
density t, the following formula is proposed for the
inductance Lr in μH [8], [20]:
ī“®ļ„ļī¤ī„²ī„²ī„“ó°£īīó°”ļ¶ļ
ļŖļ¾ļ§ó°¢ļ
ī¤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®
ļļī·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:
ļ ļī„·ī„»ī¤ī„»ī„·ī„“īīó°§ļ
ļļ
ļ§ó°”ļ
ļó°¢ļ¶ļó°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.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.22
Georgios Fotis, Vasiliki Vita