CHAPTER 2 FINITE ELEMENT MODELING AND SIMULATION …shodhganga.inflibnet.ac.in/bitstream/10603/28123/6/07_chapter2.pdf · FINITE ELEMENT MODELING AND SIMULATION SYSTEM 2.1 INTRODUCTION

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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

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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.

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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)

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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

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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

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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

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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)

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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

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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)

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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 )

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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 )

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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

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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

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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

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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)

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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.

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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.

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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

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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

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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.

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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-

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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.