
( ) [1 exp( / )] exp( / ) [1 exp( / )] exp( / )
[1 exp( / )] exp( / ) [1 exp( / )] exp( / ).
pq
rr
i t I t t I t t
I t t I t t
(6)
The trinomial (5) and quadrinomial (6) expressions provide better approximations [13] of
the ESD current and give results more similar to the goal function, but these functions
have too many parameters.
One function commonly used for lightning currents is applied in [11], having
binomial expression of two Heidler's functions [20]
3
1 1 2
24
12
13
( / )
( / )
( ) exp( / ) exp( / )
ηη
1 ( / ) 1 ( / )
n
n
nn
t
i t i
i t t t
tt
, (8)
for peak correction factors
1/
12
121
exp τ
n
n
and
n
n/1
3
4
4
3
2τ
τ
τ
τ
exp η
.
To approximate the measured human-metal ESD at 5kV current parameters are
chosen as the following: i 1 = 21.9A, i 2 = 10.1A,
1 = 1.3ns,
2 = 1.7ns,
3 = 6ns,
4 = 58ns
and n =3 . For the 4kV discharge parameters values in [13] are chosen as: i 1 = 17.5A,
i2 = 10.1A,
1 = 1.3ns,
2 = 1.7ns,
3 = 8.7ns,
4 = 42ns and n =3 . This function is
presented in Fig.3 with the dot line. After choosing n = 3 as an initial value and using GA
with minimizing relative error of the current, parameters are determined for the
experimental ESD current described in [16] as the following: i 1 = 17.46A, i 2 = 7.81A,
1 = 0.75ns,
2 = 0.82ns,
3 = 3.43ns,
4 = 68.7ns. The waveform approximating the ESD
current from IEC 61000-4-2 Ed.2 [3], for 4kV, is obtained for: i 1 = 16.6A, i 2 = 9.3A,
514 V. JAVOR
1 = 1.1ns,
2 = 2.0ns,
3 = 12ns,
4 = 37ns, n = 1.8, and presented in Figs. 3 and 4 with
the full lines. After choosing
as an initial value in [22] for GA procedure with
minimizing relative error of the current, parameters are calculated for the ESD current as
the following: i 1 = 16.3A, i 2 = 9.1A,
1 = 1.2ns,
2 = 2.05ns,
3 = 11.7ns,
4 = 37.3ns,
n = 1.82.
In [21] is proposed the following function
( ) exp[ ] exp i t At Ct Bt Dt
, (9)
for approximating IEC 61000-4-2 Ed.2 ESD current with the following parameters:
A = 38.1679A/ns, B = 1.0526A/ns, C = 1ns1 , and D = 0.0459ns1 . The function is
presented in Figs. 3 and 4 with the short-dash lines.
Fig. 3 Functions approximating the Standard 61000-4-2 ESD current waveform for 4kV
Rising time is the difference between tB for 90% of the current peak (i 90%=13.5A) and tA
for 10% of the current peak ( i 10%=1.5A). Rising times as in the Standard 61000-4-2 are
obtained with very different waveshapes behaviour in the first 5ns of functions from Fig.
3 as presented in Fig. 4. All the functions are presented from t =0 +, for i max=15A, although
the Standard function rises between 6 and 8 ns, given with tollerably lowered peak value
imax =14A, if i30ns = 8A and i60ns =4A are chosen as reference (Figs. 2 and 5). Two-Gauss
function has the greatest rising time and Wang function the shortest. Four-exponential
expression and Wang function don't have realistic rising part s . Two- Heidler's function
for n=1.8, given with the full lines in Figs. 3 and 4, represent the Standard waveshape
better than the others.
New Function for Representing Electrostatic Discharge Current 515
Fig. 4 Functions approximating the Standard 61000-4-2 ESD current waveform for 4kV
in the first 5ns, with notations from Fig. 3
3. N EW FUNCTION FOR APPROXIMATING E LECTROSTATIC DISCHARGE C URRENTS
An analytically extended function (AEF), with the same expression before and after
time moments of maxima, but for different parameters, is proposed for approximating
ESD currents. Its main advantages are: simply adjustable derivative value, rise time
value, time to the peak value, exact peak values chosen prior to adjusting other parameters
and a suitable waveform with the zero first derivative at the point t =0 +. The function is
continuous, with its first derivative also continuous at any t, so it is of differentiability
class C1 . Higher order derivatives have discontinuities at the points of maximum/minimum , so
the first derivative of the function belongs to class C 0 .
Current function CBC [14] is given with the following expression
1 1 1 1
1
1 1 1 1
( / ) exp[ (1 / )] , 0 ,
() ( / ) exp[ (1 / )] , ,
a
m m m m
b
m m m m
I t t a t t t t
it I t t b t t t t
(10)
and another with
2 2 2 2
2
2 2 2 2
( / ) exp[ (1 / )] , 0 ,
() ( / ) exp[ (1 / )] , ,
c
m m m m
d
m m m m
I t t c t t t t
it I t t d t t t t
(11)
so that
(12)
may represent ESD current. It is denoted with ESD2 and presented in Fig. 5. It may be
written in another way as
516 V. JAVOR
1 1 1 2 1 1 1
1 1 1 2 2 2 1 2
1 1 1 2 2 2 2
( / ) exp[ (1 / )] ( / ) exp[ (1 / )], 0
( ) ( / ) exp[ (1 / )] ( / ) exp[ (1 / )],
( / ) exp[ (1 / )] ( / ) exp[ (1 / )],
ac
m m m m m m m
bc
m m m m m m m m
bd
m m m m m m m
I t t a t t I t t c t t t t
i t I t t b t t I t t c t t t t t
I t t b t t I t t d t t t t
(13)
as a , b, c , and d are the constants, and
. Using LSQM to approximate IEC
61000-4-2 Standard ESD current, the parameters are determined as Im 1=14A, Im 2=8.4A,
tm1 =1ns, tm2 =21ns, a=2, b =0.3, c =3, and d =0.9. If three functions are used, based on the
same expressions, their sum better represents the IEC 62305-1 Standard current, as given
in Fig. 5 and denoted with ESD3.
1 1 1 1
1
1 1 1 1
( / ) exp[ (1 / )] , 0 ,
() ( / ) exp[ (1 / )] , ,
a
m m m m
b
m m m m
I t t a t t t t
it I t t b t t t t
(14)
2 2 2 2
2
2 2 2 2
( / ) exp[ (1 / )] , 0 ,
() ( / ) exp[ (1 / )] , ,
c
m m m m
d
m m m m
I t t c t t t t
it I t t d t t t t
(15)
3 3 3 3
3
3 3 3 3
( / ) exp[ (1 / )], 0 ,
() ( / ) exp[ (1 / )], ,
e
m m m m
f
m m m m
I t t e t t t t
it I t t f t t t t
(16)
so that ESD3 is
)()()()( 321 titititi
. (17)
This may be written also as
1 1 1 2 2 2
3 3 3 1
1 1 1 2 2 2
3 3 3 1 2
11
( / ) exp[ (1 / )] ( / ) exp[ (1 / )]
( / ) exp[ (1 / )], 0
( / ) exp[ (1 / )] ( / ) exp[ (1 / )]
( / ) exp[ (1 / )],
() ( / ) exp[ (
ac
m m m m m m
e
m m m m
bc
m m m m m m
e
m m m m m
b
mm
I t t a t t I t t c t t
I t t e t t t t
I t t b t t I t t c t t
I t t e t t t t t
it I t t b
1 2 2 2
3 3 3 2 3
1 1 1 2 2 2
3 3 3 3
1 / )] ( / ) exp[ (1 / )]
( / ) exp[ (1 / )],
( / ) exp[ (1 / )] ( / ) exp[ (1 / )]
( / ) exp[ (1 / )],
d
m m m m
e
m m m m m
bd
m m m m m m
f
m m m m
t t I t t d t t
I t t e t t t t t
I t t b t t I t t d t t
I t t f t t t t
(18)
as a , b, c, d, e and f are the constants, and
. Using LSQM the parameters
are determined as Im 1=14A, Im 2=8.2A, Im3 =2.2A, tm 1=1ns, tm2 =21ns, tm 3 =50ns, a =2, b=0.3,
c=2.5, d=1.5, e=15, and f =7. For both ESD2 and ESD3 the maximum peak value can be
set to 15A simply by choosing Im 1=15A.
ESD3 better represents IEC 61000-4-2 Standard current waveform as given in Fig. 5,
than ESD2 or Two-Heidler's function for n =1.8 . Its derivative is also continuous, but of
differentiability class C0 as the first derivative has discontinuities at tm 1 , tm 2 and tm 3.
New Function for Representing Electrostatic Discharge Current 517
Fig. 5 AEF approximating IEC 61000 -4- 2 Standard current waveform for 4kV
Fig. 6 ESD3 rising part from 6 to 8 ns
518 V. JAVOR
Fig. 7 ESD3 derivative for a =2
Fig. 8 ESD3 derivative from 15 to 100ns
The ESD3 function rising part is given in Fig. 6. The function derivative in the first
100ns is presented in Fig. 7. First derivative is greater for greater parameter a, so that for
a=10 rising time is 0.4ns, for a=5 is 0.5ns, and for a=2 is 0.6ns as defined in IEC61000-
4-2 Standard. Parameter a does not influence on the choice of other parameters. Fig. 8
shows the ESD3 derivative from 15 to 100ns, where the needed discontinuities according
to the Standard current appear. ESD2, ESD3 and Two-Heidler's functi on (for n=1.8) are
given in Fig. 9. For the comparison Two-Heidler's function is delayed for 6ns and its
peak is set to the same value as for ESD2 and ESD3 representing the Standard current.
New Function for Representing Electrostatic Discharge Current 519
Fig. 9 ESD2, ESD3 and Two - Heidler's function representing the Standard current
CONCLUSIONS
Functions for approximating ESD currents are needed for simulation of different types
of electrostatic discharges, calibration of test equipment and adequate representation of
the IEC 61000-4-2 Standard current. Important features of such mathematical functions
are good approximation of realistic waveshapes and discontinuities in specified time
intervals, zero function derivative at t =0 +, and simple choice of function parameters.
New function presented in this paper in two forms, ESD2 and ESD3, may be used to
approximate different electrostatic discharge currents. Their waveshapes are compared to
other functions from literature and show better agreement with the IEC 61000-4-2
Standard current waveshape and its defined parameters. The function derivative is also
analyzed. Rising time, maximum and minimum values, so as needed discontinuities, may
be obtained for this function independently from other parameters and without peak
correction factors simplifying any optimization algorithm used to obtain its parameters.
Further research will include calculation of parameters according to experimentally
measured ESD currents, and application of different optimization procedures.
Acknowledgement: This paper is in the frame of research within the project HUMANISM III
44004 financed by the Serbian Ministry of Education, Science and Technological Development.
520 V. JAVOR
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[23] S. Shenglin, B. Zengjun, L. Shange, "A new analytical expression of standard current waveform", High
Power Laser and Particle Beams, Vol.15, No.5, pp. 464-466, 2003.
[24] R. Chundru, D. Pommerenke, K. Wang, T. Van Doren, F. P. Centola, J. S. Huang "Characterization of
human metal ESD reference discharge event and correlation of generator parameters to failure levels –
Part I: Reference event", IEEE Transactions on EMC, Vol .46, No.4, pp. 498-504, Nov. 2004.
[25] V. Javor, "Modeling of lightning strokes using two-peaked channel-base currents", Int. Journal of
Antennas and Propagation, Vol. 2012, Article ID 318417, doi: 10.1155/2012/318417, 2012.
... The simulation methodologies for the ESD generator can be categorized into three types: analytical modeling [6,[21][22][23][24][25][26][27][28][29], circuit modeling for simulation using a SPICE-type circuit simulator [2,6,26,27,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] , and full wave electromagnetic (EM) modeling using various EM tools based on the Finite Element Method (FEM), the Finite-Integration Technique (FIT), and the Finite-Difference Time-domain (FDTD) algorithms [2,6,8,32,35,[46][47][48]. The matching of the four parts of the generated waveform: rise time, first peak current value, and the currents at 30 ns and 60 ns is required with the reference waveform in [7]. ...
... A/ns, C =1 ns-1, and D = 0.0459 ns-1. In [28], the author proposed an AEF (9) based on the sum of the two or three channel based current functions (CBC). The parameter values of the proposed AFE were determined using the least-squares method (LSQM) and are as follows: I m1 = 14 A, I m2 = 8.2 A, I m3 = 2.2 A, t m1 = 1 ns, t m2 = 21 ns, t m3 = 50 ns, a = 2, b = 0.3, c = 2.5, d = 1.5, e =15, and f = 7. ...
... The parameter values of the proposed AFE were determined using the least-squares method (LSQM) and are as follows: I m1 = 14 A, I m2 = 8.2 A, I m3 = 2.2 A, t m1 = 1 ns, t m2 = 21 ns, t m3 = 50 ns, a = 2, b = 0.3, c = 2.5, d = 1.5, e =15, and f = 7. The waveforms of [28] comply with the continuity requirements of the ESD waveform. ...
This study presents, for the first time, state-of-the art review of the various techniques for the modeling of the electrostatic discharge (ESD) generators for the ESD analysis and testing. After a brief overview of the ESD generator, the study provides an in-depth review of ESD generator modeling (analytical, circuit and numerical modeling) techniques for the contact discharge mode. The proposed techniques for each modeling approach are compared to illustrates their differences and limitations.
... This approach is similar to the model used in [52,53] to describe electrostatic-discharge currents. The function's main advantages (as mentioned in [54]) are: simply adjustable derivative value, risetime value, time-to-peak value, and exact peak values chosen prior to adjusting other parameters. ...
... This approach is similar to the model used in [52,53] to describe electrostatic-discharge currents. The function's main advantages (as mentioned in [54]) are: simply adjustable derivative value, rise-time value, time-to-peak value, and exact peak values chosen prior to adjusting other parameters. ...
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![Georgios Foskolos]()
This paper presents an aggregate current-harmonic load model using power exponential functions and built from actual measurement data during the individual charging of four different fully electric vehicles. The model is based on individual emitted current harmonics as a function of state of charge (SOC), and was used to deterministically simulate the simultaneous charging of six vehicles fed from the same bus. The aggregation of current harmonics up to the 11th was simulated in order to find the circumstances when maximal current-harmonic magnitude occurs, and the phase-angle location. The number of possible identical vehicles was set to four, while battery SOC, the start of charging, and the kind of vehicle were randomized. The results are presented in tables, graphs, and polar plots. Even though simulations did not consider the surrounding harmonics, supply-voltage variation, or network impedance, this paper presents an innovative modeling approach that gives valuable information on the individual current-harmonic contribution of aggregated electric-vehicle loads. With the future implementation of vehicle-to-grid technology, this way of modeling presents new opportunities to predict the harmonic outcome of multiple electric vehicles charging.
... The simplest 1P-AEF [17] has two parameters a 1 and a 2 , and a single peak I m at t m , whereas b 1 = b 2 = 1. It is given by ...
... For experimentally measured ESD current of the contact human-to-metal discharge, for 2 kV voltage [25], MLSM is applied to obtain an adequate approximation [17] by NP-AEF as given by (1). 3P-AEF(1,2,2,4), ...
An analytically extended function based on power-exponential functions is used in this paper for approxi- mation of electrostatic discharge (ESD) currents and their derivatives. The Marquardt least-squares method (MLSM) is applied for obtaining nonlinear function parameters. IEC 61000-4-2 Standard ESD current is approximated, as well as some measured ESD currents' wave shapes. Power-exponential terms are extended at the local maxima and minima of the represented wave shape, so that this approximation is done from peak to peak. ESD current derivative is approxi- mated using the same procedure in order to obtain the continuous second order derivative of the current, as all piecewise functions are of differentiability class C¹L . Currents and their derivatives are often measured in ESD experiments so that their analytical representation is needed for simulation of ESD phenomena, better definition of standard requirements, and computation of the transient fields and induced effects.
... Generalizing the function for representing lightning currents from [10]- [12], the proposed multi-peaked analytically extended function (AEF) has been applied by the authors to modelling of different lightning currents, including those defined in the IEC Standard 62305-1 [13], slow and fast-decaying ones, as well as measured ones, see e.g. [14]- [16]. ...
A new approach to mathematical modelling of lightning current derivative is proposed in this paper. It builds on the methodology, previously developed by the authors, for representing lightning currents and electrostatic discharge (ESD) currents waveshapes. It considers usage of a multi-peaked form of the analytically extended function (AEF) for approximation of current derivative waveshapes. The AEF function parameters are estimated using the Marquardt least-squares method (MLSM), and the framework for fitting the multi-peaked AEF to a waveshape with an arbitrary number of peaks is briefly described. This procedure is validated performing a few numerical experiments, including fitting the AEF to single- and multi-peaked waveshapes corresponding to measured current derivatives.
... A number of current functions have been proposed in the literature to model the ESD currents, [2,3,7,8,10,11,12,19,20,21,22,23]. They are mostly based on exponential functions. ...
A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents' modelling is illustrated through an essential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape.
Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents' modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current.
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![Vesna Javor]()
New engineering modified transmission line models of lightning strokes are presented in this paper. Their computational results for lightning electromagnetic field (LEMF ) at various distances from lightning discharges are in good agreement with experimental results that are usually used for validating electromagnetic, engineering and distributed-circuit models. Electromagnetic theory relations, thin-wire antenna approximation of a lightning channel without tortuosity and branching, so as the assumption of perfectly conducting ground, are used for electric and magnetic field computation. An analytically extended function (AEF ), suitable for approximating channel-base currents in these models, may also represent typical lightning stroke currents as given in \(\mathrm {IEC}~62305\text {-}1\) Standard, as well as the \(\mathrm {IEC}~61000\text {-}4\text {-}2\) Standard electrostatic discharge current.
- Ke Wang
- Jinshan Wang
- Xiaodong Wang
According to the international electrotechnical commission issued IEC61000-4-2 test standard, through the electrostatic discharge current waveform characteristics analysis and numerical experiment method, and construct a new ESD current expression. Using Laplasse transform, established the ESD system mathematical model. According to the mathematical model, construction of passive four order ESD system circuit model and active four order ESD system circuit model, and simulation. The simulation results meet the IEC61000-4-2 standard, and verify the consistency of the ESD current expression, the mathematical model and the circuit model.
The Marquardt least-squares method is applied in this paper for estimation of the Pulse function's non-linear parameters in order to approximate measured lightning currents. Such procedure is generalized so it could be used for other pulse functions representing lightning current waveshapes. The obtained results show that this method provides good results for the IEC 62305-1 standard lightning current waveshapes of the first and subsequent return stroke currents, and also for some measured fast- and slow-decaying current waveshapes.
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![Vesna Javor]()
Lightning electromagnetic field is obtained by using "engineering" models of lightning return strokes and new channel-base current functions and the results are presented in this paper. Experimentally measured channel-base currents are approximated not only with functions having two-peaked waveshapes but also with the one-peaked function so as usually used in the literature. These functions are simple to be applied in any "engineering" or electromagnetic model as well. For the three "engineering" models: transmission line model (without the peak current decay), transmission line model with linear decay, and transmission line model with exponential decay with height, the comparison of electric and magnetic field components at different distances from the lightning channel-base is presented in the case of a perfectly conducting ground. Different heights of lightning channels are also considered. These results enable analysis of advantages/shortages of the used return stroke models according to the electromagnetic field features to be achieved, as obtained by measurements.
- S.-L. Sheng
- Z.-J. Bi
- M.-H. Tian
- S.-H. Liu
According to the current waveform in standard IEC61000-4-2, two analytical expressions of the standard current are analyzed and then a new one based on pulse function is proposed. The new expression is consistent with the new standard IEC61000-4-2, in which both the current and its derivative are zero at the zero moment, and the waveform basically is agreed with the measured one.
- Steve Van den Berghe
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![Daniel De Zutter]()
A study of the effect of electrostatic discharge (ESD) to a coaxial cable which connects two systems was made. To study the effect of various pathways of ESD, we used a finite-difference time-domain (FDTD) algorithm. The disturbance induced in the inside of the cable is evaluated by using the transfer impedance of the cable shield. The effect of ESD on the cable shield is studied as well as the effect of the cable's presence when a remote part of the connected system is targeted. The results of our study show that the effect of ESD entering the cable shield can potentially be a lot more dangerous than the signal entering through a typical aperture, especially if the frequency content of the discharge is high. A cable also provides a good conductor for ESD signals to reach other parts of the system.
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![Vesna Javor]()
A new function is presented in this paper for representation of multi-peaked currents of lightning strokes. Experimentally measured lightning channel-base currents often have a few emphasized peaks. If such currents are approximated with a suitable analytical function, having analytical integral and derivative, lightning electromagnetic field is calculated based on some engineering, electromagnetic or other model of lightning strokes. For the function presented in this paper and two engineering models with new attenuation factors, calculated field results at different distances from the channel base are in better agreement with measurements. Analytically obtained Fourier transform of this function is useful for calculations of lightning electromagnetic field at a lossy ground.
- Clayton R. Paul
A Landmark text thoroughly updated, including a new CD As digital devices continue to be produced at increasingly lower costs and with higher speeds, the need for effective electromagnetic compatibility (EMC) design practices has become more critical than ever to avoid unnecessary costs in bringing products into compliance with governmental regulations. The Second Edition of this landmark text has been thoroughly updated and revised to reflect these major developments that affect both academia and the electronics industry. Readers familiar with the First Edition will find much new material, including: Latest U.S. and international regulatory requirements PSpice used throughout the textbook to simulate EMC analysis solutions Methods of designing for Signal Integrity Fortran programs for the simulation of Crosstalk supplied on a CD OrCAD(r) PSpice(r) Release 10.0 and Version 8 Demo Edition software supplied on a CD The final chapter on System Design for EMC completely rewritten The chapter on Crosstalk rewritten to simplify the mathematics Detailed, worked-out examples are now included throughout the text. In addition, review exercises are now included following the discussion of each important topic to help readers assess their grasp of the material. Several appendices are new to this edition including Phasor Analysis of Electric Circuits, The Electromagnetic Field Equations and Waves, Computer Codes for Calculating the Per-Unit-Length Parameters and Crosstalk of Multiconductor Transmission Lines, and a SPICE (PSPICE) tutorial. Now thoroughly updated, the Second Edition of Introduction to Electromagnetic Compatibility remains the textbook of choice for university/college EMC courses as well as a reference for EMC design engineers. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
- Nobuo Murota
This paper aims at improved reproducibility of the electrostatic discharge current in the electrostatic tester that simulates the electrostatic discharge from the charged human body. The variation of the electrostatic discharge current due to changed testing conditions, including the position relation, is analyzed. The derivation method, where the components of the electrostatic tester, such as the discharge gun and the ground wire, are replaced by electrical parameters, is combined with the method of circuit analysis by simulation. The characteristics of the electrostatic tester are analyzed, and the following situations are revealed. Even though the inductance of the ground wire varies greatly with the testing condition, the main discharge current satisfies the rated value. The initial current is generated depending on the switch structure of the tester, and is caused by the stray capacitance around the discharge current limiting resistor. The proposed circuit model exactly represents those characteristics of the electrostatic tester. By combining the proposed circuit model into the EDA (electronic circuit design automation) system, the circuit designer can simulate the electrostatic discharge at the design stage. This makes it easy for the designer to interpret the characteristics in the electrostatic testing, and can reduce the trial-and-error effort. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(10): 49–57, 1997
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Source: https://www.researchgate.net/publication/287531340_New_function_for_representing_IEC_61000-4-2_standard_electrostatic_discharge_current
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