Modelling and Simulation of Complex Systems

COST 286, Wroclaw 17-18 Sept 2003

Christos CHRISTOPOULOSProfessor of Electrical Engineering

Electromagnetics Research Group (ERG)

School of Electrical and Electronic Engineering

University of Nottingham, Nottingham, NG7 2RD, UK

christos.christopoulos@nottingham.ac.uk

Outline:

• Profile of ERG• Modelling and simulation of complex systems at

Nottingham Coupling models for emission and susceptibility

in multi-wire transmission systems Whole System Modelling Coupled physical domain models• Outlook

Profile of ERG:

Five full-time academic members and an experimental officer

Ten research associates

Ten research students

Five visiting scholars

22 funded research projects

Total current external funding £2,850,000

Current areas of interest:

Fundamental development of CEM methods

Multi-scale modelling

Semi-analytical modelling techniques

Modelling and simulation for EMC/SI

Modelling and Simulation in Opto-electronics and Photonics

Coupled physical domain models

Fast transients and fault detection

Modelling and simulation of complex systems at Nottingham:

Coupling models for emission and susceptibility in multi-wire transmission systems

Whole system modelling

Coupled physical domain models

Coupling models for emission and susceptibility in multi-wire transmission systems

The main effort in this area is to devise algorithms which can be embedded into general EM field solvers to describe complex wiring systems such as wire looms.

This is typical of a multi-scale problem where the details of a wire loom are just too fine to be described in the conventional way as part of the modelling mesh.

The solution is self consistent and hence accurate within the limitations of the numerical model.

Issues addressed are, arbitrary placement, field-to-wire coupling and cross-talk, both for emission and susceptibility.

There are four approaches to this problem:

1. Separated solution (not self-consistent but simple to apply)

2. Conventional Holland model for single wire (quasi-static approximation)

3. Multi-wire models based on the quasi-static formulation of Holland

4. Multi-wire models based on the a modal expansion technique (MET)

y=0

y=d

zx

y

0 0

( , ) , ( , )d d

i is z s d yV j H x y dy I j C E x y dy

Field-to-wire coupling:

DEVELOPMENT OF A WIRE INTERFACE BETWEEN TLM NODES (quasi-static approximation according to Holland)

Consider a wire directed along the z-direction. From Maxwell’s curl equations in cylindrical coordinates:

t

H

r

E

z

E zr

Integrating this equation from the wire radius ‘a’ to some radius , and using the approximation that near the wire static conditions apply ie

r

QE

r

IH r 2

,2

0r

t

Q

Ct

IL

a

rt

Q

a

r

t

IrE

ddz

1

)ln(

21

)ln(2

)(

0

00

where I is the conductor current and Q is the charge per unit length, gives after some manipulation:

In this expression Ld and Cd are the wire inductance and capacitance with respect to some reference return conductor at a radius . We will discuss latter what this

should be. Ez( ) is the field at this radius.

This expression tells us how the electric field and the conductor current and charge are related.

0r0r

0r

11

12

6

1

5

10

4273

8

91

5

10

11

427

12

3

68

9

y

xz

Let us place a wire directed along the z-axis!Port 10 of the (x,y,z)

node couples

with the wire

Port 6 of the (x+l,y,z)

node couples

with the wire

Our task now is to enforce the conditions described by the field-wire equation into the TLM mesh

x

y

z

),,(6 zyXV i l),,(10 zyxV i

ldL

ldC

lzE

ldC

KVL in each loop represents previous equation

reference

),,(101 zyxVu i

),,(62 zyxVu i l

linez

stubz

3u 4u5u2/ t 2/z

t

2/z

2/ t

Stub

round trip time

linez

The coupling to the field nodes is through ports 1 and 2 above.

A segment of a multi-wire bundle directed along the z-direction is shown through the centre of a node of length z

n-conductors

totIU and V indicate incident

and reflected voltages

hh VU ,ll VU ,

To next node at

higher coordinate

To next node at

lower coordinate

‘reference’

nz +

zu

zCoupling to the field at

the centre of the reference

Propagation delay along z is t

WZ WZ

The treatment is very similar to that of the previous case

(single wire through a node) but instead of voltage pulses

we have voltage pulse vectors, and

instead of impedances we have impedance matrices.

In what follows, if n is the number of conductors in the bundle:

dd LC ,

WZ

stubstub ZLL ,,

VU ,

Bundle capacitance and inductance per unit length, nxn matrices.

Bundle impedance matrix, nxn.

Stub parameters, nxn matrices.

Incident and reflected voltage column vectors, n-elements.

Further Reading:

‘A fully integrated multi-conductor model for TLM’, IEEE Trans on MTT, 46, 1998, pp 2431-2437, J Wlodarczyk, V Trenkic, R A Scaramuzza, C Christopoulos

‘Multi-scale modelling in time-domain electromagnetics’, Int Journal of Electronics and Communications (AEU), 57, 2003, pp 100-110 , C. Christopoulos

Modal Expansion Technique (MET) : the Holland and Simpson type of approach is inaccurate because there is insufficient information contained in the static solution for a wire. The general response of a wire to an incident field is to generate a scattered field which in combination with the incident field is rich in modal information:

00 0

0

0

( )( , ) ( ) ( ) (15)

( )

1( , ) (16)

jnz n n n

n n

z

J k aE r B e J k r N k r

N k a

EH r

j r

The static solution is but the first term in this expansion-but there is much more information

available!

At the edges of a node containing a wire, we can calculate the impedance seen by each field mode.

Without significant loss in accuracy we can use the small argument expansions for the Bessel functions to

get:

00

0

2 20

2 2

ln( ) , 0 (17)

, 0 (18)

z

n nzn

n nn

Ej n

H a

E j an

H n a

is half the nodal spacing, and a is the wire radius

It is now possible to proceed in two different ways:

•Construct an equivalent circuits to ensure that the modal components of incident voltages encountering a node

containing a wire see the correct impedance as calculated earlier

•Treat the reflection of signals as a signal processing task and by-pass the construction of the equivalent circuit.

Either method can be applied. The advantage of the circuit approach is that it keeps with the philosophy of

TLM and the fact that such a circuit can be constructed is a guarantee of stability

Electric Field, V/m

Frequency ratio, f/fmax

METanalyticbetween nodecentre node

Example: Comparison of MET with analytical results and other wire models (mesh resolution 50mm, wore radius

5mm). The problem is of an incident field scattered by the wire. The total field is shown 100mm in front of the wire.

Further reading:

‘An accurate 3D model for thin wire simulations’, IEEE Trans on EMC, 45, 2003, pp 207-217, P Sewell, Y K Choong, C Christopoulos

Whole system modelling

•Intermediate models (in collaboration with the University of York)

•Full-field models

•Full-field models with embedded algorithms (DFI)

30 cm

30 cm12 cm

Enclosure Geometry

aperture

Further Reading:“Shielding effectiveness of a rectangular enclosure with a rectangular aperture”M P Robinson et al, Electronics Letters, 15 Aug 1996, 32(17), pp 1559-1560

“An evaluation of the shielding effectiveness of cabinets”J D Turner et al, 12th Int. Zurich EMC Symp., Feb. 18-20 1997, pp 229-234

“A comparison of the analytical, numerical and approximate models for shielding effectiveness with measurements”P Sewell et al, IEE Proc. Sci. Meas. Technol., 145(2), Mar. 1998, pp 61-66

Time, ns

Further Reading:see session TU2B, ‘Numerical Methods for Challenging Problems’, 1998 IEEE EMC Symp., 24-28 Aug 1998, Denver

Co., USAin particular paper:

“Application of the TLM method to equipment shielding problems”, C.

Christopoulos, ibid, pp 188-193

How connection algorithm is modified to account for perforated wall

V11

V5

x,y,z

V10

V4

x+1,y,z

Figure Schematic showing part of the usual connection process between two adjacent TLM nodes

1

1

10111

11101

xVxV

xVxVr

ki

k

rk

ik

rk

ik VCV 1

a)

b)

- scattering,

- connection,

Where Vi are twelve incident voltages, Vr are twelve reflected voltages, k is time-step, [S] is the scattering matrix, [C ] is the connection matrix.

ir VSV

r

k

rk

ik

ik

V

V

RT

TR

V

V

11

10

111

101

Simple swapping of the voltages New scattering connection of the voltagesR and T are frequency-dependent

Figure Fine feature at the interface of neighboring nodes

x,y,z x+1,y,z

“Discrete time” domain

Extraction of zeros and poles from the Pade-approximation

Outline of the Digital Filter Interface (DFI)

Scattering coefficients:Analytical solution

Scattering coefficients:Data from measurements

Scattering coefficients:Numerical simulation

oror

Frequency domain

Sij(z)Bilinear z-transform

RT

TRS )(

jsssaa

sbsbbsS

NP

NPNP

ij

,

...

...

10

10

1

0

1

0

NP

ipi

NP

iziNPij ssssbsS

xV

xVzAzBBzS

rk

ik

NP

i

ii

NP

i

iiij

11 1

110

DIGITAL FILTER INTERFACE: FILTER IMPLEMENTATION

Figure Signal-flow graph of the equivalent digital filter

1’ z-1 B’Vincident

B0

Vreflected

+

+

+

+A

The advantages of this approach are:

• accuracy

• a small number of parameters after pre-processing

• possibility of extracting parameters from raw frequency-domain data

• low computational costs compared to the standard models

• mesh resolution determined by global considerations and not by the fine features

Figure The boundary with the digital filter between two cells

incidentz,y),x(V 1

incidentz,y,xV

reflectedz,y),x(V 1

reflectedz,y,xV

TEST ENCLOSURE WITH PERFORATED WALL

Transmission and reflection coefficients of the perforations [C.C. Chen. IEEE MTT-21,pp.1-6]: (A, B are geometrical characteristics of the screen, l is the thickness):

Figure Pattern of the perforated wall: triangular lattice.

4mm 10mm

121

1

21

1

21

1

21

1

lhcotBAjltanhBAjR

lhcotBAjltanhBAjT

292 mm

212 mm

78 mm

40 mm40 mm

20 mm

20 mm

28 mm146 mm

sensor

Figure Enclosure with perforated wall.

Two TLM meshes of different scales were used in numerical models of the enclosure:

a) 66x66x28 cells of the size X = 9.73mm ;b) 33x33x14 cells of the size X =19.5 mm.

COMPARISONS 3D-TLM SIMULATION AND EXPERIMENT RESULTS

Figure Measurement and simulation results for the shielding effectiveness of the enclosure.

200 300 400 500 600 700 800 900 1000-20

0

20

40

60

80

experiment simulation x=9.73mm simulation x=19.5mm

Sh

ield

ing

Eff

ective

ne

ss (

dB

)

Frequency (MHz)

Further reading:

‘The use of digital filtering techniques for the simulation of fine features in EMC problems solved in the time domain’, IEEE Trans on EMC, 45, 2003, pp 238-244, J Paul, V Podlozny, C Christopoulos

Coupled physical domain models

•Sophisticated models of materials to allow combined EM/thermal calculations for dossimetry

•Combined electronic/photonic models

Further reading:

‘Generalised material models in TLM-Part 1:Materials with frequency dependent properties’, IEEE Trans on AP, 47, 1999, pp1528-1534; Part 2: Materials with anisotropic properties, ibid. 47, pp 1535-1542; Part 3: Materials with non-linear properties, ibid. 50, 2002, pp 997-1004, J D Paul, C Christopoulos, D W P Thomas

Outlook:

Better models for multi-scale problems

General integrated multi-wire models arbitrarily placed in a 3D mesh

Macro-models for frequently occurring features

Direct radiation from chips

Statistical aspects of EMI source and system configuration