PhD defense

1

Presented by: Aamir RASHID

Thesis Adviser: M. Hervé Aubert

Electromagnetic Modeling of Large and Non-uniform Planar Array Structures using Scale Changing Technique (SCT)

2

Presentation Plan

1. Motivation2. Scale Changing Technique (SCT)3. Modeling of a Planar Reflector cell4. Characterization of Electromagnetic Coupling in

non-uniform array5. Scattering from 2-D Planar Arrays6. Conclusions and Perspectives

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Presentation Plan



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Motivation

Problems with simulating planar structures with large size and complex geometries (e.g. FSS, Reflectarrays) Long Execution Times Immense Memory Requirements Numerical conditioning problems

Generally used solution Simulations under Infinite array assumption using Floquet Modes

Problems with the infinite array approach not applicable to non-uniform arrays

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Presentation Plan



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RF-MEMS controlled Reflectarray – An example of a multiscale structure

10-6

Surface of Wi / Surface of W0

100 10-1 10-2 10-3 10-4 10-5

W0Reflectarray

W1

Phase-shifter cell

W2

Slot loaded by RF-MEMS switches

W3

RF-MEMS switch

W4

Region below the switch

Simulation of such structures with conventional techniques a Nightmare!!

Scale Changing Technique

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I. Decomposition of the planar surface ------- by introducing artificial boundary conditions

II. Definition of tangential electromagnetic fields on orthonormal modal basis

III. Determination of appropriate number of modes

IV. Computation of Scale-changing Networks (SCN)

V. Cascade of all SCNs

8


Partitioning of the Discontinuity Plane

b0

a0

a1

x32,5

x32,4

x32,3

x32,2

b1

x31,1

x31,2

x31,3

x31,4

x31,5

b21

b22

b42,1

Slot

RF-MEMS switch

MetallicPatch

W2W3

W4

W1

[Ref] E.Perret et al, “Scale-changing technique for the electromagnetic modeling of MEMS-controlled planar phase-shifters”, IEEE Transactions on Microwave Theory and Techniques, Vol.54, No.9, September 2006, Pages: 3594-3601.

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The choice of boundary conditions Perfect Electric Perfect Magnetic A combination of above two Periodic (Floquet)

Tangential EM fields expressed on orthonormal modal basis Lower order modes define Large scale field variations Higher order modes define Localized and fine scale variations

EM coupling between parent domain and daughter subdomains is largely due to lower order modes ---- active modes

Appropriate number of active and passive modes need to be determined --- convergence study

EM coupling between a domain at scale ‘s’ and its subdomains at scale ‘s-1’ is represented by a Scale Changing Network

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Scale Changing Network

Active modesD1

s-1

Active modesD2

s-1

Active modesDN

s-1

Active modesDo

s

Scale Changing Network (SCN)

A multiport network where the ports represent active modes

Models EM coupling between successive scales

Computation of all SCNs mutually independent --- PARALLEL PROCESSING

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Cascade of all Scale Changing Networks

b0

a0

a1

x32,5

x32,4

x32,3

x32,2

b1

x31,1

x31,2

x31,3

x31,4

x31,5

b21

b22

b42,1

Slot

RF-MEMS switch

MetallicPatch

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Structures already simulated using SCT

b0

a0

a1

x32,5

x32,4

x32,3

x32,2

b1

x31,1

x31,2

x31,3

x31,4

x31,5

b21

b22

b42,1

Slot

RF-MEMS switch

MetallicPatch

Active Patch Antenna MEMS controlled Reflector cell

Multi-frequency Selective surfaces Prefractal Multi-band scatterer

[Ref] E.Perret et al, “Scale-changing technique for the computation of the input impedance of active patch antennas”, IEEE Antennas and Wireless Propagation Letters, Vol.4, 2005.

[Ref] D.Voyer et al, “Scale-changing technique for the electromagnetic modeling of planar self-similar structures”, IEEE Transactions on Antennas and Propagation, Vol.54, No.10, October 2006.

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Presentation Plan



14

a0

b0

a1

b1

a2

b2

θ φ

z

kinc

Periodic BCMagnetic BCElectric BC

y

a0=15mm b0=15mm Dielectric thickness = 4mm Dielectric=Aira1=12mm b2=1mm b1 and a2 variable

Infinite Reflectarray Modeling

Floquet modal expansion to simulate infinite array conditions

Plane-wave Excitation (Oblique Incidence)

Nine geometric configurations simulated varying dimensions b1 and a2

Objective: To find the phase of reflection coefficients for TE00 and TM00 modes

Planar Reflector Cell under infinite array conditions

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Application of Scale Changing Technique (SCT)

Partitioning of planar geometry at three scale-levels

Cascade of SCNs

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20 30 40 50 60 70 80 90 100 110 120

-161

-160

-159

-158

-157

-156

-155

-154

-153

No of Slot Modes

Ph

ase

(d

eg

ree

s)

2003006008001000


Convergence Study (Normal Incidence)

Convergence curves between active modes in domains D1

(2) and D1(1) (slot domain)

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

-180

-175

-170

-165

-160

-155

No of Waveguide Modes (x1000)

Ph

ase

(d

eg

ree

s)

2003006008001000

Convergence curves between modes in domains D1

(2) and D1(3) (discontinuity

domain)

Modes for convergence 2500 [D1(3)] 600 [D1

(2)] 80 [D1(1)]

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Numerical Results (Normal Incidence)

____ SCT x x x HFSSConvergence study performed at the centre frequency of 12.1GHz for each case

Phase results for the reflection coefficient of TM00 mode

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Variation in the phase results of the TM00 mode with the change in the incidence angle (θ)


Numerical Results (Oblique Incidence) at 12.1 GHz (φinc = 0⁰)

0 5 10 15 20 25 30 35 40-200

-150

-100

-50

0

50

100

150

200

Theta (Degrees)

Ref

lect

ed P

hase

(Deg

rees

)

Config 9

Config 1

Config 2

Config 5

Config 7

SCT solid lines

HFSS broken lines

Phas

e S 11

(D

egre

es)

0 5 10 15 20 25 30 35 40-250

-200

-150

-100

-50

0

50

100

150

Theta (Degrees)R

efle

cte

d P

ha

se (

de

gre

es)

Config 1

Config 9

Config 5

Config 2

Config 7

Phas

e S 22

(D

egre

es)

Variation in the phase results of the TE00 mode with the change in the incidence angle (θ)

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Presentation Plan



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Bifurcation Scale Changing Network

Electromagnetic Coupling Characterization

How to model electromagnetic coupling in non-uniform arrays?

Artificial boundary conditions are introduced around each unit-cell domain

A SCN can then be used to combine two unit-cell domains into a single domain modeling the mutual interactions between them

Appropriate number of modes need to be determined in each domain

An iterative cascade of these SCNs is used to model the entire array

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Bifurcation Scale Changing Network


V0I0

VN1IN1

Ms,s-1

v0i0

vN2

iN2

v’0

v’N2i’N2

i’0

i0

i’0

I0v0

v’0

V0

L(s)

L(s)

M(s)

Multiport Representation of Bifurcation SCN

(Characterized by an impedance or admittance matrix )

Equivalent Electric Network (for only TEM excitation in each domain)

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Scattering from two planar half-wave dipoles

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dBo

02.64

0 1 2 3 4 50

1

2

3

4

5

6

7

8

9

10

d/Lambda

SE

R/S

ER

(sin

gle

dip

ole

) d

B

R

CS R

atio

RCS ratio in the absence of mutual coupling

λFor separation D >> λ

012 Z

2

22

121

4

ZZo


Scattering from two planar half-wave dipoles

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0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

14

16

18

20

d/Lambda

|Er| D

irect

Co

mp

on

en

t (m

V/m

)

IE3D

SCT

|Er| in the absence of mutual coupling (IE3D SCT)


Electromagnetic coupling modeled by Bifurcation SCN

2

2

24inc

scat

E

Er

[Ref] A.Rashid, H.Aubert , “Modeling of Electromagnetic Coupling in Finite Arrays Using Scale-changing Technique”, Progress In Electromagnetics Research Symposium (PIERS), 5-8 July 2010, Cambridge, USA.

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Modeling Linear Arrays

1

2

3

4

5

Modeling of a non-uniform linear (1-D) array of metallic stripes

A unit-cell of the array

Dimensions: a=10 mm b=9mm x=2mm Freq=5 GHz

A non-uniform array of lossless metallic strips

Partitioning process of an eight cell array

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Modeling of entire array by an iterative cascade of Bifurcation SCNs

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Array Size Unit-cell ArrangementInductance (nH)

SCT HFSS

2 cells BC 2.34 2.13

2 cells DB 2.57 2.30

4 cells DACD 1.30 1.24

16 cells ABCDBCABECAABAAD 0.30 0.29

32 cellsEAEAEAEAEAEAEAEAEAEAEAEAEAEAEAEA

0.27 0.26

ConfigurationInductance (nH)

SCT HFSSA (x0= 0mm) 8.46 8.89

B (x0= 2mm) 4.85 5.19

C (x0= 4mm) 4.0 4.32

D (x0= 6mm) 4.87 5.19

E (x0= 8mm) 8.51 8.89


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1. [Ref] A.Rashid, H.Aubert, H.Legay “ Modélisation Electromagnétique d’un Réseau Fini et Non-Uniforme par la Technique par Changements d’Echelle”, JNM 2009, Grenoble


1 2 3 4 5 6 70

2

4

6

8

10

12

14

Iteration

Te

mp

s d

e c

alc

ul N

orm

alis

é

SCTHFSS

Exec

ution

Tim

e (N

orm

alize

d)


Iteration = Number of Bifurcation SCNs used

Array size (no of unit-cells) = 2^(Iteration)

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Presentation Plan



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Modeling 2-D Planar Arrays

Bifurcation Scale Changing Network in 2-D

Partitioning of 2-D planar array

Phase results for the reflection coefficient of TM00 mode

Cascade of SCNs

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Surface Equation for electromagnetic scattering from a planar surface

When an equivalent current is assumed at the whole discontinuity plane

In spectral domain

Using Galerkin’s method

Formulation of the Scattering Problem

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Modeling 2-D Planar ArraysNormal Plane-wave Incidence

Uniform Array Simulation Results (Normal Plane-wave Incidence)

-50 0 500

100

200

300

400

500

600

700

800

Elevation (Degrees)

|Eph

i| H-p

lan

e (

mV

/m)

HFSS

SCT

8x8 uniform patch array

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Non-uniform Array Simulation Results (Normal Plane-wave Incidence)

-50 0 500

50

100

150

200

250

Elevation (Degrees)

|Eph

i| (H

-pla

ne

) (

mV

/m)

IE3D

SCT

HFSS


8x8 non-uniform patch-slot array

34

x

y

Uniform Array Simulation Results (Normal Plane-wave Incidence)



35

x

y

Non-uniform Array Simulation Results (Normal Plane-wave Incidence)


16x16 non-uniform patch array

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Uniform Array Simulation Results (Horn antenna Excitation)

Horn antenna has been modeled analytically by a radiating aperture in an infinite ground plane

Modeling 2-D Planar ArraysHorn Antenna Excitation

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Uniform Array Simulation Results (Horn antenna Excitation)

-100 -50 0 50 1000

5

10

15

20

25

Elevation (Degrees)

Eph

i (V

/m)

-100 -50 0 50 1000

10

20

30

40

50

Elevation (Degrees)

Eth

eta (

V/m

)

SCT

FEKOSCT

FEKO


H-Plane E-Plane


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Non-uniform Array Simulation Results (Horn antenna excitation)

-100 -50 0 50 1000

2

4

6

8

10

Elevation (Degrees)

Eph

i (V/m

)

SCT

FEKO

H-Plane


8x8 non-uniform patch-slot array

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Execution Times to compute surface impedance of the array

CPU Time (sec)

[Zs] complete array 43.06Zs unit-cell 11.7

SCN (1 SCN + 1 cascade) 13SCN (1 SCN + 1 cascade) 11SCN (1 SCN + 1 cascade) 6

CPU Time (sec)

[Zs] complete array 172Zs unit-cell (8 configs) 135

SCN (1 SCN + 4 cascades) 16SCN (1 SCN + 2 cascades) 12SCN (1 SCN + 1 cascade) 6

8x8 uniform array

8x8 non-uniform array

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Presentation Plan



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Conclusions

SCT has been proposed for efficient electromagnetic modeling of large and complex planar array structures

SCT models mutual coupling effects between the elements of non-uniform arrays

The unique formulation avoids the direct computation of large structures with high aspect ratios – thus prevents numerical and convergence errors

Inherent modular nature of SCT allows the parallel execution of SCNs allowing execution times to increase linearly with the exponential increase in array size

In case of a modification in geometry at a given scale only two SCNs need to be recalculated ---- an essential feature for a good PARAMETRIC and OPTIMIZATION TOOL

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Perspectives

Experimental validation in the case of a real life planar array application

A general implementation framework for grid-computing

Usage in hybrid with other techniques and methods for the simulation of multi-layered structures

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Thank You All

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Publications

1) A. Rashid et al, "Modeling of Infinite Passive Planar Structures using Scale-Changing Technique" IEEE-APS July 5-11, 2008, SanDiego, USA.

2) A. Rashid et al, "Modélisation Electromagnétique d’un Réseau Fini et Non-Uniforme par la Technique par Changements d’Echelle" JNM 2009, Grenoble, France.

3) A. Rashid et al, "Modeling of finite and non-uniform patch arrays using scale-changing technnique " IEEE-APS June 1-5, 2009, Charleston, USA.

4) A. Rashid et al, "Scale-Changing Technique for the numerical modeling of large finite non-uniform array structures " PIERS, 2009, Moscow, Russia.

5) E.B.Tchikaya et al, "Multi-scale Approach for the Electromagnetic Modeling of Metallic FSS Grids of Finite Thickness with Non-uniform Cells " APMC, 2009, Singapore.

6) F. Khalil et al, "Application of scale changing technique-grid computing to the electromagnetic simulation of reflectarrays " IEEE-APS June 1-5, 2009, Charleston, USA.

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PhD defense