Introduction to Time Domain
Electromagnetic Methods
Yanjie Zhu
Yinchao Chen
Paul G. Huray
12/03/2004
Outline
Comparison of different numerical methods
Introduction to Finite Difference Time Domain
(FDTD) Method
Applications of FDTD to electrical engineering
Initial study of CFDTD to the detection of PCB
impurities and surface roughness
Comparison of different numerical methods
Frequency Domain Methods
– MoM (Method of Moment)
• Zeland
• Agilent ADSTM (Advanced
Design System)
• Ansoft EnsembleTM
IE3DTM
– FEM (Finite Element Method)
• Ansoft HFSSTM
• UGS FEMAPTM
Time Domain Methods
– FDTD
• Remcom XFDTDTM
• Zeland FidelityTM
• RM Associate CFDTDTM
– MRTD (Multi-Resolution Time
Domain)
– PSTD (Pseudo-Spectral Time
Domain)
Advantages & Disadvantages
Features
Point frequency
approach
Frequency band
approach: time
pulse excitation
Advantages
Disadvantages
MoM
Most accurate method
Find Green Function first
FEM
Mature method, adaptive
mesh
Huge matrices
FDTD
Simple, Robust, versatile
Long computation time
MRTD Large structure simulation
PSTD
Complicated algorithm
Principle of Finite Difference
f ( x0  x 2)  f ( x0  x 2)
df ( x0 )
 f ' ( x0 ) 
dx
x
Derivative of f(x) at point P using finite difference approximations
Mesh Structure for FDTD Algorithm
A standard Yee’s lattice
Implementation of FDTD Algorithm
Starting point is Maxwell’s differential equations.



E
  H   0 r 
e  E
t



H
  E  0  r 
 m  H
t
 H z H y 
 E x 

 y

 t 

z
0 
0  Ex 
 xx 0
 exx 0



E y

 0 
  E 
 H x  H z     0 


0


0
0
yy
eyy

  t  
  y
 z
x 
 0
0  zz   E z   0
0  ezz   E z 
 H y H x 



 t 
y 


 x
Updating Equations-Hz
1 
 1
t mzz  i  , j  , k 
t
2
2 

1
1 
1 
 1
 1
2


i

,
j

,
k


i

,
j

,k 
 n 1
1
0 zz 
0 zz 
n 
1
1 
1 
2 
2 
 1
 2
 2
H z 2 i  , j  , k  
 H z 2 i  , j  , k  
1 
1 
2 
2
2 
 1
 1
 2

t mzz  i  , j  , k 
t mzz  i  , j  , k 
2
2
2 


 2
1
1
1 
1 
 1
 1
20  zz  i  , j  , k 
20  zz  i  , j  , k 
2 
2 
 2
 2
 n 1
1  n 1
1 
1
1  n 1
1 
n
E
i

,
j

,
k

E
i

,
j

,
k
E
i

,
j

,
k

E
i

,
j

,k 







x
y
y
 x
2
2 
2 
2
2 
2 
 2
 2
 

 
y
x




Updating Equations-Ez
t ezz (i, j , k  1 / 2)
t
2 0 zz (i, j, k  1 / 2) n
 0 zz (i, j, k  1 / 2)
1
1
n 1
E z (i, j , k  ) 
E z (i, j , k  ) 

t

(
i
,
j
,
k

1
/
2
)
2 1
2 1  t ezz (i, j, k  1 / 2)
ezz
2 0 zz (i, j, k  1 / 2)
2 0 zz (i, j, k  1 / 2)
1
1
1
1
n
n
n
 n  12
1
1
1
1
1
1
1
1 
2
2
2
 H y (i  , j , k  )  H y (i  , j, k  ) H x (i, j  , k  )  H x (i, j  , k  ) 
2
2
2
2 
2
2
2
2 

x
y




Selection of the parameters
★ Cell size criterion
xmax , ymax and zmax
1
 min
20
 min 
vc
f max  r max  r max
★ Excitation choices
Gaussian pulse:
Blackman-Harris pulse:
 t n  t 0 2 
g (t n )  exp 

2
Np


  t n  N p 2 

bt n   a1  a2 cos


Np 2


 2 t n  N p 2  
 3 t n  N p 2  



 a3 cos
 a4 cos




Np 2
Np 2




Boundary Conditions
Shielded boundary:
Perfect Electric Conductor (PEC)
Perfect Magnetic Conductor (PMC)
Open boundary:
Absorbing Boundary Condition (ABC)
Perfectly Matched Layer (PML)
Sequence of an FDTD Iteration Cycle
Calculation of MMICs Parameters
Hx
j2
C
j0
Hy
h
L
i1
j1
Ey
i2
j0


vtn , z0    E tn , z0   dl   E yn nx 0 x, my, nz 0 z   y
h
m 0
0
1
 i2  n  1

n

i t n 1 2 , z0     H t n 1 2 , z0  dl    H x 2 (ix, j1y, nz 0 z )  x  H x 2 (ix, j2 y, nz 0 z )  x 
C
i i1 

1
n
 n  12

   H y (i2 x, jy, nz 0 z )  y  H y 2 (i1x, jy, nz 0 z )  y 
j  j1 

j2
Calculation of MMICs Parameters
The characteristic impedance Z0 is calculated by
Z0 
FFT{V ( z i , t )}
FFT{I ( z i , t )}
For a transmission line, the effective dielectric constant εeff is defined as:
 FFT V z i , t  
 2 ( )
1

 reff ( )  2
 ( ) 
angle
with:


( z j  zi )
  00
 FFT V z j , t 
For a two-port network, S11 and S21 can be defined as:
S11 
S 21 
Input Impedance:
FFT Vref (t )
FFT Vinc (t )

FFT iref (t )
FFT iinc (t )
FFT Vtrs (t ) FFT itrs (t )

FFT Vinc (t ) FFT iinc (t )
1  S11e j 2 kL
Z in  f   Z 0
1  S11e j 2 kL
Near-to-Far Field Transformation


ˆH
Js  n


ˆ
M s  n  E
 0
A
4
 
F 0
4
 e  jkR
S J s R ds'
 e  jkR
s M s R ds'
 
~
 1

 1
E   j  A  2    A     F
k

 0
~

 1
 1
H   j  F  2    F     A
k

 0


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
Applications of FDTD in Electrical Engineering
Simulation of Wave Propagation Problems
Microwave Engineering Problems
Antenna Problems
Scattering Problems
Signal Integrity Problems
Simulation of Wave Propagation
I will show a simple 1dfdtd matlab code
to clarify the wave propagation problem.
Microstrip Low-pass filter
20.32mm
5.65mm
2.54mm
5.65mm
y
z
x
2.413mm
r=2.2
0.794mm
Result
Microstrip Low Pass Filter
10
0
|S11| and |S21 | (dB)
-10
|S11 |
-20
-30
|S21 |
Sheen et al
FDTD solver
-40
-50
0
5
10
Frequency (GHz)
15
20
Conical Horn Antenna
d1=0.71, d2=1.86, lt=1.08, l=3.75, =28degree
Result
CFDTD ------------
Result
Scattering Problems
r  1
r  1
z
 r  2.95 10  4
y
x
Result
Debye sphere 22.5 degree incidence
-25
-30
-35
RCS (dBsm)
-40
-45
-50
-55
-60
-65
-70
-75
0
0.5
1
1.5
f (GHz)
2
dispersive, theoretical
dispersive, FDTD
2.5
3
Signal Integrity Problem
Structure Stack-up:
Layer
GND
Substrate
Trace
Material
r
Copper
FR4
Height
Function
Spacing
Sig
5 mil / 20 mil space
1.4
4.4
Copper
5
1.4
Top View:
100mil*100mil
Cell size:
0.7mil*0.7mil*0.35mil
Frequency range:
10GHz-60GHz
T1
T2
Port1
T3
Port2
T4
Result
Sig
GND
Sig
GND
Sig
GND
Result
Sig
GND
Sig
GND
Sig
GND
Result
Result
Sig
GND
Sig
GND
Initial study of CFDTD to the
detection of PCB impurities
Time domain field distribution
Time domain current distribution
Initial study of CFDTD to the
detection of PCB impurity
Time domain field distribution
Time Domain current distribution
Comparison of field distribution
Comparison of current
distribution
Comparison of field distribution on yz
plane
Without impurity
With air bubble
Comparison of field distribution on yz
plane
With dielectric bubble ε =10
r
With PEC bubble