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Introduction to Time Domain

Electromagnetic Methods

Yanjie Zhu

Yinchao ChenPaul G. Huray

12/03/2004

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Outline

Comparison of different numerical methods

Introduction to Finite Difference Time Domain

(FDTD) Method

Applications of FDTD to electrical engineering

Initial study ofCFDTD to the detection of PCB

impurities and surface roughness

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Comparison of different numerical methods

Frequency Domain Methods

MoM (Method of Moment)

Zeland IE3DTM

Agilent ADSTM (AdvancedDesign System)

Ansoft EnsembleTM

FEM (Finite Element Method)

Ansoft HFSSTM

UGS FEMAPTM

Time Domain Methods

FDTD

Remcom XFDTDTM

Zeland FidelityTM

RM Associate CFDTDTM

MRTD (Multi-Resolution TimeDomain)

PSTD (Pseudo-Spectral TimeDomain)

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Advantages & Disadvantages

Features Advantages Disadvantages

Point frequency

approach

MoM Most accurate method Find Green Function first

FEM Mature method, adaptive

mesh

Huge matrices

Frequency band

approach: timepulse excitation

FDTD Simple, Robust, versatile Long computation time

MRTD

PSTD

Large structure simulation Complicated algorithm

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Principle of Finite Difference

x

2xxf2xxfxf

dx

xdf 000

0

)()()(

)( '

Derivative off(x) at point P using finite difference approximations

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Mesh Structure for FDTD Algorithm

A standard Yees lattice

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Implementation of FDTD Algorithm

E

t

EH er

0 H

t

HE mr

0

z

y

x

ezz

eyy

exx

z

y

x

zz

yy

xx

0

xy

zx

yz

E

E

E

00

00

00

t

Et

E

t

E

00

00

00

y

H

x

HxH

zH

z

H

y

H

Starting point is Maxwells differential equations.

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Updating Equations-Hz

x

kjiEkjiE

y

kjiEkjiE

kji

kjit

kji

t

kjiH

kji

kjit

kji

kjit

kjiH

n

y

n

y

n

x

n

x

zz

mzz

zzn

z

zz

mzz

zz

mzz

n

z

,21,

21,

21,

21,

21,

21,

21,

21

,2

1,

2

12

,2

1,

2

1

1

,2

1,

2

1

,2

1

,2

1

,2

1,

2

12

,2

1,

2

1

1

,2

1,

2

12

,2

1,

2

1

1

,2

1

,2

1

0

0

2

1

0

0

2

1

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Updating Equations-Ez

y

kjiHkjiH

x

kjiHkjiH

kji

kjit

kji

t

kjiE

kji

kjit

kji

kjit

kjiE

n

x

n

x

n

y

n

y

zz

ezz

zzn

z

zz

ezz

zz

ezz

n

z

)2

1,

2

1,()

2

1,

2

1,()

2

1,,

2

1()

2

1,,

2

1(

)2/1,,(2

)2/1,,(1

)2/1,,()2

1,,(

)2/1,,(2

)2/1,,(1

)2/1,,(2

)2/1,,(1

)2

1,,(

2

1

2

1

2

1

2

1

0

0

0

01

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Selection of the parameters

Cell size criterionminmaxmaxmax

20

1and, zyx

maxmaxmax

min

rr

c

f

v

Excitation choicesGaussian pulse:

Blackman-Harris pulse:

2

p

2

0nn

N

tttg exp)(

2

23cos

2

22cos

2

2cos

43

21

p

pn

p

pn

p

pn

n

N

Nta

N

Nta

N

Ntaatb

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Boundary Conditions

Shielded boundary:

Perfect Electric Conductor (PEC)

Perfect Magnetic Conductor (PMC)

Open boundary:

Absorbing Boundary Condition (ABC)

Perfectly Matched Layer (PML)

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Sequence of an FDTD Iteration Cycle

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Calculation of MMICs Parameters

C

EyL

i1 i2

j2

j0

j1h

Hy

Hx

0

0

00

0

00 ,,,,

j

m

zx

n

y

h

nn yznymxnEldztEztv

2

1

2

1

),,(),,(

),,(),,(,,

012

1

022

1

022

1

012

1

021021

j

jjz

n

yz

n

y

i

ii

z

n

xz

n

xC

nn

yznyjxiHyznyjxiH

xznyjxiHxznyjxiHldztHzti

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Calculation of MMICs Parameters

)},({

)},({0

tzIFFT

tzVFFTZ

i

iThe characteristic impedanceZ0 is calculated by

002

2 )(

)(

reff

tzVFFTtzVFFT

anglezz j

i

ij ,

,

)(

1

)(

For a transmission line, the effective dielectric constant effis defined as:

with:

)(

)(

)(

)(11

tiFFT

tiFFT

tVFFT

tVFFTS

inc

ref

inc

ref

For a two-port network, S11 and S21 can be defined as:

)(

)(

)(

)(21

tiFFT

tiFFT

tVFFT

tVFFTS

inc

trs

inc

trs

kLjkLj

ineS

eS

ZfZ 211

2

11

01

1

Input Impedance:

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Near-to-Far Field Transformation

EnM

HnJ

s

s

s

jkR

s

S

jkR

s

dsR

eMF

dsR

eJA

'4

'4

0

0

AFk

FjH

FAk

AjE

0

2

0

2

11~

11~

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Conformal FDTD

When the object to be simulated has curved surfaces and edges,

the stair casing approximation of conventional FDTD technique

can produce significant errors.

Stair case:

Conformal:

Using integral

equation

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Applications of FDTD in Electrical Engineering

Simulation of Wave Propagation Problems

Microwave Engineering Problems

Antenna Problems

Scattering Problems

Signal Integrity Problems

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Simulation of Wave Propagation

I will show a simple 1dfdtd matlab code

to clarify the wave propagation problem.

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Microstrip Low-pass filter

5.65mm

r=2.2 0.794mm

x

y

z

2.54mm

2.413mm

5.65mm

20.32mm

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Result

0 5 10 15 20-50

-40

-30

-20

-10

0

10

|S11

|

|S21

| Sheen et al

FDTD solver

Microstrip Low Pass Filter

Frequency (GHz)

|S11

|and|

S21

|(dB)

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Conical Horn Antenna

d1=0.71, d2=1.86, lt=1.08, l=3.75, =28degree

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Result

CFDTD ------------

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Result

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Scattering Problems

41095.2

1

1

r

r

r

y

z

x

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Result

0 0.5 1 1.5 2 2.5 3-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

-25

f (GHz)

RCS(dBsm)

dispersive, FDTD

dispersive, theoretical

Debye sphere 22.5 degree incidence

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Signal Integrity Problem

Layer Material r Height Function SpacingGND Copper 1.4

Substrate FR4 4.4 5

Trace Copper 1.4 Sig 5 mil / 20 mil space

Structure Stack-up:

T1

T3

T2

T4Port1 Port2

Top View:

100mil*100mil

Cell size:

0.7mil*0.7mil*0.35mil

Frequency range:

10GHz-60GHz

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Result

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ResultSig

Sig

Sig

GND

GND

GND

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ResultSig

Sig

Sig

GND

GND

GND

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Result

Sig

GND

Sig

GND

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Initial study ofCFDTDto the

detection of PCB impurities

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Time domain field distribution

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Time domain current distribution

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Initial study ofCFDTDto the

detection of PCB impurity

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Time domain field distribution

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Time Domain current distribution

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Comparison of field distribution

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Comparison of current distribution

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Comparison of field distribution on yzplaneWithout impurity

With air bubble

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Comparison of field distribution on yzplaneWith dielectric bubble r=10

With PEC bubble