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.