chapter 2 finite element modeling and simulation...
Post on 16-Oct-2020
10 Views
Preview:
TRANSCRIPT
19
CHAPTER 2
FINITE ELEMENT MODELING AND SIMULATION SYSTEM
2.1 INTRODUCTION
EMC Computer modeling and simulation are very important
tools in modern electronics world. They have a direct effect on perfor-
mances of all the electrical and electronics products. Currently the state of
art computer analysis and prediction programs are available for each spe-
cific application, with direct bearing on the reduced cost of the product
with optimum EMC performance (John et al 1989). EMI plays a vital role
in microelectronics as it packs components in smaller space envelop.
The automotive vehicle and its systems were simulated using 2D
model mainly due its symmetrical nature (XY plane), limitation of compu-
tation capacity of computer resources. However, the present desktop’s has
3D analysis capability enables us to get solutions within short time dura-
tion. The computer modeling is a welcome feature to investigate the field
levels that human cannot survive, whereas the equipment may be required
to perform remote operations. The computer modeling simulation enables
us to study these problems in depth and estimates the EMI levels as per the
MIL standards.
EMI can be handled using management of configuration at de-
sign stage itself with basic EMI knowledge. However in case EMI comes
into picture during system integration then adequate counter measures are
required to be implemented to reduce the same. In a large system it is too
20
costly to go in for such problem solving method and may result in com-
plete design change.
A system designer should restrict the EMI level at subsystem/
components to ensure EMC with allied system in military applications.
The analysis of a large system can be done in time domain and frequency
domain and matrix based numerical solution method is used for this pur-
pose. The time based analysis data can be transferred to frequency domain
through the use of Fast Fourier transform (FFT) and the inverse Fourier
transform methods. The basic criteria for the choice depends on signal le-
vels presents complexity of the system, relative dimensions of the interest-
ed frequency, range with circuit components, discrete signal availability or
whether AC or DC transient purpose is required to done by designer. A
circuit level simulation tool like SPICE can be used in such component
level modeling with various simulation signal waveforms (Handbook
Pspice 1996).
2.2 ANSOFT
The Maxwell 2D field simulator is an interactive software pack-
age that uses finite element analysis to simulate electric and magnetic field
in devices with a uniform cross section(X-Y plane) or full rational symme-
try. The simulator can be used to solve for static electric fields and magnet-
ic fields and eddy current. In order to solve a problem using the package
there are certain procedure is required to be followed. The steps to be
followed in executing Maxwell 2D field simulator are explained in this
chapter.
21
2.2.1 Electrostatic Field Simulation Theory
The electrostatic field simulator computes static electric fields
arising from potential differences and charge distributions.
The electrostatic field simulator solves for the electric potential,
r 0 - (2.1)
where
r is the relative permittivity. It is different for each material.
0 is the permittivity of free space, 8.854 x 10-12 F/m.
This equation is derived from Gauss's Law, which indicates that
the net electric flux passing through any closed surface is equal to the net
positive charge enclosed by that surface. In differential form, Gauss's Law is:
•D = - (2.2)
r 0E, then:
r 0E(x,y)) = - (2.3)
In a static field, E = -
r 0 - (2.4)
22
which is the equation on that the electrostatic field simulator solves using the
finite element method.
After the solution for the potential is generated, the system
automatically computes the E-field and D-field using the relations E =
and
D r 0E (2.5)
2.2.2 Capacitance
At the simplest level, capacitance represents the amount of energy
stored in the electric field of a structure. In a single circuit, the capacitance
represents the amount of energy stored in the electric field that arises due to a
voltage differential across dielectric. 1 Ue = C V2 (2.6) 2
where Ue is the energy stored in the electric field, C is the capacitance and V
is the voltage across the dielectric.
The Maxwell 2D Field Simulator computes the capacitance be-
tween two conductors by simulating the electric field that arises when a
voltage differential is applied and by computing the energy stored in the
field. 2Ue C = (2.7) V2
23
2.2.3 Capacitance in terms of charges and voltages
A capacitance matrix represents the charge coupling within a group
of conductors - that is, the relationship between charges and voltages for the
conductors. Given the three conductors in Figure 2.1, with the outside
boundary taken as a reference, the net charge on each object will be:
Q1 = C10 V1 + C12(V1 - V2) + C13(V1 - V3) (2.8)
Q2 = C20 V2 + C12(V2 - V1) + C23(V2 - V3) (2.9)
Q3 = C30 V3 + C13(V3 - V1) + C23(V3 - V2) (2.10)
Figure 2.1 Capacitance between objects
24
This can be expressed in matrix form as:
Q1
Q2
Q3
=
C10+
C12+C13
-C12
-C13
-C12
C20+C12+C23
-C23
-C13
-C23
C30+C13+C23
V1
V2
V3
(2.11)
The capacitance matrix above gives the relationship between Q
and V for the three conductors and ground. In a device with n conductors,
this relationship can be expressed by an n x n capacitance matrix. If
one volt is applied to conductor 1 and zero V is applied to the other two con-
ductors, the capacitance matrix becomes:
Q1 Q2 Q3
=
C
100
=C10+C12+C13
-C12 -C13
(2.12)
The diagonal elements in the matrix as (C(1,1)) are the sum of all
capacitances from one conductor to all other conductors. These terms
represent the self-capacitance of the conductors. Each is numerically equal to
the charge on a conductor when one volt is applied to that conductor and the
other conductors (including ground) are set to zero. For instance,
C(1,1) = C10 + C12 + C13 (2.13)
The off-diagonal terms in each column (such as C(1,2), C(1,3)) are
numerically equal to the charges induced on other conductors in the system
25
when one volt is applied to that conductor. For instance, in column one of the
capacitance matrix, C(1,2) is equal to -C12. This is equal to the charge induced
on conductor 2 when one volt is applied to conductor 1 and zero V is applied
to conductor 2.
The off-diagonal terms are simply the negative values of the
capacitances between the corresponding conductors (the mutual
capacitances). In column one of the example capacitance matrix, the off-
diagonal terms represent the capacitances between conductor 1 and the other
two conductors; in column two, the terms represent the capacitance between
conductor 2 and the other conductors and so forth.
Note that the capacitance matrix is symmetrical about the diagonal.
This indicates that the mutual effects between any two objects are identical.
For instance, C(1,3), the capacitance between conductor 1 and conductor 3 (-
C13), is equal to C(3,1), the capacitance between conductor 3 and conductor 1.
2.2.4 Capacitance in terms of currents and Time varying voltages
A capacitance matrix can also represent the relationship between
currents and time varying voltages in a system of conductors. Given the three
transmission lines shown in Figure 2.2, the currents caused by the time
varying voltage source on each line are given by the following relationship:
i1
i2
i3
=
C10+C12+C13
-C12
-C13
-C12
C20+C12+C23
-C23
-C13
-C23
C30+C13+C23
dV1/(dt)
dV2/(dt)
dV3/(dt)
(2.14)
26
Figure 2.2 Capacitance between transmission lines
if dV2 / dt and dV3 / dt are set to zero, this relationship becomes:
i1i2i3
=
C
dV1/(dt)00
=
C10+C12+C13
-C12 -C13
(dV3/(dt))
(2.15)
This gives the currents that are induced on Line 2 and Line 3 when
a time varying voltage source is applied to Line 1 - that is, the capacitive
coupling between the three lines, or the short circuit capacitance.
2.2.5 Computing Capacitance
To compute a capacitance matrix for a structure, the Maxwell 2D
Field Simulator performs a sequence of electrostatic field simulations. In
each field simulation, one volt is applied to a single conductor and zero volt
27
is applied to all other conductors. Therefore, for n-conductor system, n field
simulations are automatically performed.
The energy stored in the electric field associated with the
capacitance between two conductors is given by the following relation:
1 Uij = __ Di • Ej (2.16)
where
Uij is the energy in the electric field associated with flux lines that
connect charges on conductor i to those on conductor j.
Di is the electric flux density associated with the case in which one
volt is placed on conductor i.
Ej is the electric field associated with the case in which one volt is
placed on conductor j.
The capacitance between conductors i and j is therefore:
2Uij
C = ____ Di • Ej (2.17)V2
2.2.6 Flux linkage (Electrostatic)
To compute the electric flux linkage, the electrostatic field solver
uses the following relationship:
= E • dA (2.18)
28
where E is the electric field and A is the area over which flux density is
computed.
In cartesian (XY) models, the area is found by sweeping the flux
line drawn in the xy-plane into the z-direction - forming a 3D surface. The
electric flux value computed is the flux per meter depth in the z-direction.
In axisymmetric (RZ) models, the area is found by rotating the flux
line drawn in the rz-plane 360 degrees about the z-axis. The electric flux
computed is the total flux that passes through this surface.
A separate flux linkage value is computed for each cross section of
model surface, based on line drawn on X-Y or RZ plane by user.
2.3 MAGNETOSTATIC FIELD SIMULATION
The magnetostatic field simulator is used to compute static
magnetic fields arising from DC currents and other sources like permanent
magnets and external magnetic fields. Magnetic fields in both linear and non-
linear materials can be simulated.
2.3.1 Theory of Magnetostatic Field Simulation
The magnetostatic field simulator solves for the magnetic vector
potential, Az(x,y) in this field equation:
1 Jz(x,y) = X _____ ( xAz(x,y)) (2.19) ( µrµ0 )
29
where
Az(x,y) is the z component of the magnetic vector potential.
Jz(x,y) is the DC current density field flowing in the direction of
transmission.
µr is the relative permeability of each material.
µ0 is the permeability of free space.
Given Jz(x,y) as an excitation, the magnetostatic field simulator computes
the magnetic vector potential at all points in space.
Note: In general, both J and A are vectors. However, J is assumed to have a
z-component only. A consequence of this is that A only has a z-component
as well. Both quantities can therefore be treated as scalars.
The equation that the magnetostatic field solver computes is
derived from Ampere's law, which is:
x H = J (2.20)
1 Since H = _____ , then (2.21) µrµ0B
B x _____ = J (2.22) ( µrµ0 )
Since B = xA, then (2.23)
1 x _____ ( x A) = J (2.24) ( µrµ0 )
30
which is the equation that the magnetostatic field simulator solves using the
finite element method.
After Az(x,y) is computed, the magnetic flux density, B, and the
magnetic field, H can then be computed using the relationships:
B = x A (2.25) 1 H = (2.26) r 0B Both B and H lies in xy cross section being analysed.
2.3.2 Inductance
At the simplest level, inductance represents how much energy is
stored in the magnetic field when current flows.
1 Um = __ Li2 (2.27) 2
where Um is the energy stored in the magnetic field, L is the inductance, and
i is the current flowing in the circuit.
The Maxwell 2D Field Simulator computes inductances associated
with a structure by simulating the magnetic field that arises when various
voltages and currents are applied. Then, by computing the energy stored in
those fields, we can compute the necessary inductances.
2Um L = (2.28) i2
31
To compute inductances using this method, the B-field and H-field
associated with a distribution of currents must first be computed. The
magnetostatic field simulator, which computes the magnetic vector potential
at all points in the problem region, performs this task.
2.3.3 Inductance in terms of voltages and time varying currents
An inductance matrix can also represent the relationship between
voltage and current fluctuations in a system. Given the three transmission
lines shown in Figure 2.3, the voltage changes caused by the time varying
current source on each line are given by the following relationship:
1 2
3
= L11 L12 L13
L12 L22 L23 L13 L23 L33
(di1)/(dt) (di2)/(dt) (di3)/(dt)
(2.29)
Figure 2.3 Inductance between transmission lines
32
The inductance matrix above gives the relationship between V
and di/dt for the three independent transmission lines.
If di2/dt and di3/dt are set to zero, this relationship becomes
V1 (di1) / (dt) L11
V2 = L 0 = L12 (di1) / (dt) (2.30) V3 0 L13
This gives the voltage changes that are induced on Lines 2 and 3
when a time-varying current source is applied to Line 1 - that is, the induc-
tive coupling between the three loops.
2.3.4 Computing an Inductance Matrix
To compute an inductance matrix, the Maxwell 2D Field Simula-
tor performs a sequence of magnetostatic field simulations. In each field
simulation, 1A current is allowed to flow in a single conductor. The cur-
rent returns as defined under Setup Executive Parameters – either in the
conductor identified as the return path, or along outside balloon, value (Di-
richlet) or odd symmetry boundaries. No current is allowed to flow in any
other conductor.
For an n-conductor system, n field simulations are automatically
performed. The energy stored in the magnetic field that couples two con-
ductors is :
1 1 Uij = Li2 = Bi Hj d (2.31) 2 2
33
where,
Uij is the energy stored in the magnetic field linking conductor i
with conductor j.
I is the current in conductor i.
Bi is the magnetic flux density associated with the case in which
one amp is allowed to flow through conductor i.
Hj is the magnetic field associated with the case in which one
amp is allowed to flow through conductor j.
The inductance coupling conductors i and j is therefore:
2Uij Lij = = Bi Hj d (2.32) i2
The user can compute the inductance matrix associated with a
particular structure, using the Maxwell 2D Field Simulator, which auto-
matically performs the necessary magnetostatic field simulations and inte-
grations. Thus the inductance matrix associated with the structure is com-
puted.
2.4 AC CONDUCTION FIELD SIMULATION
The AC conduction field solver can be used to analyze conduc-
tion currents due to time-varying electric fields in conductors and lossy di-
electrics.
2.4.1 Theory of AC Conduction Field Simulation
The AC conduction field simulator solves for in the following
equation :
( + j (x,y)) = 0 (2.33)
34
where (x,y) is the magnitude and phase of the electric potential at each
value of x and y.
is the angular frequency at which the potential is oscillating.
is the conductivity.
is the permittivity
This equation can be expanded to:
(J + j D) = 0 (2.34)
where J is the current density, E
D is the electric flux density, E
E is the electric field,
The AC conduction field solver makes the following assumptions
about the field quantities it solves for :
All times-varying electromagnetic quantities are assumed to have
the periodic waveform
F(t) = Fm cos( t + ) (2.35)
All quantities must have the same value of , but can have dif-
ferent phase angles ( ). If a current is not a pure sinusoid, it is decomposed
into sinusoidal harmonies, and solved separately at each frequency.
The component of E due to time-varying magnetic fields caused
by conduction currents can be neglected.
35
2.4.2 Admittance
Admittance can best be explained as the inverse of impedance,
and is expressed by this equation:
Y = G – jB (2.36)
where Y is admittance
G is conductance and is given in mhos
B is susceptance
Impedance in simple circuits is equal to resistance. Therefore
admittance is the inverse of resistance and is analogous to conductance. If
a material has a high admittance, then current will more readily flow
through it.
2.4.3 Current Flow (AC Conduction)
To compute current flow, the AC conduction field solver uses the
following relationship:
I = J dA (2.37)
where
I is the current
J is the current density, given by J = E
A is the area over which the current flow is computed. It is found
by sweeping the current flow line that has been drawn in the xy-plane into
the z-direction, forming a 3D surface. The current flow computed is the
current per meter depth in the z-direction. A separate current flow value is
computed for each line drawn by the user.
36
2.5 FINITE ELEMENT METHOD FOR ANSOFT
The finite element method for Ansoft uses following steps to ar-
rive at final solution (Dommel 1974). These steps can be followed by the
user based on the individual problem to be solved.
2.5.1 Types of solver
This is to select the type of solver required. They are:
1. Electric field
2. AC magnetic field (with variable step frequency)
3. DC magnetic field.
The following steps define the step wise procedure to solve an
electric problem in this package. This has to be systematically followed to
get accurate results.
2.5.2 Drawing plane
This is used to select a Cartesian model (xy plane) or an axis
symmetry model ( rz plane). In xy plane the drawing space is centered at
the origin. In rz plane z-axis lies on the left edge of the drawing space.
The user has to draw the cross section geometry based on his requirements
and problem for a specific application.
2.5.3 Define model
This has two options
1. Draw model
2. Group object
37
2.5.4 Draw model
This is used to draw a geometric model. Here we can specify the
size of drawing and also the drawing units. The grids are available to help
in the same. The models can be drawn in both XY and RZ plane depend-
ing on the symmetry of the object.
2.5.5 Group object
It is used to identify groups of geometric objects that are to be
treated as a single object, eg. the path of parallel conductors. The software
has got provision for indicating the return path for the conductors during
the analysis.
2.5.6 Setup Materials
This is used to add materials to a database and then assign them
to objects in the geometric model. The identified objects are first required
to acknowledge by the system software by user name. This is followed by
the process of assigning material data base, for example magnetization
curve, material characteristics etc.
2.5.7 Setup Boundaries
A boundary condition allows specifying the behaviors of the
electric or magnetic field at object interfaces and the edges of the problem.
2.5.8 Setup Executive Parameters
It is used to compute matrix (capacitance, impedance, conduc-
tance, or admittance), force, torque and flux linkage. The sources and
boundary conditions should be assigned accurately as any discrepancy in
this assignment may lead to an error at a later stage. The erroneous data is
38
not segregated and so user has to be careful and cross check the same. In
case of time varying solution linear with stepwise solution, the solutions
are also in steps. The program has to be run several times with the same
setup with incremental solution. The mesh can be made to solve manually
to get best results in specified area. The accurate results can be obtained by
more number of passes. More the number of iterative passes to solve, the
longer it takes to solve to arrive at precise solution.
2.6 SOFTWARE ADVANTAGES
The software has the advantage of giving the results for a particu-
lar set up within limited time without the actual hardware. The same simu-
lated model conditions, setup can be used to analyse the results in frequen-
cy as well as time domain. The parameter extractions is much easier using
the Ansoft after drawing model in appropriate plane (XY or RZ), and ana-
lyzing at frequency of interest. The Pspice is more suitable for the transient
time domain analysis. The post processor is a powerful tool that gives
graphical interpretation of outputs on solved parameters. The average time
taken to solve a problem is of the order of about 1-2 hours provided all da-
ta inputs are correct with Pentium based machines of 1GHz. The generated
data on user request gets stored. The post processor has to be applied to get
the results in the user required formats for the essential parameters. It is
possible to carry out Fast Fourier transform analysis on the results using
post processor. The graphical output of the various parameters can be plot-
ted on the screens.
39
2.7 SIMULATED MODEL FIELD STUDY
2.7.0 Introduction
The vehicle and its subsystems were studied for EMI effects with
the following sources to derive the possible electrical parameters such as
‘L’ and ‘C’, admittance matrices, inductance matrices and coupling ma-
trices. The objective of simulation is to study the field pattern and deriva-
tion of coupling matrices in the presence of known sources. It can be fur-
ther extended to a study leading to derivation of equivalent circuit diagram
from the mechanical dimensions with known sources.
1. Vehicle modeling with external EMI sources such as transmis-
sion line and lightning (Diedforfer 1990).
2. Individual vehicle modeling in the presence of power sources on
board the vehicle with surface current. The coupling effects of
the same to the various parts within the vehicle.
3. Multiple vehicles EMI coupling in the presence of known power
source in close proximity.
4. Modeling of power cables within vehicle in the presence of asso-
ciated current source.
5. Modeling of Slipring assembly (product catalog) on along with
power elements
The main objective of the simulation is to study field patterns,
coupling matrices for vehicle in the presence of known external source
(Clay 1978). The second part of the study is associated with effect of EMI
sources for internal modules leading to derivation of equivalent circuit dia-
gram from the mechanical dimensions. The presence of known source vol-
40
tage or current helps us to investigate EMI problem thoroughly for combi-
nation of sub system with external sources. The lightning is considered as a
straight segment of current with a negligible cross section for the purpose
of calculation for cloud to ground discharge in modeling (Rokosh 1996).
The cloud-to-cloud discharge can be modeled as straight horizontal column
of current. The electromagnetic noise exists in the transmission line along
with the presence of radiated electromagnetic energy from lightning dis-
charge. The horizontally polarized waves are picked up and they appear on
the line.
NEMP is considered a major threat for the automobile and has to
be addressed properly. The NEMP source can be modeled as a circle with
assigned values of current and voltage in the simulation (Janes 1999). The
EMI levels in the presence of external disturbances like transmission line,
EMP field etc. has been modeled in this case study. Air Burst NEMP (2-20
km) results in small net vertical dipole current along with weak radiated
field. Surface Burst NEMP (0-2 km) results in a large net vertical dipole
current due to air, earth interface asymmetry also there is large radiated
field with local coverage (Braisy series 1987), Naidu et al (1990).
2.7.1 Lightning and EMP
The Lightning ( CA Nucci et al 1993) and NEMP are two threats
that requires careful study by a system designer. A 100 kA severe lightning
stroke at 100 m distance is a good assumption for study purpose; similarly
the NEMP corresponds to High altitude burst. The radiated spectral density
from the lightning at low frequencies (less than 10 kHz) from the lightning
is about 40 to 60 dB greater than NEMP. The NEMP spectral density at
41
higher frequencies above 100 MHz is about 30 dB greater than lightning.
They are comparable at 2 MHz range.
The fields strengths encountered are of order of 10 V/m to sever-
al 50 kV/m (Cooray 1998), (Farhad 1997). It is also typical that radiated
frequencies lie in the range of 10 KHz to GHz which is normally the oper-
ating frequencies of the various systems in defence. They inject current in-
to the exposed cables mounted on the vehicle basically by radiated fields
coupling into cables. Similarly the transmission line at higher point is more
prone to the strokes and induced voltages may of the very high order (Lo-
thar 1986).
EMI threats are lower at low frequencies owing to low coupling
factor and leaky cables and boxes. However at mid range of spectrum (1-2
MHz), attenuation of about 60 dB is required due to meet threat levels of
about 10 V/m and additional attenuation of about 20 dB at GHz range. The
nearby lightning stroke is typically two or three orders of magnitude great-
er in rise time and pulse duration than these values of NEMP. Hence more
hardening is required to meet the threats due to lightning than NEMP, also
the occurrence of NEMP is much reduced phenomena (Jorden 1992).
The transient simulation is carried out to assess the nature and
likely impact of the overvoltage’s on a given system ( Melville 1984 ). The
transients arise due to control action, faults and surges such as lightning
surges, NEMP etc. The response to these events is initially dominated by
resonances in the lumped RLC parameters and traveling waves in a distri-
buted parameter components such as transmission lines, cables etc.
42
2.7.2 Model representation for tracked vehicle
The vehicle system model is usually a large multi node electrical
equivalent circuit containing both active and passive elements, time de-
pendent components and sources (Tront 1984).The solution is required in
steady state as well as transient state operation and the calculation time
step must be small enough to predict the events in milliseconds range.
There two approaches suitable for this application, first one is based on dif-
ference equation technique, and other on the nodal analysis with linearisa-
tion. The difference equation technique, based on theory of multi conduc-
tor lines was developed by Dommel (et al 1974) for analysis of traveling
wave and surge phenomena in power transmission line networks. The
second method is based on nodal analysis of discrete components electrical
networks, is the spice package developed by university of California,
Berkeley.
The vehicle dimensions are 3.1m x 4m x 2.6 m. The components
of the 2D model namely the transmission tower, insulator strings and con-
ductors; the vehicles can be easily modeled using the software package
called Ansoft. A 2D vehicle model simulation for worst EMI as shown in
Figure 2.4 depicting external coupling with a transmission line source has
been modeled in the present study. The vehicle was placed just below the
transmission tower in close proximity.
The antenna is located on the rear centre of vehicle to enable the
communication with each other in field areas. The vehicle roof top is large
gives a uniform and symmetrical ground plane and provides Omni direc-
tional coverage. The opening on the top is assumed to be all closed, mod-
ules such as lights, siren etc. located outside are grounded properly. The
transient response of line is described by Agarwal et al (1980) in the mag-
43
netic field. The ground conductivity is assumed to be nearly perfect
( -2 s/m) at close distances less than 2kms (Farhad et al 1996). Positive
field convention is used in all calculations though both positive and nega-
tive wave shapes exists in reality.
2.7.2.1 Capacitance and inductance of transmission line and
lightning channel
Farhad (et al 1996) in his studies has indicated the assumption that
lightning channel has been considered as vertical one-dimensional antenna;
the line has been considered as infinitely long. The vertical component of
electric field and horizontal component of magnetic field several studies
have shown that the intensity can be calculated to reasonable accuracy by
assuming ground as perfect conductor. The radial distance from the ligh-
tening channel to the observation point is about 100m located 6m above
ground. The horizontal component of the electric field about 6m (4m
height of vehicle + 2 m height of antenna) with a ground conductivity of
about 0.01S/m with a stroke current value of about( analytical model )
i(o,t)=Io [exp (- -exp (- ... (2.37.1)
with I 4 7 /s
and return stroke velocity of about 1.1x108m /s
Consider an overhead transmission line wire above at 10m height
the distributed conductor inductance and capacitance can be computed by
formula
44
The inductance per unit length of lossless wire above perfectly con-
ducting ground is given by the formula µo L = ln (2h/a) for h >> a (2.38) Similarly the capacitance per unit length of the wire is given by the for-
mula o
C = for h >> a (2.39) ln (2h/a) where ‘a’ conductor diameter , ‘h’ is the height of conductor from ground,
µo ,, o permeability and permittivity resp.
This transmission line model is more valid for frequency up to range of
100 MHz is accurate in the range below 30 MHz. This approximation is
not valid for fast NEMP transients and poor ground conductivities
<< s/m.
Tracked Vehicle Transmission line
EMP source
Figure 2.4 Flux plot of the vehicle with the transmission line
(external EMI source)
45
46
2.7.2.2 Software Model assumptions
The field levels under an EHV transmission line can be measured
precisely and enough literature is available on the same. However the
transmission line response in the event of lightning strike on one of the
conductor, the induced transients results in interferences. It is assumed that
there are no trapped charges on the EHV lines, no corona losses, switching
surges or pre-existing faults. The tower footing resistance is assumed to be
having no effect for EMI calculations of short transmission lines. The lines
are terminated into matching impedances at load end. The simulation con-
dition is based to depict the early transient that sets in as soon as there is
strike in the EHV line accompanied by traveling wave phenomena under
ideal conditions. The vehicle is placed at about 10 m from the base of
tower transmission line. The separation between two vehicles is 10 m for
the field simulation studies involving multiple vehicles. The distance also
varied in steps to visualize the effects of EMI with distance in the individ-
ual vehicle case on a particular point on vehicle. The other conditions in-
cluding source, model, and initial conditions are assumed to be fixed dur-
ing the distance effect case study.
2.7.3 Source Assignment (Nominal Problem)
The Transmission line with vehicle below it is modeled in the
following current and voltages on one of the conductors. The studies made
on dart leaders and return strokes indicate that the lightning channel can be
assumed to be a vertical one-dimensional antenna above perfectly conduct-
ing ground. The linear charge density is assumed to be small charge of the
order of 0.01 c (Kuffel 1984).
47
The horizontal component of the lightning electric field in the
calculation of the induced overvoltage on overhead power and distribution
lines in the context of coupling formulation of Agarwal et al (1984) has
been well established. The horizontal component of lightning is assumed to
couple with one conductor only.
V = V0 (e (- t) – e (- t) ) (2.40)
I = I0 ( e t) - e(- t)) (2.41)
where I0 = 10 kA
V0 = 15 kV
= 3.1 x 104 / s
= 10 7 / s
The nuclear EMP from the high altitude EMP can be approx-
imated to plane wave in the vicinity of power transmission line near the
surface of the earth. The nuclear pulse can represented as an exponential
waveform given by
E (t) = E0 et/ (2.42)
strong electromagnetic field produces transients on the power lines .They
also couple into cables with improper shielding. They produce spherically
rays collide with the air molecules to produce fast moving electrons hence
current with similar symmetrical distribution.
48
2.7.4 Electrical Data
The following materials have been assigned to the 2D model simulated:
Transmission tower structure - Steel 1010
Insulator strings Porcelain - 14 nos. – 220 kV
(254x146 mm disks used) 23 nos. – 400 kV
Conductor Size - 54/3.53 mm aluminum
Vehicle - Steel 1010 with Rubber track links
Barrel - Air
Antenna Insulating Base - Teflon
Antenna Material - Copper
2.7.5 Boundary conditions
For the Electrostatic solver
1. Potential of outer boundary 2D model = 2.3 V
2. The initial charge on the vehicle before simulation = 0.001 C
3. The initial potential of the tower (leakage Voltage) = 10 V
For the Magetostatic solver
1. Vector potential of outer boundary = 0.005 Wb/m
2. Vector potential of the vehicle = 0.01Wb/m
The vector potential of the vehicle has been assumed as 0.01
Wb/m, since a small leakage current present on the vehicle surface. The
material data (P Neelakanta 1999 ) used for the FEM simulation on Ansoft
is indicated in Table 2.1.
49
Table 2.1 Material data used for FEM simulation
Description Material r- Relative permittivity
-Conductivity Siemens/m
Vehicle chassis pads Rubber 3.25 1 E –015 Vehicle chassis Stainless steel 1.0 2.0 E +006 Conductor Copper 1.0 5.8 E +007Background Air 1.006 0.0 Aluminum 1.00 3.72 e+007 Bakelite 4.8 1 E – 009Teflon 2.8 0.0 Ground - 0.01
2.7.6 Type of Problem - Nominal / Variable
The present simulation of interference due to lightning source has
been considered. The interference caused due to the lightning lies in the
frequency range of 10 kHz to 300 MHz (Diedorfer 1990). These are the
frequencies where coupling with cable is dominant, forms susceptible
range for automotive systems. The standard double exponential wave
shape has been simulated for this purpose.
There are several ways through which a problem can be solved in
either electrostatic or magnetostatic solvers or AC conduction solvers. The
problems are:
Nominal problem
Variable problem
In the nominal type of problem, the source is assigned the actual
magnitude. No functional variation is assigned to the nominal value. In
50
the variable type of problem, the relevant function is assigned to the
source. The 2D model of EHV tower (Murthy et al 1990) with dimensions
mentioned as in and vehicle has been considered to simulate the interfe-
rence caused due to the lightning .The sources are assigned to both the
nominal and variable problems as indicated in Section 2.7.3 , Section 2.74
and Section 2.7.5. The crucial electronics are frequency dependent and the
energy is concentrated in the specified frequencies. The FEM can be used
to solve frequencies up to several hundreds of MHz. The EHV line switch-
ing overvoltage factor is indicated in Table 2.2.The transmission lines have
considerable electric and magnetic fields in near vicinity including present
case of EHV circuit line (Lalli 1994).
Table 2.2 Switching Surges – Overvoltage Factors
Description Voltage level (p.u) Maximum operating voltage 1.1 220 kV
1.05 400 kVSwitching surges 2.5 220 kV
2.0 400 kVImpulse flashover voltage 1.15 Positive impulse withstand voltage (1/ 50 s)
6.5 Vph 220 kV 5.0 Vph 400 kV Where Vph is phase to neutral voltage
Figure 2.6 indicate the voltage profile below an EHV transmission line
form midspan to either sides of EHV line. Table 2.3 indicates the electric
field intensities under transmission line for various system voltages.
51
Table 2.3 Electric field intensities at mid span under electric power
transmission line carrying different voltages at ground level
System voltage kVElectric field intensities
kV/m
123
245
420
800
1200
1-2
2-3
5-6
10-12
15-17
Figure 2.6 Electric field intensity profiles at ground level for an
supply frequency EHV line from mid span on either sides
of transmission line
The wave impedance is the ratio of the vertical electric fields (Ex) to that
of horizontal magnetic fields (Hy) is denoted as Zz.
Zz.= .
20
E Kv/m
020 meters
52
The surge impedance is the ratio of the voltage to the current for power
lines during the surge phenomenon.
Figure 2.6.1: Magnitude profile of vertical electric field generated by
EHV power line above the ground ( 10m ) at 10 MHz.
A lightning channel a 100 kV wave front, with capacitance has a charge
given by
Charge (Q) = C.V = 12 X 100 x
= 1200 x C = 1.2 µC /m
The total transmission line voltage developed and lossy ground
effects due to open termination with finite length and matched imped-
ances wherein the voltages are on higher side but less frequent due to
source to load impedance mismatch. The effect of corona is also neglected
for the first few cycles as its onset is generally delayed on a transmission
line (Harrington1983).
Distance in meters
f (frequency of interest) = 10 MHz I (current) = 1 A d (height above ground) = 10ma(conductor diameter) =.025my(electric field component)=0
53
2.7.7 Discussion of simulation results for vehicle
The simulated studies are mainly done to predict the EMI interfe-
rence effects during various contingencies like lightning impulse surge,
NEMP etc. The EMI design engineer keeps these levels to the lowest poss-
ible values. The aim of the present study is to estimate the levels of EMI
voltages that will be present when the threat condition exists. The role of
each model and its affect on the other can be clearly demonstrated using
software simulation. The study was mainly confined to the interference
caused due to lightning surges. The levels of EMI were predicted for a par-
ticular case to enable us to see whether it is possible to deploy critical
equipment in the close vicinity, and knowledge of the safe distance is a
great advantage. The equivalent circuit is valid only for early response pe-
riod within few hundred of microseconds in case of duration is large than
the other factors shall be taken into consideration.
2.8 MODELING FOR VARIABLE PROBLEM
The tracked vehicle may be susceptible to EMI in close proximi-
ty to the interfering radiating source. An interference pattern in E (electric
field intensity) and H (magnetic field intensity) were observed. The inter-
fering frequencies were simulated in between 10-100 MHz which is nor-
mal communication band for the defence. The vehicle was placed below
the insulator strings of the transmission line as shown in Figure 2.4 and so-
lution was obtained at RF frequency of 10 MHz (Nominal problem). This
is to check the performance at lowest frequency end of communication for
vehicle.
54
In the next step with given position of vehicle with transmission
line, the frequency assigned to the source was varied. The step wise varia-
tion of source frequency was done from 10 MHz to 100 MHz covering the
entire communication band for vehicle (Variable problem).
The source assignment is indicated in section 2.7.3, the electrical
data in section 2.7.4 and the boundary conditions in 2.7.5 of this thesis.
The voltage flux plots for given frequency of interest were obtained and
are indicated in Figure 2.5. The interference levels were observed to be de-
pendent on the relative position of the vehicle with the tower. EMI levels
increased with increase in the proximity of vehicle to the source for a given
frequency with other variable constant. The inductance matrix and capacit-
ance matrix indicate the interdependence or influence of the individual
components among each other as indicated in Tables 2.4 and 2.5.
The interference signal levels are significant and can get coupled
through open ports and antenna mounted externally to the vehicle. Similar-
ly the onboard cable coupling is a predominant phenomenon within the ve-
hicle as cables lie in close proximity (Edward 1978).
2.8.1 Wire to Wire Coupling:
The signals couple from wire to wire due to inductive or capacitive
coupling. The countermeasures for the same are separation of wires,
twisted pairs, shielded wires, noise tolerant systems and noise suppression
at source.
55
Electrical transients are created whenever inductive loads are dis-
connected. A voltage across switch contacts exceeds air breakdown than a
spark/arch takes places creating ( Kley 1993) EMI transients.
Table 2.4 Inductance coupling matrix due to conductor on the
Vehicle (mH/m)
Conductor conductorC1 conductorC2 conductorC3 Vehicle Model
C1 2.42 x 10-3 4.23 x 10-3 5.3 x 10-3 12.3 x 10-6 C2 4.23 x 10-3 14.4 x 10-3 87 x 10-3 41 x 10-6
C3 5.3 x 10-3 87 x 10-3 23 x 10-3 1.4 x 10-6
Vehicle Model
12.3 x 10-6 41 x 10-6 1.4 x 10-6 4.3 x 10-3
Table 2.5 Capacitance coupling matrix due to conductor on the
Vehicle (pF/m)
Conduc-tor conductorC1 conductorC2 conductorC3 Vehicle
ModelC1 8.1 6.23 7.1 9.3C2 6.23 8.8 8.7 3.1C3 7.1 8.7 9.2 1.2Vehicle Model
2.3 3.1 1.2 4.2x10-3
2.9 INTRODUCTION TO PSPICE
PSPICE (1996) is an analog simulator that was developed at the
University of California at Berkeley ( Pspice 1996). PSPICE is one of the
many commercial SPICE derivatives, and has been developed by MICRO-
56
SIM Corporation. SPICE stands for SIMULATION PROGRAM WITH
INTEGRATED CIRCUIT EMPHASIS.PSPICE'S strong point is that it
helps the user to simulate the circuit. Hence, the designer has flexibility to
make changes on the prototype model without any hardware. As soon as
the test design is completed, PSPICE can help us run a check on it before
deciding to commit ourselves to build a hard model. Hence, PSPICE al-
lows checking the operability of the circuit model in real time simulation
to validate its suitability. Since all the tests, designs and modifications are
made over a terminal; the designer can save a lot of money and time that
would have otherwise been spent on the building of actual hardware mod-
els and modifying them to achieve the desired results. PSPICE can enable
us to the check the circuit operations before building an actual physical
breadboard. It also allows us to develop the models and can simulate the
real time effects from it. It also enables us to carryout test measurements
that can be either difficult or inconvenient.
2.10 FEM ANALYSIS OF SLIPRING ASSEMBLY
The automotive system of fighting vehicle consists of several
critical subassemblies that cause EMI problems to the others systems
working in close proximity. The Slipring Assembly (Figure 2.7) is a sys-
tem where a large amount of power and signals are being sent in short
space envelope from a stator to rotor at about 50 rpm speed. These assem-
blies are critical for the proper functioning of the various systems that are
controlled by them. The modules are required to work in the harsh envi-
ronmental field conditions carrying enormous power of the order of 600 A
along with analog and digital signals (Defence catalog).
57
Figure 2.7 Slip ring assembly
The studies were carried out on a model of slipring assembly on
power and signal rings in both X-Y & RZ plane. A pancake type slipring
assembly about 330 mm diameter and 100 mm height with 30 rings was
used for simulation study in desktop computer. The slip ring assembly
forms an integral part of power supply distribution inside the vehicle.
2.11 SIGNAL INTEGRITY
Signals are transmitted from one component to another in digital
form. The EMI is basically associated with the signal waveform distortions
caused by several factors. The reflection noise is caused due to imped-
ance's mismatch, stubs and other discontinuities. The cross talk that is
caused due to electromagnetic coupling between the signals intended to
matching impedance for the simulation purpose.
58
FIGURE 2.7.1 Conductors lying to close proximity in slip ring
assembly with test setup
The cable dimensions and its characteristic impedances of 50
modeled as accurately as possible (Alan et al 1996). The resonance fre-
quency of the cable is fo and peaks occur at multiples of fundamental fre-
quencies. The resultant shield currents are also seen to peak at these fre-
quencies.
At higher frequency the current is uniformly distributed at the annu-
lus at the surface of the conductor thickness equal to skin depth (
(equation 2.43).
(2.43)
Where µ = permittivity,
Thus at high frequency resistance increases as and internal imped-
ances decreases as .The internal impedance of conductor of circular
cross can be given as equation 2.44 (Alan et al 1996),
50 50
V V
++
+
+
-
VNE
2
Ground
VFE
Vs VL
+ +
+
50 50
1
Vs(t)
59
(2.44)Where Vdc, lidc = dc resistance and inductance resp.
Rhf lihf = High frequency resistance and inductance
f0 = frequency cutoff
equals twice skin depth based ‘wheeler’s inductance rule’.
At high frequencies the resistance equals inductive reactance
rhf = . li hf
Load resistance, source impedance is set equal to 50
conductors .The source voltage is set to Vs = 1V, Step input given is 50 X
10-9 at one end of the conductor as in Figure 2.7.1.The per unit capacit-
ance matrices (C= pF/m) and inductance matrices (L = µH /m) is com-
puted and depicted in Figure 2.10 for signal ring and Figure 2.11 for pow-
er ring. The noise levels assorted are indicated in below Table 2.5.1 for
both end impedance 50
TABLE 2.5.1 Track noise level of Slip ring assembly
Track width Track height Track length Noise level
1. 2.0 mm 2.5 mm 22 Cms 0.6V
2. 3.5 mm 2.5mm 15 cms 1.13V
3. 3.5 mm 2.5mm 33 cms 0.43V
=
60
2.12 CROSS TALK AND COUPLING IN VEHICLE
Cross talk is defined as interference to the signal path from other
localized signal paths. This is often limited to circuits /conductors working
in close proximity where the coupling path is characterised by either mu-
tual capacitance or mutual inductance of circuits. The cross talk source
may be both intended and spurious noise that gets coupled into signal paths
of circuits. It includes coupling due to electromagnetic field, and either
electric field or magnetic field into a systems. The modes of coupling
depend on the circuit impedance, frequency and other factors. When the
product of source and receptor circuit impedance is less than 3002
.Coupling is predominantly magnetic field. When the product of source
and receptor circuit impedance is more than 10002 , then the coupling is
predominantly electric field. When the product lies in between 3002 and
10002 , then the coupling may be either magnetic field or electric field
depending on the geometry and frequency ( David 1991).
The present study pertains to parallel signal tracks located above
a ground plane. The source and receptor circuits are terminated into 50
resistors for the analysis purpose.
2.13 MODELING OF SLIPRING ASSEMBLY BY FEM
ANSOFT / PSPICE
2.13.1 Introduction
The slipring assembly is a module where a large amount of single
power and several signals are being sent in short space envelope from a
stator to rotor. These assemblies are critical for the proper functioning of
the various turret systems that are powered by them.
61
2.13.2 Capacitance of power supply rings (Busbars)
The capacitance of supply rings was computed using ANSOFT,
the following steps were followed. Electrostatic problem was made in X-Y
plane after drawing the RBJ cross section 2D model. The RBJ module
power supply rings are made of copper conductor with outer frame of alu-
minum alloy. The various insulating materials used are mica, teflon, epoxy
etc as shown in the cross-section,( Figure 2.8). The busbars rings carry a
voltage of 28.3 V. The executive parameters were set for the measure-
ment of stator capacitance in between busbars 1,2,3 etc. and rotor busbars
1,2,3 etc. (mutual & self). The solution of the above problem was obtained
Ansoft. The value of capacitance was computed and equivalent circuit was
drawn for the RBJ. The electrostatic solver was used for the above compu-
tation and potential plot is shown in Figure 2.9.
2.13.3 Inductance of power supply rings
The inductance of supply rings was computed by repeating the
above steps which were used to determine the capacitance of supply rings
except that the magneto static solver was used with setup boundaries with
currents in power conductors. The conductor current source was assumed
to be 600 A, with boundary condition 0.001 Wb /m. With the above condi-
tions the problem was solved and the inductance of power supply rings
was computed.
62
2.13.4 Capacitance of Signal Slip Rings
The capacitance of signal slip rings was computed using
ANSOFT 2D modeler. In the electrostatic problem the plane of cross
section for simulation study based on symmetry a XY and R -Z Plane were
used. The signal slip rings that the dimensions: Size of rings: 2.5mm * 3.5
mm, with about 30 rings for transfer of signals. The distance between the
rings is about 3.5 mm. The setup materials for modeling: Signal Rings -
Copper conductor, insulating material Mica. The sliprings were assigned a
voltage level of V = 28.3 V. The computation of the capacitance between
rings stator 1,2,3 etc. and rotor rings 1,2,3 etc. were carried out during the
course of simulation for a standard input signal applied to rings.Error!
Figure 2.8 Slipring assembly -cross section
2.13.5 Inductance of Signal Slip Rings
For determining the inductance of slip rings the steps which are
used to determine the capacitance of slip rings were followed except the
problem and setup boundary. In the magnetostatic problem with normal
PositiveNegative
Signal ring
63
boundary condition, for all sliprings were assigned a load current of 10A.
The solution was obtained for the signal slip rings and the inductance of
slip rings was computed.
2.14 DISCUSSION OF SLIPRING ASSEMBLY SIMULATION
The slipring assembly was modeled using pspice and Ansoft 2D
FEM modeler for the performance evaluation and extraction of the R , L ,
C parameters. The lab measurements made were found to be in concur-
rence with the simulation results within reasonable accuracy of 8-10%. The
deviation is mainly due to the complexity of RBJ internal layout and the
other interface elements like connectors, ground conductors which were
not included in the model.
Figure 2.9 Flux distribution pattern within the Slipring.
The slipring simulation results in the form of equivalent circuit
diagram of signal, power rings and complete circuit from source to load are
shown in Figures 2.10, 2.11 and 2.12 respectively.The Pspice simulation
slipring assembly (RBJ) results are shown in Appendix ‘2’ of this book.
64
where Rs : Signal ring resistance
Figure 2.10 Equivalent circuit diagram for signal rings .
where Rp : Power ring resistance
Figure 2.11 Equivalent circuit diagram for power rings.
µH
µH
µH
µH
µH
µH
Rs
Rs
Rs
Rp
Rp
Rp
65
Figure 2.12 Equivalent Circuit diagram from source to load
66
2.15 CAPACITANCE OF INTER CONNECTING CABLE
The 4-wire conductor arrangement configuration as indicated
Figure 2.13 shows parallel near field signal lines. The circuits have the
second conductor as return at same potential then this can be replaced by
two-wire configuration. If the capacitance of the wires connected are c1
and c2, also if the conductor are same height i.e then c1= c2 and capacitance
is given by (equation 2.45) ( David 1991).
3.688 r c1= c2 = (pF/ft) (2.45)
log{h/d + 2 - 1 } Where r = Relative permittivity of medium in between wires
h = Height of the conductor wires
d = Diameter of the wires
d
D
h
Figure 2.13 Four wire capacitive arrangement
The mutual capacitance for dielectric medium with air as insula-
tion around wires then (equation 2.46) C2 {ln 2 }
C12 = (pF/ft) (2.46) ln (2h/d –h/2.72)
where D is the distance between the circuits.
67
2.16 MODEL DIMENSIONS FOR INTERCONNECTING
CABLES
For determining the capacitance of RBJ interconnecting cables
the following steps are to be followed. The cable details are given below.
Radius of the conductor = 5.1 mm
Thickness of dielectric 1 = 2 mm
Thickness of dielectric 2 = 1 mm
Thickness of aluminum sheath = 1.5 mm
Conductor material = Copper
Outer sheath = Braided Aluminum sheath
Dielectric 1 = Nylocast
Dielectric 2 = Nylon
Dielectric 3 = Rubber hard
Setup boundaries for model: Conductor -Voltage source 28.3 V
The capacitance of the cable was computed using input signals.
2.17 HEAVY DUTY CABLES IN CLOSE PROXIMITY
For determining the inductance of cable the above indicated steps
are required to be followed to compute capacitance of interconnecting ca-
ble. The magnetostatic with boundary conditions with conductor-positive
current source -550 A. With above conditions the problem was solved and
the inductance of cable was computed. The twin cables Figure 2.14 are ly-
ing in close proximity are carrying currents of the order of 550 A onboard
the vehicle. These cables have shield at the top of them. The cables are as-
sumed to have uniform cross-section as shown in the 2D model. This is
solved as typical magnetostatic problem based on the details as per section
68
2.16 and the results are indicated in Figures 2.15, Figure 2.16. The coupl-
ing coefficient (inductance) matrix between each of these elements has
been listed out at user request in matrix form and are indicated in the
Tables. Tables 2.6 and Table 2.7 indicate the coupling coefficient (induc-
tance) and inductance matrix (distributed) for two power cables along with
sheaths lying in close proximity with each other.
The following power cable elements have been modeled in for ease of ref-
erence.
C1 Conductor 1
C2 Conductor 2
Sh1 power cable Sheath 1
Sh2 power cable Sheath 2
Similarly, the solution for the signal cables lying in close prox-
imity, for was obtained at high frequency of 10 MHz with following source
assignment.
Conductor1 = 100V
Conductor2 = 10V
Chassis leakage Voltage = 3V
Shield = 0.3V.
The problem was solved in AC conduction and coupling coeffi-
cient obtained in shown Table 2.8.The Table 2.8 gives results of iteration
obtained at 10 MHz for signal cables lying close to each other.
Pos1 signal lead1
Pos2 signal lead 2
Sh1 Signal cable Sheath 1
Sh2 Signal cable Sheath 2
69
Table 2.6 Coupling coefficients (inductance) power cables along
with sheaths lying in close proximity with each other
Conductor 1
Conductor 2 Sheath 1 Sheath 2
Conductor 1 1.00000 0.99818 0.38416 0.05032Conductor 2 0.99818 1.00000 0.32830 0.10987Sheath 1 0.38416 0.32830 1.00000 0.86475Sheath 2 0.05032 0.10987 0.86475 1.00000
Table 2.7 Inductance matrix (distributed) for power cables along
with sheaths lying in close proximity with each other
Conductor 1 Conductor 2 Sheath 1 Sheath 2C1 7.5299 E-007 -7.44589E-007 9.53025E-007 -1.13640E-007
C2 -7.4458 E-007 7.38974E-007 -8.06843E-007 2.45808E-007 Sh 1 9.5302E-007 -8.06843-007 8.17338E-006 6.43414E-006
Sh 2 -1.1360E-007 2.45808E-007 6.43414E-006 6.77330E-006
Table 2.8 Coupling coefficient (Admittance) at 10 MHz for signal
cables
gn pl pos2 shl sh2 gn 1.00000 0.00000 0.00000 0.22077 0.22176 pl 0.00000 1.00000 0.00000 0.90808 0.00000 pos2 0.00000 0.00000 1.00000 0.00000 0.90795 shl 0.22077 0.90808 0.00000 1.00000 0.07160 sh2 0.22176 0.00000 0.90795 0.07160 1.00000
70
Figure 2.14 Twin power cables in close proximity flux plot
with known sources of Currents
Figure 2.15 Arrow Plot of twin cables in
close proximity
Cable 1 Cable 2
71
The self capacitance of the receptor circuit plays a vital role in coupling of
energy into system and coupling coefficient ‘K’ is given by the formula
K=C12/ C2 +C12 (2.47)
Figure 2.17 Crosstalk circuit equivalent for an EMI source coupling
into nearby circuit (susceptor)
Figure 2.16 Signal cables in close proximity Electric flux plot elements
C1
RLRS C2V1
72
Where C12 is the mutual capacitance between source and susceptor
C1 self capacitance of circuit
V1 is the EMI voltage
Rs and RL are source and susceptor circuit impedances
Crosstalk coupling coefficient for cable with shields equal to mutual
capacitance divided by sum of all capacitances with respect to ground
(Figure 2.17).The maximum crosstalk voltage is therefore source voltage
times coupling factor. The time constant of the circuit is
s RL / RL+ Rs } * (sum of circuit capacitance) … (2.48)
c-
tion is greater than the time constant.
2.18 TRACKED VEHICLE FIELD DISTRIBUTION WITH
KNOWN SOURCE
The tracked vehicle with barrel, along with antenna used for
communication (6 m height) has been modeled for study purpose. The
vehicle chassis is made of stainless steel 1010. The vehicle antenna has
excitation voltage of 10 V. The voltage distribution in such a case is shown
in the Figure 2.18. The close study of output profile clearly indicates the
effect of medium high voltages in the presence of system surface currents
and voltage. Table 2.9 shows the coupling coefficient admittance matrix
for the individual tracked vehicle alone in the presence of sources.The in-
terference E fields generated with the external fields is shown in the
Figure 2.18.
73
Table 2.9 Coupling coefficient admittance matrix for the individual
vehicle alone in the presence of EMI
Antenna Chassis Barrel Inte-rior (Air) Gun
Antenna 1.00000 0.98832 0.00000 0.00313Chassis 0.98832 1.00000 0.00000 0.14718Barrel Interior (Air) 0.00000 0.00000 1.00000 0.00000Gun 0.00313 0.14718 0.00000 1.00000
The lightning source is depicted as a vertical column in the study
with following source assignment at discrete EMI frequency 10 Hz, 60 Hz
etc. The Source Voltage= 50 kV, Antenna voltage= 100 V, Chassis
voltage 10V for FEM purpose .
The Figure 2.19 shows E (V/m) fields generated at the surface of
the vehicle/ vertical source. The Figure 2.20 shows Voltage flux (V) profile
generated during simulation study of the vehicle. Figure 2.21 shows the
Maxwell admittance at 10 Hz during simulation for vehicle with lightning
source. The Figure 2.22 depicts Maxwell capacitance (lumped) for the ca-
ble assembly set up. The Figure 2.23 depicts Coupling coefficient (Capa-
citance) for the vehicle. The Figure 2.24 shows SPICE Capacitance matrix
(Lumped) vehicle. The Figure 2.26 indicates the Maxwell Capacitance ma-
trix (Distributed pF/m) vehicle. The Figure 2. 27 shows Coupling coeffi-
cient for the automotive cables. The Figure 2.28 depicts Conductance
matrix for the automotive cables. The Figure 2.29 shows SPICE admit-
tance matrix with EMI source 60 Hz.
74
75
76
77
78
79
80
81
82
Figure 2.29 SPICE admittance matrix with EMI source 60 Hz
2.19 MULTIPLE VEHICLES WITH ANTENNA AND SURFACE
CURRENTS
The multiple models of the vehicle in close deployment are
shown in Figure 2.30 and a flux plot is shown Figure 2.31. Figure 2.32.
The vehicles have surface currents of 100 A / m2 with a balloon boundary
of 0.001 wb/m2. The antenna is assumed to be excited by a voltage with
known frequency.
83
2.20 SIMULATION OBSERVATIONS
The electric fields attenuation level increases with the fre-
quency and also distance from the source. It is observed that at lower fre-
quencies of about 300 KHz there is no effect less than 10 db. However for
EMI frequencies of the order of couple of MHz the attenuation quite sig-
nificant of the order of about 60 dB.
Figure 2.30 Multiple vehicle in close proximity at a distance
Figure 2.31 Multiple vehicle flux plot close proximity
10m-300m
84
The calculation of one field to the other is possible using Max-
well’s equation. It is known that E and H fields are coupled together using
Maxwell’s equation. If one quantity is known it is possible to determine
the other quantity easily.
2.21 CONCLUSION OF SIMULATION STUDY
1. The FEM Simulation studies were successfully utilized to model the
vehicle in the presence of external source viz. lightning NEMP etc.
The Ansoft and Pspice are very effective in arriving at optimum solu-
tion for a given scenario.
2. The slip ring assembly (RBJ) study indicates that
Figure 2.32 Vehicles admittance matrix at 10 Hz in close proximity
85
i. Reducing the track/ wire heights above ground plane or decreas-
ing the distance between the track/wires in circuit results in less
cross talk.
ii) The increase in track distance results in lesser cross talk.
iii) The cross talk is less by choice of distant rings in RBJ layout.
3. During the estimation of noise using Ansoft simulation it was observed
that EMI levels to be dependent on the relative position of the vehicle
with the tower.
4. EMI levels increased with increase in the proximity of vehicle to the
source, for a given frequency with other variables constant. The pre-
dominant attenuation is seen at higher frequencies (60-80 dB) about
40- 200 MHz, whereas the corresponding levels were about (10 dB)
for lower frequency ranges (few KHz to 2 MHz).
5. The cables lying in close proximity exhibited cross talk that resulted in
spurious EMI common mode and differential mode noise in power
supply (Appendix B).
6. The field plots and coupling matrix were successfully obtained and ta-
bulated for further analysis. The field plots were also obtained for in-
ternal modules within the vehicle. The variation in distance resulted in
weak interfering fields for frequency range from 10-100MHz.
7. The mechanical parameters enabled us to get electrical equivalence for
impulse response studies using the software. The equivalent circuit
diagram was obtained for the power system after parameter extraction
from the associated assemblies.
top related