EXTRACTION OF DIELECTRIC PROPERTIES OF PCB LAMINATE DIELECTRICS ON PCB STRIPLINES TAKING

INTO ACCOUNT CONDUCTOR SURFACE ROUGHNESS

SPEAKER: DR. MARINA KOLEDINTSEVA, IEEE SENIOR MEMBER,

ORACLE

(THE WORK IS DONE IN EMC LAB OF MISSOURI S&T, SPONSORED BY CISCO AND NSF)

1

2

Outline I. Introduction – motivation, objectives,

and state-of-the-art

II. Idea of an “effective roughness dielectric” (ERD)

III. PCB stripline cross-sectional analysis and roughness profile quantification

IV. Experiment-based input data for numerical electromagnetic modeling

V. Modeling results & validation

VI. Building of “design curves” regarding conductor surface roughness

VII. Conclusions

3

3 Gbps 28 Gbps

• Conductor surface roughness lumps into laminate dielectric parameters.

• Any existing analytical and numerical models of conductor surface roughness are approximations.

• Study and adequate modeling of wideband behavior of dielectrics and conductors in PCBs is important from SI point of view.

VLP

• Conductor roughness affects both phase and loss constants in PCB transmission lines and results in eye diagram closure.

STD

HVLP

Motivation

The same dielectric, the same geometry, but different copper foil profiles

Low roughness - HVLP

Medium - VLP

High - STD

VLP

STD

4

Objectives • Develop a technique to accurately measure and extract laminate

dielectric parameters (DK=' & DF=tan) removing effects of conductors.

• Develop a physics-based model, which allows for simple incorporation of conductor surface roughness in electromagnetic numerical models of transmission lines.

• Test and validate the proposed model using measurements on a multitude of various test boards with different cross-sections and roughness profiles.

• Test and validate the proposed model using electromagnetic numerical simulations with different software tools.

• Develop a database for roughness parameters, corresponding to different types of copper foils used in PCBs.

5

A. Koul, M. Koledintseva, et al, Proc.

IEEE Symp. Electromag. Compat., Aug.

17-21, Austin, TX, 2009, 191-196

'2 "24. .cos2

r rc

'2 "24. .sin2

d r rc

Measured S-parameters

Causality , Passivity &

Reciprocity check

ABCD parameters

T c d

arccos h A D

linelength

jT

Solve the system of equations

to obtain complex permittivity

d T c

Model or experimentally

retrieve conductor loss for

rough stripline conductor

OPTIONS

• Analytical Models

• Numerical Models

• Experimental

S-parameters are measured using VNA or TDR with “Through-Reflect-Line” (TRL) calibration in f-domain or t-domain, respectively

Measurements & Material Parameter Extraction

6

Existing Methods for Conductor Roughness Modeling

I. Correction coefficients for attenuation

• Periodic roughness models (Morgan, Sanderson, Sundstroem, Lukic)

• Hammerstad model (Hammerstad, Bekkadal, Jensen)

• “Snowball” model (Huray)

• Roughness hemispheres (Hall, Pytel)

• Stochastic models (Sanderson, Tsang, Braunisch)

II. Impedance boundary conditions

• Holloway, Kuester

III. Numerical electromagnetic modeling

• Deutsch

• Shlepnev

• X. Chen

IV. Experimental separation of conductor & dielectric loss

• Koledintseva et al

Stain-proof layer

Anti-tarnish layer

Drum foilDrum foil

Dendrite plating

Protective barrier

Stain-proof layer

Oxide treatment

7

• Experiment-based Differential and Extrapolation Roughness Measurement techniques (DERM and DERM-2) have been proposed to refine wideband DK and DF from roughness.

[1] A. Koul, M.Y. Koledintseva, S. Hinaga, and J.L. Drewniak, “Differential extrapolation method for separating dielectric and rough conductor losses in printed circuit boards”, IEEE Trans. Electromag. Compat., vol. 54, no. 2, Apr. 2012, pp. 421-433. [2] M.Y. Koledintseva, A.V. Rakov, A.I. Koledintsev, J.L. Drewniak, and S. Hinaga, “Improved experiment-based technique to characterize dielectric properties of printed circuit boards”, IEEE Trans. Electromag. Compat. (to be published soon in 2014)

• An Effective Roughness Dielectric (ERD) approach has been proposed to substitute inhomogeneous roughness boundary layer by a layer with homogenized dielectric properties.

[3] M.Y. Koledintseva, A. Razmadze, A. Gafarov, S. De, S. Hinaga, and J.L. Drewniak, “PCB conductor surface roughness as a layer with effective material parameters”, IEEE Symp. Electromag. Compat., Pittsburg, PA, 2012, pp. 138- 142.

Our Recently Published Works

8

Idea of “Effective Roughness Dielectric”

8

1fG

R R1C

1C

1G

1G

2C

2C

2G

2G

1fC

2fC2fG

L L

Equivalent circuit model to

calculate per-unit-length parameters

Roughness leads to the capacitance increase!

1C

2C

w

01C

02C

1C

2C

t

/ 2A

/ 2A

1fC

2fC

This effect was first noticed in:

9

Tr

Ar t r

y

x

, 1(1 ) ( )

incl matrixeff y matrix incl

matrix incl y incl matrix

vv N

.matrix m mj 0

iincl i

j

2

1ln( )yN a

a

Maxwell Garnett Mixing Rule for aligned metallic inclusions

Depolarization factor of cylindrical inclusions

a=Ar/d Aspect ratio of inclusions

rA

d r

i rT Average peak-to-valley

roughness amplitude

Thickness of “roughness dielectric”

Intrinsic conductivity of “roughness inclusions”

Roughness quasi-period

Mixing Rule for “Effective Roughness Dielectric”

10

• HPF (high-performance foil) - 10 µm <Rz <15 µm

• STD (standard foil) – 5 µm <Rz<10 µm

• VLP (very-low profile foil) – 3 µm <Rz<6 µm

• RTF (reverse-treatment foil) – 3 µm <Rz<6 µm

• HVLP (hyper-very-low profile foil) – 1 µm <Rz<3 µm

• ULP (ultra-low roughness foil) – 0.5 µm < Rz < 1 µm

Various Types of Foils

Foils are mostly

isotropic in X and Z

11

1 2 3 4 5 1 2 3 4 5

5

p p p p p v v v v v

z

Y Y Y Y Y Y Y Y Y YR

Surface Profilometer

Roughness of conductors on PCB are

evaluated based on the amplitude data

only: Ra, Rq, Rz, and Rt.

• Mechanical

• Optical

Roughness data from board vendors

Foil / Trace Thickness t=12µm t=18µm t=35µm

Low rough (HVLP) 1.5 µm 1.5 µm 1.5 µm

Medium rough (VLP) 3 µm 3.5 µm 4 µm

Standard foil (STD) 5 µm 6 µm 8 µm

Standard Profilometer Roughness Evaluation

Problem: foil measured is not the same as “in situ”.

SEM & Oprical Cross-sectional Analysis of PCB Striplines

12

Cutting board for cross-sections

SEM

Optical

13

0 20 40 60 80 100 120 140 160 180-4

-3

-2

-1

0

1

2

3

4

1

2

34 56

7

1

2 3 4 5

67

8

Surface roughness profile image

x, m

y, m

0 20 40 60 80 100 120 140 160 180-1.5

-1

-0.5

0

0.5

1

1.5

2

1

2

3

4 5 6 7

8

9

10

11

12

1 2

3 4

5 6 7

8 910

1112

Surface roughness profile image

x, m

y, m

[S. Hinaga, S. De, A.Y. Gafarov, M.Y. Koledintseva, and J.L. Drewniak, “Determination of copper foil surface roughness from microsection photographs”, Techn. Conf. IPC Expo/APEX 2012, Las Vegas, Apr. 2012]. [S. De, A.Y. Gafarov, M.Y. Koledintseva, S. Hinaga, R.J. Stanley, and J.L. Drewniak, “Semi-automatic copper foil surface roughness detection from PCB microsection images”, IEEE Symp. EMC., Pittsburg, PA, 2012, pp. 132-137].

Conductor Roughness Profile Extraction

13

14

14

Roughness Characterization Flow Chart

1 2 3 4 5 6 7 8 91 2 3 4 5 6 7 9 8

SEM or optical image

Scale calculation

Object selection

Preprocessing noise removal

High boost filtering

Trace profile (foreground)

extraction

Trace side selection

Skin depth calculation &

morphological processing

Translation of pixel map to coordinate

data

Roughness profile coding & maxima/minima

searching

Non-linear de-trending

Removal of artifacts

Roughness quantification

(Ar, Λr, QR)

Image Processing Part

Computer Vision – Roughness Quantification Part

15

1 2 3 4

5 6 7 8 9 10 11

12

1 2 3 4 5 6 7

8 9 10 1112 13 14 15 16

Profile length L

Ar

-valley

-peak

Oxide side

Foil side

Average peak-to-valley amplitude:

Roughness quasi-period:

Roughness factor: r r

oxide foil

A AQR

peakvalley

peakvalley

NN

NLNL

2

valley

N

i

valleyi

peak

N

i

peaki

rN

Y

N

Y

A

valleypeak

1

1

Roughness Factor QR

Roughness Surface Generation from Statistical Analysis of Profile

16

Oxide Side

0

5

10

15

200

5

10

15

20

0.00

0.01

0.02

0.03

Foil Side

Rayleigh

=

2D PDF Generated Surfaces 3D PDF

0

2

4 0

2

4

0.0

0.2

0.4

Gauss

=

Finding Ar from PDF

17

Side STD VLP HVLP

Oxide Gaussian Gaussian Gaussian

Foil Rayleigh Rayleigh Gaussian

mean[pixel]

Blue line is measured from actual profile Red line is generated from PDF

𝐴𝑟 = 2 ∙ 𝑚𝑒𝑎𝑛 𝑝𝑖𝑥𝑒𝑙 ∙pixel’s value

𝑚𝑒𝑎𝑛 𝑖𝑠 𝐸 𝑥 = 𝑥∞

0

𝑓𝑥 𝑥 𝑑𝑥 𝐴𝑟 = 2 ∙ 𝐸 𝑥 ∙ 𝑝𝑖𝑥𝑒𝑙′𝑠 𝑣𝑎𝑙𝑢𝑒

Mean

STD VLP HVLP

Set 1

Oxide 0.862 µm 0.914µm 0.863 µm

Foil 6.250 µm 2.557 µm 1.234 µm

Set 2

Oxide 1.100 µm 1.195µm 1.250µm

Foil 6.066 µm 3.430µm 1.119µm

Set 3

Oxide 1.318 µm 1.308µm 1.778µm

Foil 6.169 µm 2.592µm 1.217µm

Average Peak-to-Valley Roughness Amplitude and PDF R

ou

ghn

ess

Leve

l, µ

m

Length of sample, m

Missouri S&T EMC Laboratory 18

𝐴𝑟 = 2 ∙ 𝐸 𝑥 ∙ 𝑝𝑖𝑥𝑒𝑙′𝑠 𝑣𝑎𝑙𝑢𝑒

19

w1,

m

w2,m H, m P,

m

h1,

m

h2,

m

Ar1,

m

Ar2,

m

1,

m

2,

m

QR1 QR2 QR

STD 337.9 343.2 16.44 712.8 308 286 0.85 6.2 25 14.2 0.034 0.44 0.474

VLP 364.3 368.5 16.8 769 308 286.4 0.87 2.38 24.7 13 0.035 0.18 0.215

HVLP 329.3 331.3 15.3 691.7 303 292 1.25 1.13 14.3 19.2 0.087 0.06 0.147

Geometry and Roughness Parameters of Some Test Samples with Different Foils

The presented samples have almost the same cross-sectional geometry, but different copper foil roughness profiles.

20

Inspection of SEM/optical image

Estimation of “roughness dielectric” parameters Ar, Tr,

d, a, vincl, and i

Calculation of “roughness dielectric” DK and DF using

MG mixing rule

2D-FEM Model

Measurements of S-parameters

Extraction of true DK and DF of PCB dielectric (DERM,

DERMW)

Comparison of measured and modeled S21

(both IL & phase)

Acceptable (< 0.1 dB)

Extracted ERD rough= rough-j rough

Unacceptable (> 0.1 dB; 10o)

rough= rough-j rough

Correction

Correction

rA

d

rT

“Effective Roughness Dielectric” Extraction

Validation by full-wave simulation

w1

w2

Tr oxide

Tr foil

21

Numerical Model Setup Using ERD Layers

22

0 5 10 15 200

100

200

300

400

500

600

700

800

900

d

, rad

/m

Frequency, GHz

extracted

-9

d =6.6*10 - 0.99*10

-22 2

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Frequency (GHz)

T (

Np/

m)

High roughness -STD foil

Medium roughness - VLP foil

Low roughness - HVLP foil

Curve-fit data behaves as 2, &

2 2

1 2 3 1 2 3T r r rK K K K K K

Smooth conductor loss

Dielectric loss

Loss due to conductor roughness

Curve-fit data behaves as 2, &

2 2

1 2 3 1 2 3T r r rB B B B B B

Due to skin depth in conductor

Due to propagation in the dielectric

Due to conductor roughness

T c d

T c d

Spectral Approach to Propagation Constant

23

0 5 10 15 20 25 30-30

-20

-10

0

Frequency, GHz

Ma

gn

itude

of

S 21,

dB

STD

VLP

HVL

0 5 10 15 20 25 30-80

-60

-40

-20

0

Frequency, GHz

Ma

gn

itu

de

of

S1

1,

dB

STD

VLP

HVL

Measured Magnitudes of S11 and S21

• Length of all the test striplines =15,410 mils.

• Striplines are 13 mils wide.

• Laminate dielectric and cross-sectional geometry are the same for all the boards.

24

0 2 4 6 8 10-4

-2

0

2

4

Frequency, GHz

Phas

e S 21

, deg

rees

STD

VLP

HVLP

10 12 14 16 18 20-4

-2

0

2

4

Frequency, GHz

Phas

e S 21

, deg

rees

STD

VLP

HVLP

10 15 20 25 30-4

-2

0

2

4

Frequency, GHz

Pha

se S

21, d

egre

es

STD

VLP

HVLP

0 10 20 300

500

1000

Frequency, GHz

T,

rad/m

STD

VLP

HVLP

0 5 10 15 20 250

2

4

6

8

Frequency(GHz)

T,

Np/m

STD

VLP

HVLP

Measured Phase of S21 and Propagation Constant

25

0 0.1 0.2 0.3 0.4 0.51.2

1.4

1.6

1.8

2

2.2

2.4x 10

-6

K

1 = - 4.2e-06*QR

2 + 2.6e-07*QR + 2.1e-06

X: 0.001672

Y: 2.147e-06

QR

K1

Experimental

quadratic

HVLP

VLP

STD

0 0.1 0.2 0.3 0.4 0.51

1.5

2

2.5

3

3.5

4x 10

-11

K

2 = 1.7e-11QR

2 + 3.4e-11*QR + 1.5e-11

X: 0.003344

Y: 1.506e-11

QR

K2

Experimental

quadratic fitting

HVLP

VLP

STD

0 0.1 0.2 0.3 0.4 0.5-0.5

0

0.5

1

1.5

2

2.5

3

3.5x 10

-23

K

3 = 1.1e-23*QR

2 - 7.9e-23*QR + 3.3e-23

X: 0.003344

Y: 3.323e-23

QR

K3

Experimental

quadratic fitting

VLP

STD

HVLP

6

0

11 23 2

2.15 10

1.51 10 3.3 10

c

d

Extrapolation to Zero Roughness in α to Refine Dielectric Loss

26

Extrapolation to Zero Roughness in β to Refine Dielectric-Related Phase Constant

0 0.1 0.2 0.3 0.4 0.54.5

5

5.5

6

6.5

7

7.5

8

8.5x 10

-6

B

1 = 6.6e-06*QR

2 + 2.8e-06*QR + 5e-06

X: 0

Y: 4.966e-06

QR

B1

Experimental

quadratic fitting

HVLP

VLP

STD

0 0.1 0.2 0.3 0.4 0.5

6.36

6.38

6.4

6.42

6.44

6.46

6.48

6.5x 10

-9

B

2 = 2.2e-10*QR

2 + 1.6e-10*QR + 6.4e-09

X: 0

Y: 6.37e-09

QR

B2

Experimental

quadratic fitting

HVLP

VLP

STD

0 0.1 0.2 0.3 0.4 0.5-11.5

-11

-10.5

-10

-9.5

-9

-8.5

-8x 10

-23

B

3 = - 3.2e-23*QR

2 - 4.1e-23*QR- 8.2e-23X: 0.001672

Y: -8.194e-23

QR

B3

Experimental

quadratic fitting

HVLP

VLP

STD

6

9 23 2

5.0 10

6.37 10 0.82 10

c

d

27

0 0.1 0.2 0.3 0.4 0.50.5

1

1.5

2

2.5x 10

-6

QR

K1

BO

quadratic

CZ

quadratic

MB

quadratic

0 0.1 0.2 0.3 0.4 0.51

2

3

4

5

6

7x 10

-11

QR

K2

BO

quadratic

CZ

quadratic

MB

quadratic

0 0.1 0.2 0.3 0.4 0.5-4

-2

0

2

4x 10

-23

QR

K3

BO

quadratic

CZ

quadratic

MB

quadratic

6

0

11 23 2

2.15 10

1.5 10 3.0 10

c

d

Additional Procedure to Refine Dielectric Loss (with Two other Sets of Test Vehicles with Different Types of Foil)

1

1

1

2

2

2

3

3

3

This increases accuracy of extraction.

28

Additional Procedure to Refine Phase Constant (with Two other Types of Foil)

6

9 23 2

5.0 10

6.38 10 0.8 10

c

d

0 0.1 0.2 0.3 0.4 0.5-1.6

-1.4

-1.2

-1

-0.8x 10

-22

QR

B3

BO

quadratic

CZ

quadratic

MB

quadratic

1

2

3

0 0.1 0.2 0.3 0.4 0.5

5

6

7

8

9

10x 10

-6

QR

B1

BO

quadratic

CZ

quadratic

MB

quadratic

1

2

3

0 0.2 0.4 0.6 0.86.3

6.4

6.5

6.6

6.7

6.8

6.9x 10

-9

QR

B2

BO

quadratic

CZ

quadratic

MB

quadratic

1

2

3

This increases accuracy of extraction.

29

0 5 10 15 20 25 30 350

2

4

6

8

10

Frequency, GHz

, N

p/m

C0

D

T

11 23 21.51 10 3.3 10d

Extracted Loss in a Smooth Conductor (Roughness Parts are Removed)

smooth 0T C d

6

0 2.15 10c

30

The refined dielectric data (DK and DF) for all the test vehicles is used in

numerical electromagnetic modeling (2D-FEM)

Extracted Dielectric Properties of PCB Laminate Substrate

0 5 10 15 20 25 303.6565

3.657

3.6575

3.658

3.6585

Frequency, GHz

DK

Extracted DK for Megtron 6 "Old"

0 5 10 15 20 25 304.5

5

5.5

6

6.5x 10

-3

Frequency, GHz

DF

Extracted DF for Megtron 6 "Old"

Numerical model 1: Ansoft Q2D (2DFEM)

This model is used to extract

parameters of Effective Roughness

Dielectric (ERD): bright-green layers

31

Modeled & Measured S21 for Stripline with HVLP Foil (Q2D)

32

Modeled & Measured S21 for Stripline with VLP Foil (Q2D)

33

Modeled & Measured S21 for Stripline with STD Foil (Q2D)

34

The refined dielectric data (DK and DF) for all the test vehicles is used in

numerical electromagnetic modeling (2D-FEM)

Extracted Properties of Effective Roughness Dielectric

Foil Type

Tr1 (ox), µm

Tr2 (foil), µm

tanr (ox)

tanr (foil)

r (ox)

r (foil)

QR (ox)

QR (foil)

VR (ox), m

VR (foil), m

STD 1.7 12.4 0.01 0.17 5.0 12.0 0.034 0.44 0.085

25.30

VLP 1.74 4.76 0.02 0.13 5.1 9.0 0.035 0.18 0.178

7.42

HVLP 2.50 2.26 0.06 0.04

5.1 4.8 0.087 0.06 0.765 0.433

Set 1

35

Effective Roughness Dielectric Parameters as a Function of Roughness Factor

36

Effective Roughness Dielectric Parameters as a Function of Roughness Factor

Sets 1,2,3 – 13mil trace width Sets 4, 5 – 7 mil trace width

Region of Oxide Sides & HVLP

Region of Oxide Sides& HVLP

Region of VLP/RTF

Region of VLP/RTF

Region of VLP/RTF

Region of Oxide Sides & HVLP

Region of STD Region of STD

Region of STD

37

Numerical model 2: CST

Studio Suite 3D (Full-wave

FD MoM) – this model is

used for validation of the

extracted ERD data

Validation Using Full-wave Model (CST)

HVLP

VLP

STD

T. Vincent, M. Koledintseva, A. Ciccimancini, and S. Hinaga,

“Effective roughness dielectric in a PCB: measurement and full-

wave simulation verification”, IEEE Symp. EMC, Aug. 2014

(accepted)

38

T. Vincent, M. Koledintseva, A. Ciccimancini, and S. Hinaga, “Effective roughness dielectric in a PCB: measurement and full-wave

simulation verification”, IEEE Symp. EMC, Aug. 2014 (accepted)

STD

Unwrapped phase of S21

S21 CST Modeled vs. Measured)

STD

39

0(1 )c c r 0

r

c

r

0r c c

Modeled & Measured Magnitude of S21 for Striplines with Different Foils

Slope of S21 as a function of frequency increases with the increase of surface roughness

0 5 10 15 20 25 30-25

-20

-15

-10

-5

0

Frequency, GHz

S2

1,

dB

Smooth conductor

STD

VLP

HVLP

21 08.686( )D csmoothS L

HVLP

STD

VLP

Smooth

40

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

QR

Ad

diti

ona

l slo

pe

R,

dB

/GH

z

Experimental points

linear

quadraticSTD

VLPHVLP

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

QR

Rn,

dB

/GH

z/m

Experimental points

linear

HVLP

VLP

STD

R=(S smooth- S rough)/f [dB/GHz] Rn=(S smooth- S rough)/f/L [dB/GHz/m]

Additional Slope in S21 as a Function of Roughness Factor

0 0.1 0.2 0.3 0.4 0.5-1

0

1

2

3

4

5

6

7x 10

-23

Q, m

K3~

2

SET I

SET II

QR, µm

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

3.6

3.7

3.8

3.9

4

4.1x 10

-6

Q, m

K1~

sq

rt(

)

Extrapolation to Zero Roughness

SET I

SET II

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

x 10-11

Q, m

K2~

Extrapolation to Zero Roughness

SET I

SET II

QR, µm QR, µm

41

Extrapolation to Zero Roughness in α (7-mil Lines)

SET I

RTF

STD

HVLP

RTF

STD

HVLP

RTF

STD

HVLP RTF

STDR

STDR

HVLP RTF

RTF

SET II

41

HVLP

HVLP

STDR

0 0.1 0.2 0.3 0.4

-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

-1.8

x 10-22

Q, m

B3~

2

SET I

SET II

QR, µm 42

0 0.1 0.2 0.3 0.4 0.56.2

6.4

6.6

6.8

7

7.2

7.4

7.6

7.8

8

8.2x 10

-6

Q, m

B1~s

qrt(

)

SET I

SET II

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.46.44

6.46

6.48

6.5

6.52

6.54

6.56

6.58

x 10-9

Q, m

B2~

SET I

SET II

SET I SET II

HVLP

HVLP

HVLP

RTF

RTF

STD

STDR

RTF

HVLP

HVLP RTF

STD

STDR

STD

RTF

HVLP

STDR

RTF

QR, µm QR, µm

Extrapolation to Zero Roughness in β

43

Refined DK and DF

0 5 10 15 20 25 303.7

3.72

3.74

3.76

3.78

3.8

Frequency, GHz

DK

DK SET I

DK SET II

0.7%

0 5 10 15 20 25 30

6.5

7

7.5

8

8.5

9x 10

-3

Frequency, GHz

DF

DF SET I

DF SET II

2.5%

Excellent agreement between the results of extraction of dielectric parameters of two independent sets of boards (3+3 boards total) with the same dielectric and the same geometry, but different types of foil roughness has been obtained! Frequency range is from 10 MHz to 30 GHz.

44

Dielectric Loss and Smooth & Rough Conductor Losses

0 5 10 15 20 25 300

1

2

3

4

5

6

d,

Np

/m

Frequency, GHz

SET I

SET II

0 5 10 15 20 25 300

0.5

1

1.5

c0,

Np

/m

Frequency, GHz

SET I

SET II

0 5 10 15 20 25 30-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Frequency, GHz

ro

ug

h,

Np

/m

SET I STD

SET I RTF

SET I HVLP

SET II STDR

SET II RTF

SET II HVLP

SET II- STDR

SET I - STD

SET I - RTF

SET II - RTF

SET II - HVLP

SET I- HVLP

Total

conductor

loss

Smooth

conductor

loss

Rough conductor loss

Concentration of “roughness inclusions” decreases with distance from

zero-roughness plane

Maxwell Garnett mixing rule requires knowledge of volume concentration of

“roughness inclusions”. This volume concentration varies as a function of the

height y. Hence the dielectric properties homogenized by Maxwell-Garnett in each

incremental layer are also functions of y.

( ) 1 ( )(1 ( )) ( )

incl matrixMG matrix

matrix y incl matrix

y yy N

)(y

Effective Roughness Dielectric Approximation

Close to smooth conductor, y0=0

Deeper inside ambient dielectric, y1>y0

Deeper inside ambient dielectric, y2>y1

Closer to ambient dielectric, y3>y2

Ny is the depolarization

factor in y-direction.

and

45

d=Ar

1

2

3

Using Maxwell Garnett mixing rule the roughness could be described as gradient

layer with exponential distribution

Loss is due to non-propagating surface waves in the structure with variable permittivity.

0 12

0

01 0

( )( ) arctan ( 1)

4

tyMG eff

MG eff

MG eff

k y dy l

( ) ' ( ) " ( ).MG MG MGy y j y

The characteristic equation for wave

propagation in a gradient waveguide:

effeffeff j '''

Boundary Layer – Gradient Waveguide Model

d

0 1 z

x

)(y )(0 yk

Turn point

(y)= 0 +d f(y)

0

y

0( ) ( )MG MGy f y

0MG

Resultant effective roughness dielectric

46

47

Set 1

STD 15 6.489 0.203 12.7

6.496 0.17 12.0 13 5.05 0.124 5.02

VLP 6 2.739 0.130 8.08

2.752 0.13 9.0 5 1.932 0.100 13.58

HVLP 2 1.083 0.048 5.01

1.086 0.04 4.8 1 0.158 0.203 44.76

Extracted from Gradient Model (on Foil Sides) Extracted from Q2D

Solution #

Turning point= Ar tanrough

𝜺′𝒓𝒐𝒖𝒈𝒉 𝒆𝒇𝒇 Ar tanrough 𝜺′𝒓𝒐𝒖𝒈𝒉 𝒆𝒇𝒇

Results for the Gradient Model: Set 1, Foil Side

There is a reasonable agreement; however, the results were obtained only for a limited number of samples.

Conclusions

48

• A new improved technique DERM2 to extract dielectric properties of a

laminate dielectric for a set of five test vehicles is demonstrated.

• A semi-automatic roughness profile extraction and quantification procedure

has been applied to SEM or optical microscopy pictures of microsections of

PCB stripline.

• A metric called “roughness factor” QR to quantify roughness profiles has

been introduced.

• The correlation between the additional slope in insertion loss due to

roughness and the roughness factor QR has been established. The effective

roughness dielectric layer concept was applied to numerically model (in 2D

FEM) all the five test vehicles.

• In the numerical models, the dielectric parameters of ambient dielectric

were taken as those obtained using the DERM2 procedure; the boundary

roughness layers were substituted by Effective Roughness Dielectric.

• This model and analysis lead to the development of the “design curves”

(additional slopes of insertion loss, or additional conductor loss as a

function of roughness parameter), which could be used by SI engineers in

their designs.

Acknowledgment

49

• I am very grateful to Scott Hinaga (Cisco) for collaboration, weekly discussions at

conference calls, support of ideas, and sponsoring this research in 2008-2014.

• I would like to thank graduate and undergraduate students of Missouri S&T who

contributed to this work: Amendra Koul (Cisco), Praveen Anmula (Mentor

Graphics), Soumya De (Cisco), Fan Zhou (Semtech), Aleksandr Gafarov (Mentor

Graphics), Aleksei Rakov (Moscow Power Engineering Institute), Oleg Kashurkin

(Missouri S&T), and Alexei Koledintsev (Missouri S&T).

• I would like to thank Prof. James Drewniak for an opportunity to work with EMC

Lab of Missouri S&T in 2000-2014, motivation for this research, and useful

discussions.

• I would like to thank Missouri S&T Materials Research Center colleagues – Dr.

Clarissa Wisner , Dr. Beth Culp, Prof. Matt O’Keefe, and Dr. Signo Reis (Saint

Gobain) for their help with SEM and optical micro photographs.

• This work was also partially supported by the National Science Foundation under

Grant No. 0855878 through NSF I/UCRC Program.

50

Thanks &