modeling complex structures in electromagnetics using ... · modeling complex structures in...

Modeling complex structures in

electromagnetics using hybrid algorithm

Presented by: Kapil Sharma

110th Annual Symposium on Signal Integrity

Presentation Outline

• Introduction

• Research motivation

• Common CEM techniques

• Problem definition

• Past research work

• Novel hybrid technique

• Numerical examples and simulation results

• Observations

• Future research

• References


Introduction: Modeling Challenges in

Current Technologies

3

Solar Cells (Plasmonics)

Composite Layers (Inhomogeneous)

Embedded Antenna (Multiscale)

Nano Rods (Thin and Long)

Sub micron Die (Signal Integrity)Graphene

(Fine Thickness )


Research Motivation

• Ubiquity of complex multi-scale problems in numerical

electromagnetics


Research Motivation

• Simulation of structures with multi-scale features is highly

challenging

5

Fine feature captured by

conventional FDTD mesh

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Distance along Z in

Am

plit

ude in V

/m

Amplitude Variation of Scattered Ey

DM Appraoch

HFSS

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.4

0.6

0.8

1

1.2

1.4

1.6

Distance along Y in

Am

plit

ude in V

/m

Amplitude Comparison of Ez from New Conformal FDTD

New Conformal FDTD

GEMS

FEKO

HFSS

Spurious Ripples!

Dielectric Cuboid

Plasmonic Nano-spheres


Common CEM techniques

• FDTD

• Solves for a wide frequency range

• Computationally expensive when handling fine structures, resonant structures, and

dispersive media

• MoM

• Solves at a single frequency

• Singularity extraction requires special treatment

• Handles dispersive media well, but computationally expensive when handling fine

structures

• FEM

• Solves at a single frequency

• Computationally expensive for fine and resonant structures

• FIT

• Solves for a wide frequency range

• Computationally expensive when handling fine structures, resonant

structures, and dispersive media


Problem definition:

Example of a multi-scale problem in

numerical electromagnetics

7

OR

arbitrary shaped wire-like

antenna with fine features

(fraction of wavelength)

electrically large

pec reflector

(many wavelengths

long)

Transmit case

(wire-like antenna is the source)

Receive case

(external plane wave is the source)

arbitrary shaped wire-like

antenna with fine features

(fraction of wavelength)

electrically large

pec reflector

(many wavelengths

long)0 0.5 1 1.5 2 2.5

-3

-2

-1

0

1

2

3

4x 10

9

t (ns)

x(t

)

analytical

iDFT

Incident modulated

gaussian pulse


Proposed hybrid technique

8

The novel hybrid FDTD

technique combines the MoM

and FDTD techniques directly in

the time domain

Fine features are handled by

MOM code

Special basis functions are used to

represent current on wire-like

geometries with fine features

Time domain scattered fields are

sampled at a planar interface

Sampled time domain scattered fields

are then combined with the

conventional FDTD update equations


Problem Definition – validation of

MoM code

X

Z

λ @ highest frequency of interest: 4 GHz

Observation Line

A straight wire is directed along x.

Length of the straight wire is 0.75 cm

Straight wire antenna of length 0.75 cm with

a delta gap voltage source

9

Wire antenna radius = 0.005*length


MoM code vs FEKO results

-1.5 -1 -0.5 00

5

10

15

20

Amplitude of Ex

Distance Along Z in

Am

plit

ud

e in

V/m

MOM code

FEKO

Magnitude comparison

-1.5 -1 -0.5 0120

140

160

180

200

220

240

Phase of Ex

Distance Along Z in

Ph

ase

in

De

gre

e

MOM code

FEKO

Phase comparison


Transmit Case: Example 1

11

X

Z

FDTD domain mesh size: λ/20


λ0 @ center frequency of interest: 4 GHz

Observation Line

A straight wire antenna is directed along x at a distance of 7.5 cm

from a pec plate

Length of the straight wire antenna is 0.1875 cm from the wire antenna

Straight wire antenna of length 0.1875 cm

with a delta gap voltage source7.5 cm

pec plate(26.25 cm x 26.25 cm)

Planar Interface (26.25 cm x 26.25 cm)

0.1875 cm

Variable Value

λ 3.75 cm

λ0 7.5 cm

λ/20 0.1875 cm

FDTD domain

MoM domain


MoM domain solution is obtained in the

time-domain


Ex amplitude comparison at 4 GHz

12

-2 -1.5 -1 -0.5 00

0.1

0.2

0.3

0.4

0.5

Amplitude of Ex

Distance Along Z in

Am

plit

ud

e in

V/m

MOM code

Hybrid FDTD

Results are in close

agreement when

the wire antenna

length is 0.1875 cm


Ex phase comparison at 4 GHz

13

-2 -1.5 -1 -0.5 0-50

0

50

100

150

200

250

Phase of Ex

Distance Along Z in

Ph

ase

in

De

gre

e

MOM code

Hybrid FDTD


agreement when

the wire antenna

length is 0.1875 cm


Transmit Case: Example 2

14

A straight wire antenna is directed along x at a distance of 7.5 cm

from a pec plate

Length of the straight wire antenna is 0.75 cm from the wire antenna

X

Z

FDTD domain mesh size: λ/20



Observation Line

Straight wire antenna of length 0.75 cm

with a delta gap voltage source7.5 cm

pec plate(26.25 cm x 26.25 cm)

Planar Interface (26.25 cm x 26.25 cm)

0.1875 cm

Variable Value

λ 3.75 cm

λ0 7.5 cm

λ/20 0.1875 cmFDTD domain

MoM domain



time-domain



15

-2 -1.5 -1 -0.5 00

5

10

15

20

Amplitude of Ex

Distance Along Z in

Am

plit

ud

e in

V/m

MOM code

Hybrid FDTD


agreement when the

wire antenna length is

increased to 0.75 cm



16

-2 -1.5 -1 -0.5 0-50

0

50

100

150

200

250

Phase of Ex

Distance Along Z in

Ph

ase

in

De

gre

e

MOM code

Hybrid FDTD


agreement when the




Receive Case: Example 1

17

X

Z

Mesh size: λ/20



Observation Line

0.1875 cm

Planar Interface(26.25 cm x 26.25 cm)

A straight wire antenna is directed along x at a distance of 7.5 cm from a pec plate

Length of the straight wire antenna is 0.1875 cm

Planar Interface is at a distance 0.1875 cm from the wire antenna

Straight wire antenna of length 0.1875 cm7.5 cm

pec plate

(26.25 cm x 26.25 cm)

Variable Value

λ 3.75 cm

λ0 7.5 cm

λ/20 0.1875 cm

FDTD domain

MoM domain

0 0.5 1 1.5 2 2.5-3

-2

-1

0

1

2

3

4x 10

9

t (ns)

x(t

)

analytical

iDFT

k


Incident modulated

gaussian pulse


time-domain



18

-2 -1.5 -1 -0.5 00

1

x 10-4 Amplitude of E

x

Distance Along Z in

Am

plit

ud

e in

V/m

MOM code

Hybrid FDTD


agreement when the

wire antenna length

is 0.1875 cm



19

-2 -1.5 -1 -0.5 0-100

-50

0

50

100

150

200

Phase of Ex

Distance Along Z in

Ph

ase

in

De

gre

e

MOM code

Hybrid FDTD


agreement when the

wire antenna length

is 0.1875 cm


Receive Case: Example 2

20

X

Z

Mesh size: λ/20



Observation Line

0.1875 cm

Planar Interface(26.25 cm x 26.25 cm)

A straight wire antenna is directed along x at a distance of 7.5 cm from a pec plate

Length of the straight wire antenna is 0.75 cm

Planar Interface is at a distance of 0.1875 cm from the wire antenna

Straight wire antenna of length 0.75 cm7.5 cm

pec plate

(26.25 cm x 26.25 cm)

Variable Value

λ 3.75 cm

λ0 7.5 cm

λ/20 0.1875 cm

FDTD domain

MoM domain

0 0.5 1 1.5 2 2.5-3

-2

-1

0

1

2

3

4x 10

9

t (ns)

x(t

)

analytical

iDFT

k


Incident modulated

gaussian pulse


time-domain



21

-2 -1.5 -1 -0.5 00

1

2

3

4

5

6

7

8x 10

-3 Amplitude of Ex

Distance Along Z in

Am

plit

ud

e in

V/m

MOM code

Hybrid FDTD


agreement when the





22

-2 -1.5 -1 -0.5 0-100

-50

0

50

100

150

200

Phase of Ex

Distance Along Z in

Ph

ase

in

De

gre

e

MOM code

Hybrid FDTD


agreement when the




Observations

• Amplitude and phase of the scattered field along the

observation line obtained using the proposed hybrid method

are in close agreement to that obtained using the method of

moments code

• Accurate results are obtained using the proposed novel hybrid

technique for the cases when the scatterer size is small as well

as large


Applications

24

Numerous other

applications … !!


References

• [1] Kane S. Yee, “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic

Media,” IEEE Trans. On Antennas and Propagation, vol.14, no.3, pp. 302-307, May 1966.

• [2] Jean-Pierre Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves”, Journal of

Computational Physics 114, 185-200 (1994).

• [3] Wenhua Yu, Xiaoling Yang, Yongjun Liu and Raj Mittra, Electromagnetic Simulation Techniques Based on the

FDTD Method, John Wiley & Sons, Inc., 2009.

• [4] Raj Mittra, J.N. Bringuier, “A Technique for Solving Multiscale Problems in CEM Utilizing Dipole Moments and

Macro Basis Functions,” Proceedings of the Fourth European Conference on Antennas and Propagation (EuCAP), 2010.

• [5] Raj Mittra, Jonathan Bringuier, Chiara Pelletti, Kadappan Panayappan, Ozlem Ozgun, Agostino Monorchio, “On

the Hybridization of Dipole Moment (DM) and Finite Methods for Efficient Solution of Multiscale Problems”,

Proceedings of the Fifth European Conference on Antennas and Propagation (EuCAP), 2011.

• [6] E.C. Jordan and W.L. Everitt, “Acoustic Models of Radio Antennas”, Proc. IRE, 29, 4, 186 (1941).


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