Circuit modeling and simulation of the ESD generator for various
tested equipment according to the IEC 61000-4-2
GEORGIOS FOTIS, VASILIKI VITA
Department of Electrical and Electronics Engineering Educators
ASPETE - School of Pedagogical and Technological Education
N. Heraklion, 14121, GREECE
Abstract: - The existing IEC Standard for Electrostatic Discharge (ESD) contains a general and simplified circuit
for the generator that produces ESD discharges, without entering into details. The present work tries to fill this
gap and proposes a circuit which will generate the ESD current in the limits that the current Standard defines.
Two circuit models are examined through simulations with SPICE software, with the one to be the most suitable.
This circuit model is also examined for various loads that simulate the Equipment under Test (EUT) and useful
conclusions derive up to what type and size of equipment can be safely tested by ESD generators so that the test
results are reliable.
Key-Words: - Circuit modeling, electrostatic discharge, ESD generator, Equipment Under Test (EUT), IEC
61000-4-2, SPICE Software.
Received: July 27, 2021. Revised: July 12, 2022. Accepted: August 18, 2022. Published: September 1, 2022.
1 Introduction
The abrupt transfer of charge between objects at
various electrostatic potentials is known as
Electrostatic Discharge (ESD) [1]. Triboelectric
charging is the process of creating electrostatic
charge through the contact and separation of
materials. It entails the transfer of electrons among
various materials. ESD is clearly a transient
overvoltage pulse with a sharp rising edge, a large
current amplitude, and little energy. ESD has a great
impact on electronic equipment, which may be
destroyed if it not shielded and designed properly [2].
The majority of ESD procedures are referred to
the most recent version of the IEC Standard 61000-
4-2 [3]. The purpose of this Standard is to create a
consistent and repeatable framework for assessing
how electrical and electronic equipment performs
when exposed to electrostatic discharges. The
Human Body Model (HBM), which simulates the
electrostatic discharge of the human body on
electrical or electronic equipment, is the starting
point of this Standard. The study of the ESD current
waveforms has involved an in depth investigation.
The amplitudes and rise times of ESD current
waveforms have been demonstrated to change with
charging voltages, approach speeds, electrode types,
and humidity [4-7].
There have been various publications which
propose an enhanced circuit for ESD generators [8-
12]. A modified ESD generator and an equation for
the reference waveform have both been proposed in
[9]. The redesigned ESD generator has a reference
waveform that is quite similar to the one specified by
the IEC Standard. Another study uses SPICE
software to the accepted HBM, which is broken down
into 11 basic building pieces [10]. The factors that
control the discharge current waveforms of ESD
generators are clarified in [11], which also proposes
an analogous circuit model based on the design and
dimensions of the ESD generator. Two precise
models for electrostatic discharge generators are put
out in [12] and allow for the reproduction of the
discharge current in the contact mode while taking
the load effect into account.
There have also been studies of finding an
accurate equation that can describe the ESD currentās
waveform as it is described in the IEC Standard [3].
The ESD current can be approximated using an
equation separate from the circuits for the ESD
generators. The ESD generator can be correctly
described using this equation in modeling software.
These studies enable a Genetic Algorithm by whom
the ESD currentās equation parameters are optimized
[13-15]. Also, there have been previous works that
describe the procedure where the ESD circuit can
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derive from this accurate equation using the Pronyās
method [16].
Another crucial issue in the ESD study is the
electromagnetic field that the ESD generators
produce, which may affect in various ways the
equipment they test each time affecting the test result
[17-19]. This is something that is still studied and it
is mentioned without certain directions in the current
IEC Standard for ESD [3].
In this paper a new circuit for the ESD generator
is proposed according to the IEC Standard. After
simulations in the SPICE program the waveform of
the ESD current that derives from the proposed
circuit it is found that is in the specified limits by the
Standard.
2 The IEC 61000-4-2
The current that the ESD generators have to produce
is depicted in Figure 1, according to the IEC 61000-
4-2 [3]. There are four parameters whose values have
to be in specific limits: the rise time (tr), the peak
discharge current (Ip), the current at 30 ns (I30) and
the current at 60 ns (I60). These two current values I30
and I60 are determined for a period of 30 ns and 60 ns,
respectively, commencing at the time point when the
current equals 10% of the peak current, as shown in
Figure 1. These parametersā limits, as given in Table
1, are valid only for contact discharges.
Figure 1 Typical waveform of the output current of
the ESD gun for contact discharges.
A simplified diagram of the test generator is
presented in Figure 2 and it consists, in its main parts:
the charging resistor Rc, the energy-storage capacitor
Cs, the distributed capacitance Cd, the discharge
resistor Rd, the voltage indicator, the discharge
switch, the charge switch, the interchangeable tips of
the discharge electrode, the discharge return cable
and the power supply unit.
Table 1 Waveform parameters of the ESD current
for contact discharges according to the IEC 61000-
4-2.
Indicate
d
Voltage
[kV]
Imax
[Ī]
(Ā±15%
)
tr
[ns]
(Ā±25%
)
I30
[A]
(Ā±30%
)
I60
[A]
(Ā±30%
)
2
7.5
0.8
4
2
4
15
0.8
8
4
6
22.5
0.8
12
6
8
30
0.8
16
8
Figure 2 A simplified diagram of the ESD generator
according to the IEC 61000-4-2.
The generator must comply with the requirements
given the IEC 61000-4-2. Therefore, neither the
diagram in Figure 2, nor the element values are
specified in detail. This significant gap of the IEC
Standard need to be investigates and this is the main
objective of this work.
3 ESD circuit for SPICE simulations
For the needs of SPICE simulation it is necessary to
find an equivalent discharge circuit for the ESD
generator. Next, the individual elements of which the
electrostatic discharge generator was composed
during the SPICE simulation are presented.
According to the Standard [3] the ESD gun and the
Equipment under Test (EUT) are connected via the
electrode and the 2m long ground wire permitting the
current return. The cable is twisted and covered with
insulating material designed to have reduced
resistance and inductance. Its resistance has a very
small value and can be neglected compared to the
resistance of the discharge circuit and the resistance
of the load.
3.1 Calculation of inductive elements
The value of the inductance of the ground wire
mainly affects the response of the circuit. For a cable
of length l and permittivity Ī¼, with width w and
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density t, the following formula is proposed for the
inductance Lr in Ī¼H [8], [20]:
ī“®ļ„ļī„²ī¤ī„²ī„²ī„“ó°£īīó°”ļ¶ļ
ļŖļ¾ļ§ó°¢ļ
ī„²ī¤ī„“ī„·ī„²ī„¶ī„»ļ
ļŖļ¾ļ§
ļ·ļ ļ
ļļó°ļ«ó°
ļøó°¤ (1)
where T(x) is a frequency dependent function and
in the case of high frequencies T(x)=0.
When designing a high frequency circuit there is
difficulty in directly calculating the line inductance
due to the non-uniform distribution of the charge on
the line. In practice, the value of cable inductance is
not affected by the type of cable cross-section. This
is how a cable with a circular cross-section is studied.
Since the wire is twisted, the angle is smooth, so the
circular cross-section assumption facilitates the
analysis. Considering a straight conductor of length l
with a circular cross-section of radius a, the
inductance Ls is given by the sum of the conductor's
internal inductance Lsi and the external inductance
Lse:
ī“®ļ¦ļī“®ļ¦ļ ļ
ī“®ļ¦ļ (2)
ī“®ļ¦ļ ļļļ¬ļ
ļ¼ļ (3)
ī“®ļ¦ļ ļļļ¬
ļ¶ļļ¬īµīīļļ¾ī¦¾ļļ®ļ¾ļļ®
ļļī¦¾ī·ļ¶ļ
īµļ¶ļ
ī·ļ° (4)
Equation (4) gives only the contribution of the
magnetic field around the conductor and does not
take into account the effect of other conductors. The
test to check the immunity of equipment to
electrostatic discharge currents is done inside an
anechoic chamber and the equipment is placed on a
conductive plate. Since the current flows on the
conductive floor due to the magnetic field of the
ground wire, the inductance cannot be neglected.
Assuming that the distance between the floor and the
center of the conductor is h with h<<l, the inductance
Lsm of the ground wire is:
ī“®ļ¦ļ ļī“®ļ¦ļ ļ ļ
ī“®ļ¦ļ ļ (5)
ī“®ļ¦ļ ļ ļļļ¬ļ
ļ¼ļ (6)
ī“®ļ¦ļ ļ ļļļ¬ļ
ļ¶ļ īīļ¶ļļæļ
ļ (7)
In the high frequency region, the magnetic field
inside the conductor is zero and the inductances Lsi
and Lsmi of equations (3) and (6) can be ignored.
3.2 The ground wire as a transmission line
In equation (5) it is assumed that the ground wire is
placed above the conductive surface. Then a
transmission line is created, which has the ground as
its return path. Although the ground wire has an
insulating sheath, which is some kind of dielectric,
this layer is thin and does not affect the dielectric
constant of the overall system. Therefore, the
dielectric material can be neglected. Then, the
transfer line satisfies (5) and (7). The characteristic
resistance Zm is given by the formula:
ī“¼ļ ļī„·ī„»ī¤ī„»ī„·ī„“īīó°§ļ
ļļ
ļ§ó°”ļ
ļó°¢ļ¶ļī„³ó°Øīó°ī·ó° (8)
3.3 ESD generatorās capacity
The construction of the gun as well as the capacitance
Cm to earth can be represented by a metal sphere of
radius a. If the distance of the center of the sphere
from the floor is h, the capacitance can be calculated
by considering its mirror image. The resulting
expression is a series from which, ignoring terms of
higher order, the following approximate formula is
obtained:
ī“„ļ ļļ¼ļļļ¬ļļ
ļ¶ļļæļ (9)
3.4 Electrostatic discharge generator models
for numerical analysis
The design of electronic automation is an ongoing
development in electronics design, and methods for
the numerical analysis of circuit response are already
established. SPICE software for circuit analysis, is
widely used to overcome many problems such as
convergence [21]. In addition, models for integrated
circuits are provided in SPICE. There are still models
that describe various electromagnetic phenomena
[22].
As can be seen from Figure 3, the construction of
the equivalent circuit is complicated by the parasitic
elements in the experimental space. For the existence
of distributed capacitances, which are not included in
the equivalent circuit, reference is made to the
Standard but they are not shown in the circuit. If the
allocated capacity does not exist, the initial maximum
is not produced.
Figure 3 An ESD generator during discharges in a
laboratory environment.
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First, the values of the circuit constants are
determined. Figure 4 shows the first circuit model
used for the analysis. The circuit constants are
interpreted as follows: R1, R2 and C1 are defined by
the Standard. For the determination of the remaining
circuit elements, the parasitic elements should also be
taken into account.
Figure 4 A proposed circuit model for the ESD
generator (Circuit Model 1).
The value of the inductance should be determined
independently since there are no specifications. The
discharge gun electrode length is specified to be
50mm and the radius 6mm. Then, equation (4) is
applied assuming that there is no magnetic field
inside the conductor. Substituting l=50mm and
Ī±=6mm gives L1=0.0193Ī¼H. In practice the
discharge electrode and the discharge resistor are
connected by a common wire. Taking into account
the inductance of the cable, the value of L1 is taken
as 0.04Ī¼H. The surface inductance of the conductive
target L2 is sufficiently small and can be neglected
compared to the inductance of the ground wire as
long as it is 1m long and the surface is sufficiently
large.
We assume that the ground wire has a diameter of
10mm. Substituting in (8) Ī±=5 mm and h=6.84mm,
Zm=50Ī© results. Subtracting the radius a of the
conductor the ground wire is above the conductive
surface by 1.84mm. This situation corresponds to a
transmission line with a resistance of 50Ī©, consistent
with the real situation, if we also take into account the
insulating surface. When the wire is shorter, but still
considered a 50Ī© transmission line, the inductance
decreases more or less depending on the gap between
them. Inside the conductor it is assumed that there is
no magnetic field. Applying (7) and substituting
h=6.84mm, l=1m it follows that L3 of the conductive
plate is equal to 0.11Ī¼H.
Equation (7) is not valid for calculating L4 if the
ground wire is more than 30cm from the metal plate
on the target side. Applying (4) and substituting l=1m
we get L4=0.861Ī¼H. The inductances L3 and L4 differ
by a factor greater than 8, even though they have the
same lengths. This happens because the distances
from the metal plate are different.
R2 is the target resistance. The inductance L5 of
the ground wire is equal to the sum of L2, L3 and L4,
so L5=1Ī¼H.
Equation (9) is applied to calculate the
capacitance of the cable to earth. For Ī±=3cm and
h=20cm from the floor it follows that Cm=3.6pF. In
practice the gun is held by a person who has a
capacitance of C5=150pF. Consequently it is not
sufficient to replace the target capacitance by Cm
alone. Thus C4=10pF is set, including the capacitance
of the human body.
Voltage V3 is the supply to charge capacitor C1.
SW1 is the charge switch which is closed for the first
9ns and then opens, while SW2 is the discharge
switch which is open for the first 10ns and then
closes. Capacitor C2 represents the stray capacitance
around resistor R1, which corresponds to the surface
resistance. Capacitor C3 simulates the parasitic
capacitance around the sensor of the discharge
current. L6 is the inductance of the external ground
wire connecting the supply to the gun. Finally, R7 and
R8 are dummy resistors used to prevent oscillations.
In the equivalent circuit of Figure 5 the charge
switch and the discharge switch are connected
separately. They should be properly handled so that
they are not both open or closed at the same time. To
overcome this problem we proceed to redesign the
switch as shown in Figure 5.
In Figure 6 which models the circuit of Figure 5,
switch SW2 has been moved to the left of capacitor
C2 and resistor R1. The circuit constants remain the
same.
Figure 5 Circuit diagram of actual charger.
R1
330
C5
150p
R7
0.1
L6
2uH
1
2
0
C3
5p
L1
0.04 uH
1 2
+
-
+
-
SW1
S
C1
150p
V3 R2
2
I
0
R3
0.1
R8
0.1
0
V2
+
-
+
-
SW2
S
<Do c> <RevCod e>
<Title>
A
1 1Tuesday, November 29, 2005
Title
Size Doc ument Number Rev
Date: Sheet of
C2
1p
C4 10p
V1
L5
12
0
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Figure 6 A proposed circuit model for the ESD
generator (Circuit Model 2).
4 Current waveform analysis
4.1 Effect of ground wire on current
waveforms
As demonstrated the ground wire inductance depends
on the relative position of the ground wire to the
ground plate. As previously mentioned it was
assumed that the ground wire is parallel to the ground
plate and L5=1Ī¼H was calculated. When the ground
wire is remote from the ground plate or no ground
plate is present during the test then L3=L4 and
therefore L5=2Ī¼H. Figures 7 and 8 show the
simulation results for L5=1Ī¼H and L5=2Ī¼H, for
charging voltages of +1kV for both circuit models.
Figure 7 The produced ESD current of the Circuit
Model 1.
Figure 8 The produced ESD current of the Circuit
Model 2.
Comparing Figures 7 and 8 we notice that the
change in the switch mechanism affected Imax and in
fact its value decreased. This is because the parasitic
capacitance C2 has changed from source to load due
to the displacement of the discharge switch. For this
reason it is important to determine the conditions
under which the test is carried out so that all
parameters are adjusted in such a way that the value
of C2 remains constant. It is also observed that the
value of Imax obtained from model 1 is very high. This
can be compensated by increasing the inductance L1
which is affected by the length of the discharge
electrode.
4.2 Comparison of the two electrostatic
discharge generator circuits
With the help of the SPICE program, the two circuits
of the electrostatic discharge generator (models 1 and
2) were implemented and a simulation was carried
out for charging voltage values of +2kV and +4kV.
Based on the results of the simulation it is possible to
check the satisfaction of the criteria of the
specifications by the parameters of the electrostatic
discharge current as recorded in Table 1. In Table 2
the values of the discharge current parameters for
model 1 and model 2 are presented for charging
voltages of +2kV and +4kV. The discharge current
for the two models and for the two charging voltages
from the SPICE simulation are presented in Figures
9-12.
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Figure 9 Response of the circuit model 1 for +2kV
charging voltage.
Figure 10 Response of the circuit model 1 for +4kV
charging voltage.
Figure 11 Response of the circuit model 2 for +2kV
charging voltage.
Figure 12 Response of the circuit model 2 for +4kV
charging voltage.
Observing the values of Ī¤able 2 and comparing
them with the limits of Table 1 we conclude that the
specification limits met only for model 2, since the
values of model 1 are out of the specified limits of the
IEC Standard.
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