Signal Scattering from Impurities in PCBsPaul G. Huray University of South Carolina
First ITESO-Intel International Workshop on Signal Integrity12:00 – 12:30 AM, April 7, 2005 Guadalajara, México
Talk Outline• Who is participating in the project?
• Importance of the project.
• TDR tool development.
• Preliminary Results.
• Analytic Scattering Theory.
• Numerical Scattering Outcomes.
• Future Directions.
ParticipantsIndustry Academia
IntelRichard Mellitz, Columbia, SCPaul Hamilton, Hillsboro, ORJim McCall, Hillsboro, ORJanjie Zhu, DuPont, WA
University of South CarolinaPaul G. Huray, ProfessorYinchao 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.
cmsx
smx5
/1103
/103
2
19
8
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-ohmresistiveSplitter /combiner
TDR headson extensioncables
1250 micronCascadeprobes
Analysis Options
AreaArea
Pulse HeightPulse Height
Pulse Width @ 50%Pulse Width @ 50%
Pulse Width * Pulse HeightPulse Width * Pulse Height
PRELIMINARY RESULTS: Peak Analysis
Nelco 6000 di-electric, RTC
-0.02
0
0.02
0.04
0.06
0.08
0.1
36.4 36.45 36.5 36.55 36.6 36.65
time (ns)
V (
vo
lts
)
Vin Vo trace 6 Vo trace 7
Vo trace 8 Vo trace 9 Vo trace 10
Input pulse
Output pulses
PRELIMINARY RESULTS: Shape Analysis
Loss in PCB traces by pulse energy method, measured on 4 20/32 inch traces
012345
trace 6 trace 7 trace 8 trace 9 trace 10
sample trace #
los
s (
po
we
r d
B/f
t)
FR4 Nelco 6000 RTC Nelco 6000 rough copper
Differentiates di-electric material and rough vs smooth copper.
PRELIMINARY RESULTS Sensitivity Analysis
PRELIMINARY RESULTS: pulse amplitude response tracks S21
Pulse Peak Amplitude Attenuation vs. s21.
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
S21Pulse Peak RX amplitude
GHz
Atte
nuat
ion
Conclusion: Normal TDR with superposition can measure PWB line loss
PRELIMINARY Derivative Peak Analysis
Analytic Theory Steps1. An external pulse at z=0 on a microstrip waveguide leads to a Magnetic
Vector Potential, , 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.
),( txAz
Dimensions
`
h
w
l
t
Jz
t
Jz
t
Output
Input
Variables of FR4 inclusion model
Hy
yyinc aHH ˆ
xxinc aEE ˆ
zz akk ˆ a
Scattered Radiation
yyyy aHaHH ˆˆ
xxxx aEaEE ˆˆ
k
Scattering Sphere
Jz Jz
Jz
t
Jz
t
Ground Plane
Signal Trace
FR4 Dielectric
Orthogonal View of inclusion Model
a
incH
incE
Ground Plane
FR4 Dielectric
Signal Trace
Scattering Sphere
Scattered Radiation
`
Current Distribution
Current Distribution
Variables of surface hemisphere
Hy
yyinc aHH ˆ
xxinc aEE ˆ
zz akk ˆ
a
Scattered Radiation
yyyy aHaHH ˆˆ
xxxx aEaEE ˆˆ
k
Scattering Hemisphere
Jz Jz
Jz
t
Jz
t
Ground Plane
Signal Trace
FR4 Dielectric
Orthogonal View of surface hemisphere
a
incH
incE
Ground Plane
FR4 Dielectric
Signal Trace
Scattering Hemisphere
Scattered Radiation
`
Current Distribution
Current Distribution
Step 1: Calculate Az(x,t)
r
zzz
z
Vz
cu
userbyspecifiedtJtJxtxJ
tu
xxt
xx
txJtdxdtxA
)(;)()(),(
)(),(
4),(
'
30
Jz
t'
Step 2: Calculate Einc(x,t) and Hinc (x,t)
zincr
inc
zzinc
atxHtxE
TEMiswaveif
atxAtxH
ˆ),(),(
ˆ),(1
),(
0
0
0
Step 3: Calculate Esc(x,t) from a spherical inclusion
),(),(),(
),(),(),(
txHtxHtxH
txEtxEtxE
scinc
scinc
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:
)(1
),()1(
1),(
)()()()(
)12(42
),(
)()(
)()()12(42
1),(
,,
1,)1(
1,)1(
10
0
11,
)1(1,
)1(
ri
LandYLll
Xwhere
XkrhliXkrhk
lilitxH
Xkrhk
lXkrhllitxE
mlml
lllll
lrsc
lllll
lsc
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
s
s
kax
ls
l
ls
l
Z
Z
Z
Zwithsamel
with
xxhdxd
xZZ
ixh
xxhdxd
xZZ
ixh
l
0
0
1
0
1
2
0
2
1)(
)(1
)(
)(1
)(
1)(
Cross Sections
)()(Re12
1)(1)(2122
)()(122
2
22
2
22
2
lllk
lllk
lllk
lextinction
labsorbed
lsc
Step 4: Calculate Hsc(x,t) from a spherical scattering center
Equations are the same as Step 3 with Boundary Conditions at r=a:
0ˆ0ˆ HaandEa rr
)(
)(tan
)(
)(tan
)(sin)(sin
)12(42
1),(
'
1,)1('
1,)1(
10
0 '
krrdrd
krrjdrd
andka
kaj
XkrheXkrhk
elitxH
l
l
ll
ll
llli
lll
i
l
lrsc
l
l
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:
),,,2
(),,,2
(),,,2
(
),,,2
(),,,2
(
tzyh
EEtzyh
Etzyh
sotzyh
Etzyh
SxextrS
yrS
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 distributionsWithout impurity
With air bubble
Comparison of field distributionsWith 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.