Transcript Scattering Theory for inclusions in FR4 and surfaces Nov

Signal Scattering from Impurities in PCBs
Paul G. Huray University of South Carolina
First ITESO-Intel International Workshop on Signal Integrity
12:00 – 12:30 AM, April 7, 2005 Guadalajara, México
Talk Outline
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Who is participating in the project?
Importance of the project.
TDR tool development.
Preliminary Results.
Analytic Scattering Theory.
Numerical Scattering Outcomes.
Future Directions.
Participants
Industry
Academia
Intel
Richard Mellitz, Columbia, SC
Paul Hamilton, Hillsboro, OR
Jim McCall, Hillsboro, OR
Janjie Zhu, DuPont, WA
University of South Carolina
Paul G. Huray, Professor
Yinchao Chen, Assoc. Prof.
Peng Ye, PhD candidate
Femi Oluwafemi, DuPont, WA
Importance of the project
• Silicon density approximately doubles
every 18 months (Moore’s law).
• PWB electrical technology improvement is
much slower.
• PWB’s have afforded excess electrical
capability since the 1970’s.
• Now, GHz signal presents new signaling
challenges for PWB.
• PWB properties could throttle system
speed improvements.
8
1 3x10 m / s


5
cm
9
2 3x10 1 / s
PCB Manufacture
• PCBs are made from dielectrics that have been clad with
copper foil.
• They are available in different materials and thicknesses
• FR4 (Flame Retardant ε=4) is a glass fiber epoxy laminate
Glass Cloth Samples
1080 glass
2116 glass
7628 glass
Copper Surface Roughness
Can we develop a sensitive, simple
TDR Tool for Manufacturers?
• Should be a simpler method than a VNA.
• It is sensitive enough to show differences
in board and copper types?
• Can PWB manufacturers use the tool for
performance analysis?
Pulse Application and Measurement
of Transmitted Energy
50-ohm
resistive
Splitter /
combiner
TDR heads
on extension
cables
1250 micron
Cascade
probes
Analysis Options
Pulse Height
Pulse Width * Pulse Height
Pulse Width @ 50%
Area
PRELIMINARY RESULTS: Peak Analysis
PRELIMINARY RESULTS: Shape Analysis
Nelco 6000 di-electric, RTC
Input pulse
0.1
V (volts)
0.08
Output pulses
0.06
0.04
0.02
0
36.4
-0.02
36.45
36.5
36.55
36.6
time (ns)
Vin
Vo trace 6
Vo trace 7
Vo trace 8
Vo trace 9
Vo trace 10
36.65
PRELIMINARY RESULTS Sensitivity Analysis
loss (power
dB/ft)
Loss in PCB traces by pulse energy method,
measured on 4 20/32 inch traces
5
4
3
2
1
0
trace 6
trace 7
trace 8
trace 9
trace 10
sample trace #
FR4
Nelco 6000 RTC
Nelco 6000 rough copper
Differentiates di-electric material and rough vs smooth copper.
PRELIMINARY RESULTS: pulse
amplitude response tracks S21
Pulse Peak Amplit ude At tenuation v s. s21.
Attenuation
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
GHz
12
14
16
18
20
S21
P u lse P eak RX amp li t ud e
Conclusion: Normal TDR with superposition can measure PWB line loss
PRELIMINARY Derivative Peak Analysis
Analytic Theory Steps
1. An external pulse at z=0
 on a microstrip waveguide leads to a Magnetic
Vector Potential, Az ( x, t ) , in a volume of homogeneous FR4 that can be
calculated by Green’s Theorem.
2. The Magnetic Vector Potential yields ~ TEMz electric field intensity, Einc, and
magnetic field intensity, Hinc, in homogeneous FR4.
3. An inclusion (bubble or fiberglass cylinder) in FR4 provides a scattering
center for incident Einc and Hinc fields.
4. A conducting hemisphere on the surface of a microstrip trace provides
another type of scattering center for incident fields.
5. Scattered fields lead to a redistribution of the current density in the
microstrip trace and in the ground plane.
6. Use multiple scattering centers of various radii (absence of FR4,
conducting hemispheres) to model manufactured PWB traces with
statistical distribution of bubbles, fiberglass cylinders and rough surfaces.
Dimensions
Jz
Output
t
w
t
l
`
h
Jz
Input
t
Variables of FR4 inclusion model
Jz
Jz
t
t
Signal Trace
Jz
Jz
Scattered Radiation

H inc  H y aˆ y
Hy

k  k z aˆ z

Einc  E x aˆ x
FR4 Dielectric

H  H y aˆ y  H y aˆ y
a

k

E  E x aˆ x  E x aˆ x
Scattering Sphere
Ground Plane
Orthogonal View of inclusion Model

H inc
Current Distribution
Signal Trace
Scattered Radiation
Scattering Sphere
a

Einc
`
Current Distribution
Ground Plane
FR4 Dielectric
Variables of surface hemisphere
Jz
Jz
t
t
Signal Trace
Scattering Hemisphere
Jz
Jz
a
Scattered Radiation

H inc  H y aˆ y
Hy

H  H y aˆ y  H y aˆ y

k  k z aˆ z

E  E x aˆ x  E x aˆ x

Einc  E x aˆ x
FR4 Dielectric

k
Ground Plane
Orthogonal View of surface hemisphere

H inc
Current Distribution
Signal Trace
a
Scattered Radiation
Scattering Hemisphere

Einc
`
Current Distribution
Ground Plane
FR4 Dielectric
Step 1: Calculate Az(x,t)
 

x  x

0
J z ( x, t )
3



Az ( x , t ) 
d
x
d
t

(
t

 t)




4 V '
x  x
u


J z ( x, t )   ( x) J z (t ) ; J z (t ) specified by user
u
c
r
Jz
t'
Step 2: Calculate Einc(x,t) and Hinc (x,t)
 

1 
H inc ( x , t ) 
  Az ( x , t )aˆ z
0
if wave is TEM
 
0  
Einc ( x , t ) 
H inc ( x , t )  aˆ z
 r 0
Step 3: Calculate Esc(x,t) from a
spherical inclusion
Center is a sphere of radius a that produces absence of FR4.
Center may absorb and scatter external fields.
Fields are outgoing waves at infinity that may be expanded as:
 
 
 
E ( x , t )  Einc ( x , t )  Esc ( x , t )
 
 
 
H ( x , t )  H inc ( x , t )  H sc ( x , t )
 

 
1  l
  (l )  (1)

(1)
Esc ( x , t )   i 4 (2l  1)   (l )hl (kr) X l , 1 
  hl (kr) X l , 1 
2 l 1
k


 

 
 r 0  l
  i  (l )  (1)
(1)
H sc ( x , t ) 
i 4 (2l  1) 
  hl (kr) X l , 1  i  (l )hl (kr) X l , 1 

2 0 l 1
 k



 1  
1
where X l ,m ( ,  ) 
L Yl ,m ( ,  ) and L  (r  )
i
l (l  1)
Scattering Parameters
• Coefficients α±(l) and β±(l) are determined by the
boundary conditions at r=a.
• If the spherical surface impedance is Zs,
Etan=Zs aRxH and
 2
 Zs  1
 hl ( x)  i 
Z0  x


  (l )  1  
 1
 Zs  1
 hl ( x)  i 

 Z0  x

d
2
xhl ( x) 
dx

with

d
1
xhl ( x) 
dx
 x ka




 Z s   Z0 
  (l )  1  sam ewith     
 Z0   Z s 
Cross Sections
 sc 

2k
2
 absorbed 
 2l  1
l

2k
 extinction  
2

 2l  12  
2

(l )  1    (l )  1
2

l

k
(l )    (l )
2
2
 2l  1 Re 
l

(l )    (l )
2

Step 4: Calculate Hsc(x,t) from a
spherical scattering center
Equations are the same as Step 3 with Boundary
Conditions at r=a:


aˆr  E  0 and aˆr  H  0
 

 
 r 0 1  l
 ei l sin  l  (1)
i l'
' (1)
H sc ( x , t ) 
i 4 (2l  1) 
  hl (kr) X l , 1  e sin  l hl (kr) X l , 1 

k
2  0 l 1


tan l 
jl (ka)
l (ka)
and
d
rjl (kr)
tan l'  dr
d
rl (kr)
dr
Step 5: Calculate Jz(x,t) due to
scattering from centers
Scattered fields lead to a redistribution of the current density
in the microstrip trace and in the ground plane.
For the microstrip:
h
h
 S ( , y, z, t )   r E y ( , y, z, t ) so
2
2


h
h
h

 S ( , y, z, t )   r  Eext ( , y, z, t )  E x   ES ( , y, z, t )
2
2
2



Step 6: Calculate for Multiple
scattering centers
• Evaluate Jz(x,t) for a variety of scattering radii
(volume bubbles and surface hemispheres)
• Evaluate the effect of off-center spheres
• Evaluate the effect of a random distribution of
volume bubbles and surface hemispheres
Initial Numerical CFDTD with PCB impurities
Time domain field distribution
Time domain current distribution
Initial CFDTD model with PCB impurity
Time domain field distribution
Time Domain current distribution
Comparison of field distributions
Comparison of current distributions
Comparison of field distributions
Without impurity
With air bubble
Comparison of field distributions
With dielectric bubble εr=10
With PEC bubble
Compare model predictions, numerical
outcomes with measured output
• Validate model by comparing measured
outputs and numerical outcomes with
“manufactured” spherical inclusion samples.
• Validate the model by comparing measured
outputs and numerical outcomes with
“manufactured” rough surface samples.
• Refine the model to compensate for irregular
shaped inclusions or trace surface features.
Customize TDR input pulses for
differential “measurements”
• Determine if a choice of input pulses can
differentiate scattering from volume sphere
inclusions and surface conducting
hemispheres.
• Plan regimen of input pulses for unknown
samples to “measure” distribution of FR4
inclusions and microstrip trace roughness.