Electric Properties of

Dielectrics

吳瑞北

Rm. 340, Department of Electrical Engineering

E-mail: rbwu@ew.ee.ntu.edu.tw

url: cc.ee.ntu.edu.tw/~rbwu

S. H. Hall et al., High-Speed Digital Designs, Chap.6

R. B. Wu

What will you learn

• How varies with frequency?

• Can ’ and ” be arbitrarily defined?

• What is the physical constraint?

• How to set suitable model for ’ and ” ?

• How to measure it?

R. B. Wu

Tx-Line Losses

• Polarization of Dielectrics

• Dielectric losses

• Environmental & Localization Effects

• Measurements

R. B. Wu

Nonideal Effects in Dielectrics

• Dielectric working well for lower frequencies

becomes difficult to design since

– Frequency-dependent permittivity and loss tangents

– Environmental factors

– Localized interactions (fiber weave effect)

• Improper model results in inaccurate phase delay

and signal losses, even nonphysical behaviors

• Dielectric loss in PCB is significant at >3 GHz.

• Simulation-based bus design at >3GHz is possible

only if with suitable model for dielectric material.

R. B. Wu

Freq.-Dependent Dielectric Constants & Losses

• Loss tangent

• Dielectric constant

;2

tan

fd

112 fCG

From R, L, C, then

Ref.: S. Mumby, “Dielectric properties of FR-4 laminates as a function of thickness and the electrical

frequency of measurement (IPC-IP-749), Inst. Interconnect. & Packag. Electron. Circuits, 1988.

;glsglsrsnrsn VVr

R. B. Wu

Dielectric Loss vs. Conductor Loss

ac dominant

1:1

2:1

W. Humann, Proc. ITC 2002

ac

ad

loss) dielectricf

loss)conductor f

d

c

a

a

Polarization of Dielectrics

R. B. Wu

Electronic Polarization

• When electric field applied,

electron cloud is displaced until

force between +/- charges equal

the force of applied field.

• Electric inside electron cloud:

• Electric dipole moment:

electronic polarizability:

• Polarization vector:

3

0

ˆ ; 4

er r

e

q rE rE E

r

e e rp q r p Ea

3

04e era

; : # atoms per unit volumeP Np N

R. B. Wu

Other Polarizations

• Orientational (dipole)

polarization

• Ionic (molecular)

polarization

ip Ea

op Ea

R. B. Wu

Relative Permittivity

• Usually measured rather than calculated.

• Polarizability

• Electric flux density:

( )e o i totP N Ea a a

0 0 0

0 0

0 0 0 0 0

) ; (

(1 )

st

r

E E E E P P E

D E P

f

D E E E

: electric susceptibility

: relative dielectric permittivityr

Dielectric Loss

R. B. Wu 12 Interconnect: Adv

Classic model of dielectric losses derived from damped oscillations of electric dipoles in the material aligning with the applied fields

• Dipoles oscillate with the applied time varying field – this takes energy

Dielectric constant becomes complex with losses

PCB board manufacturers specify this was a parameter called “Loss Tangent” or Tan

''' ''

'j Tan

12 ''dielectric

dielectric

f

The real portion is the typical dielectric constant, imaginary portion represents losses, or conductivity of the dielectric

Dielectric Losses

R. B. Wu

DC Dielectric Losses

• Due to conduction electrons in dielectric

• Do not confuse d discussed here with dielectric,which is

due to the energy it takes to polarize the electric dipoles in

dielectric.

• The term d is small and usually neglected.

dJ E

0

0

( )

d

dr r

H J j E E j j E

j j j E

R. B. Wu

Single-Pole Model

• Mechanical spring model analogy

2002 2

0

; = q E m k

mx bx kx F xj b m m

2

0

2 2

0 0 0

r

N q mPP Nqx

E j b m

2 2 2

0 0

2 22 2

0

2

0

2 22 2

0

1r

r

N q m

b m

N q m b m

b m

R. B. Wu

Multipole Model

• Several resonance:

• A more pragmatic approach

2

0

2 21

1n

i i

r

i i i i

N q m

j b m

2

1 01, 2,1

ni d

r

ii i

jj

1 2,

Damping factor dominant

Debye equation:

1

ni

r

i ij

R. B. Wu

PCB Example

• Model can be fit empirically

2 2

2 21 32 4

1 2 peaks two poles: 1 1

r rj j

2 4

1 2

1 3

, : 19, 32GHz

3.8

variations near peaks

0.0163, 0.012

damping tuned for match

, : 20, 63GHz

Only suitable 15-35GHz

R. B. Wu

Infinite-Pole Model • One freq. only model?

2

1

1 2

1 2 12,

22 1

2 1 2 1 2 1

1

ln ln 11

lnln ( ) ( ) 2

ln ln ln

ni

r r

i i

r

dy

j y yj

j jj

11

2 1

Ex. : / tan 3.9 / 0.0073@1G

choose 10 , 10

r

3.9 0.0073 0.028

0.417

3.9@1

3.85

G

11

11

0.028

3.85 0.0178ln 10

3.85 0.0178ln 10( )

tan =

R. B. Wu

’ vs. ” in Debye Model

• ’ decreases with a corresponding increase in losstan.

0

Debye equation: 1

jj

2

0

0

2

0

1

1

0

1

00

tan 1

R. B. Wu

Causality

• Kramers-Kronigs relations,

– between real and imaginary parts of any complex function that is

analytic in the upper half-plane:

2 20

2 20

2 ( )( ) 1

2 1 ( )( )

x xdx

x

xdx

x

* Analytic functions:

( ) Re Im

Re Im Re Im ;

* Reality

( ) ( )

r i

r i i r

j j

0

0 0

2 2

0

0

2 2

0

0

1

Ex.: Debye model:

1

Re( )=

Im( )=

r i

i

i r

r

i r

j j

j

0( ) ( ) ( )

K.K. relation ( ) 0 0

P t t E d

t t

R. B. Wu

Improve 3-dB BW on Lossy Lines

• Use more copper

• Don’t go as far,

otherwise using

repeaters

• Use a higher-

impedance trace

• Add equalization

• Use a better

dielectric material

Environmental & Localization

Effects

R. B. Wu 22

Resin

Material

Glass

Material

9 0 6 3

9 6 3

Fiber Weaves in FR4

• Woven fiberglass bundles in FR4

• Bulk dielectric constant

• Spatially dependent r, eff will

deteriorate differential lines

significantly.

, fiber r, resin6; 3;r

, fiber fiber r, resin resinr r V V V

R. B. Wu

Fiber-Weave Effects & Mitigation

• Worse-case difference

• It can be larger for

thinner microstrips.

• May cause severe

impact for differential

lines @ 5 to 10 Gb/s

• One way to mitigate

this effect is to route

the lines 450 to the

direction of weave.

,eff 0.23r

R. B. Wu

• 2D fiber-weave modeling

– Trace between bundles

– Trace over a bundle

Model of Fiber-Weave Effects

,eff 3.5 4.6r r

,eff 3.72 4.95r r

R. B. Wu

Humidity & Temperature Effects

• Material: FR4-7628

• Effects:

– Large increase in losstan

(+50% from 15-95% RH)

– Small increase in r

(+5% from 15-95% RH)

Malaysia (95% RH, 95oF)

Arizona (15% RH, 60oF)

R. B. Wu

Have you learned?

• What is physical model for dielectric loss?

• Do you know dielectric polarization,

oriental polarization, and ionic polarization?

• Do you know the common models: signal-

pole model, multi-pole model, infinite-pole

model, and Debye model?

R. B. Wu

Further Reading

• T. Chretiennot, et al., "A microwave and microfluidic planar resonator

for efficient and accurate complex permittivity characterization of

aqueous solutions,” IEEE T-MTT, vol. 61, Feb. 2013.

• E. Piuzzi, et al., "A comparative analysis between customized and

commercial systems for complex permittivity measurements on liquid

samples at microwave frequencies,” IEEE T-IM, vol. 62, May 2013.

• M. Hofmann, et al., "Microwave-based noninvasive concentration

measurements for biomedical applications,” IEEE T-MTT, vol. 61,

May 2013.

• J. Roelvink, et al., "A planar transmission-line sensor for measuring

the microwave permittivity of liquid and semisolid biological

materials,“ IEEE T-IM, vol. 62, 2012.

• G. Hislop, “Permittivity estimation using coupling of commercial

ground penetrating radars,” IEEE T-GRG, vol. 53, Aug. 2015

28

Measurement of Dielectric Constants

Student: Chia-Hao Chang

Adviser: Ruey-Beei Wu

Date : 06/27 2009

R. B. Wu 29

Waveguides

• Measuring S-parameters of filled waveguides to derive

propagation constant

• Costly, available above fcutoff

Square WaveguideSquare Waveguide

Dielectric sample

l

ConnectorConnector

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability

at microwave frequencies,” Proc. IEEE, vol. 62 no. 1 pp. 33-36, Jan 1974.

0

2

rk

r

cutoffa

cf

2

kck

β

a

R. B. Wu 30

Substrate-Integrated Waveguide

• Two SIW (Substrate-Integrated Waveguide) to calculate

FDEW (Freq.-Dependent Equivalent Width)

• Unknown conductive attenuation

• Available above fcutoff

Wave

Propagation a'

a

Wave Propagation

ain

s

C. H. Tseng and T. H. Chu, “Measurement of frequency-dependent equivalent width of substrate

integrated waveguide,” T-MTT, pp. 1431-1437, Apr. 2006.

2

0

2

2

2

41

r

a

2

0

2

2

2

41

r

a

Wave

Propagation a"

aa

R. B. Wu 31

Cavity Resonance

• Observing resonant frequencies and Q factors

• Edge effect

• Bad resolution at higher modes

A. Namba, et al., and T. Watanabe, “A simple method for measuring the relative

permittivity of printed circuit board materials,” T--EMCpp. 515-519, Nov. 2001.

Dielectric

Metal 2

Metal 1

2 2

2 2mn

r

c m nf

a b

222

22 b

n

a

m

f

c

mn

r

a

b

R. B. Wu 32

Ring Resonator

• Periodical resonance

• Difficult feeding and coupling loss

a

Feeding

LineFeeding

Line

P. A. Bernard and J. M. Gautray, “Measurement of dielectric constant using

microstrip ring resonator,” T-MTT, Mar. 1991

,2

n

r eff

c nf

a

2 2

,2

r eff

n

c n

f a

R. B. Wu 33

T-stub

J.-H. Liu, Y.-C. Lin, J.-T. Lue, and C.-J. Wu, “Resistivity measurements of

layered metallic films at various microwave frequencies and

temperatures using the micro-strip T-junction method,” Meas. Sci.

Technol. 13, pp.1132-1137, Apr. 2002.

)(4

)12(

fP

cnf

eff

res

0

212

2

ZZ

ZS

in

in

• Periodical resonance

• Acquiring attenuation constant from |S21|

• Drawbacks of resonance method:

– Limited by the fixture dimension

– Sensitive to determination of resonant freq.

ZinZ0 Z0

, 0in resZ Z Pa

Zin

P

R. B. Wu

Time

TDT

Delay

AttenuationIncident

Pulse Transmitted

Pulse

34

Time-Domain Tx-Line Measurement

• Observing the TDT pulse response

• Require perfect match

A. Deutsch, G. Arjavalingam, G. V. Kopcsay, M.J. Degerstrom, “Short-pulse

propagation technique for characterizing resistivepackage

interconnections,” T-CHMT, pp. 1034-1037 , Dec. 1992

Ground

Dielectric

Microstrip Line

ProbeProbe

R. B. Wu

Ground

Dielectric

Microstrip Line

ProbeProbe

35

• Applying transmission line property

• Measuring S-parameters to derive propagation constant

effr ,00

a j

dc aaa

Freq.-Domain Tx-Line Measurement

T S le

a j

2

00

,

effr

a d

eff

2tan

M. Cauwe and J. De Baets, “Broadband material parameter characterization for

practical high-speed interconnects on printed circuit board,“ T-AdvP,

pp.649-656 Aug 2008

R. B. Wu 36

Pros & Cons of Tx-Line Method

• Pros:

– Broadband

– Easy fabrication

– Conductor effect can be calculated

• Cons:

– Inhomogeneous microstrip line requires data conversion

– Accuracy of empirical formula and manufacturing tolerance is uncertain

Ground

Dielectric

Microstrip Line

ProbeProbe

W

T

H

Adapt stripline structure to avoid data conversion

M.N.O. Sadiku, S.M. Musa, S.R. Nelatury, “Comparison of dispersion formulas

for microstrip lines,” 2004 IEEE SoutheastCon. Proc., pp. 378-382, Mar. 2004.

R. B. Wu 37

G. F. Engen, and C. A. Hoer, “’Thru-Reflect-Line’: An improved technique

for calibrating the dual six-port automatic network analyzer,“ T-MTT,

pp. 987-993, Dec. 1979.

1. S-parameter Measurement

• Use VNA built-in TRL calibration to capture scattering

parameters of an ideal tx-line

• All connectors are assumed identical

P1

P2

TR

L

DUT

S11 S22

S21

S12

DUT

a1

b1

Sx11 Sx22

Sx21

Sx12

a2

b2

Sy11 Sy22

Sy21

Sy12

Error Box X Error Box Y

Connector

X

Connector

YDUT

R. B. Wu 38

TRL calibration

• TRL works well except

when q ~ /2,

• P is chosen /4 of max.

freq. to minimize higher

order wave

VNA

port 1

VNA

port 2ROpen

or

Short

|Γ|=1 |Γ|=1

Reference Plane

T

Reference Plane

|Γ|=0 |Γ|=0VNA

port 1

VNA

port 2

L

Reference Plane

|Γ|=0 |Γ|=0

p

VNA

port 1

VNA

port 2

q

a

sin2

1,

R. B. Marks, “A multiline method of network analyzer calibration,” T-MTT,

pp. 1205-1215, Jul. 1991.

VNA

port 1

p

R. B. Wu

2. Transmission Matrix • The S-parameters can be transformed to ABCD

transmission matrix

• It describes the cascading relation of voltage and current

• Theoretically, [T] satisfies:

2112221121122211

2112221121122211

21)1)(1()1)(1(

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

2

1

SSSSSSSS

SSSSSSSS

ST

DUTV1 V2

I1 I2

+

-

+

-

2

2

1

1

I

VT

I

V

ll

Z

lZl

T

coshsinh1

sinhcosh

0

0

R. B. Wu

Re{λ}

Im{λ}

θ θ+2π

λ

40

3. Propagation Constant Solution

• Solving complex eigenvalue for [T], they are

fx. of propagation constant & line length:

let

• By selecting correct root and phase,

propagation constant is obtained:

le 21,

a lnl

n

2

a j

ll

Z

lZl

T

coshsinh1

sinhcosh

0

0

le

2

1

1

2

1

R. B. Wu 42

Simulation: Parallel Plate Cavity

• Simulating a parallel plate PCB with feeding port at center,

default relative dielectric constant=4, loss tangent=0.02

50 mm

50 mm

25 mm

25 mm

Port

Zero point

(2,0)(0,2)

(2,2)

(4,0)(0,4)

(4,2)(2,4)

(4,4)

(6,0)(0,6)

(6,2)(2,6)

(6,4)(4,6)

(8,0)(0,8)

(8,2)(2,8)

(6,6)

(8,4)(4,8)

Simulation software: Ansoft HFSS v11

R. B. Wu 43

Simulation -Ring Resonator

• Simulating a ring resonator with radius a=13mm, default

relative dielectric constant=4, loss tangent=0.02

1

23 4 5 6

a

Simulation software: Ansoft HFSS v11

R. B. Wu 44

Simulation -Stripline

• Results fit with each other but suffer from

plate mode and finite conductivity

W

H T

L

Abnormal ripple due to plate resonance

R. B. Wu 45

Stripline with Via Fence

• In order to suppress plate mode,

use ground via fence to force the

two ground layers of zero

potential difference Signal

Radiation

Signal

line

Ground

Ground

Feeding Port

Ground Vias

Stripline

R. B. Wu 46

Stripline with Via Fence

• The S-parameters of a 1mm txline on

a 45mm square board

Freq. limit of via

protection D=4mm,

f~17GHz

Simulation software: Ansoft SIwave v3.0

D

S

H

W

y

x

z

R. B. Wu 47

Via Fence Design Guide

• Calibration standards and DUT

should be surrounded by ground vias:

• Ground layers and vias form a SIW

structure. To avoid SIW mode, D shall

satisfy

rm

m

f

cD

2

1

2

D

S

H

W

y

x

z

r

cutoffD

cf

2

1

R. B. Wu

48

Via Fence Design Guide (2/3)

• Small D lowering characteristic impedance is

unfavorable in transmission

• 80% ground current are concentrated in ±3h region

below signal line, H=2h, it is better choose that:

D

S

H

W

y

x

z

W

h

0 1h 2h 3h-1h-2h-3h

D

Ground Plane

WD 3HD 3

2

1

1

h

DI gs

S. H. Hall, G. W. Hall, and J. A. McCall, High-Speed Digital System Design,

New York: Wiley, 2000.

R. B. Wu 49

Via Fence Design Guide (3/3)

• To form a effective wall for avoiding resonance,

S shall satisfy

rm

m

f

cS

4

1

4

D

S

H

W

y

x

z

H. Uchimura, T. Takenoshita and M. Fujii, “Development of a laminated

waveguide” T-MTT, pp.2438-2443, Dec. 1998.

R. B. Wu

50

Conductor Internal Inductance

• The current flowing inside the conductor contributes to

inductance effect

• Determined by W

rather than H

Hexternal

Hinternal

w

tL freqlow

4

0int

acR

L int

R L

G C

LC

R. B. Wu

51

Modified Tx-Line Model

• the transmission line model should be modified as

• The phase constant without Lint effect is

R Lext

G C

Lint

intLLL ext

ext

ext

extext L

LCLj

L

LGZ

L

L

Z

R

21

21

221

2

intint0int

0

C

LZ ext

0

0 0

int 2

r ext

ext

L C

L C

L

extext

cL

CL

L

L

Z

R

221

2

intint

0

a

ext

dL

LGZ

21

2

int0a

ca

ext

extL

LCL

21 int

2

00

1

r

R. B. Wu 52

Internal Inductance Effect

R. B. Wu 53

Attenuation Ratio (1/2)

• Simulating for loss ratio

rather than exact loss value

• Two sets of tx-line made with

different conductive

attenuation

• Simulate for the attenuation

ratio:

dc aaa 11 dc aaa 22

2

1

c

c

a

a

W1 W2H

1

H2

d2

d1

R. B. Wu 54

Attenuation Ratio (2/2)

• Then acquire dielectric attenuation:

• The drawback is that it amplifies error

• should be kept away from 1 by increasing difference in

line resistance or impedance

aaa

1

21d

a d2

tan dc aaa 11

dc aaa 22

r

111 aa

r

122 aa

1dd aa

1

1r

R. B. Wu 55

Experiment Setting

• Striplines on typical FR4 PCB, NP-140

• Two sets of line T1, T2

• p=25.4mm (~0.25λ@1.48GHz)

• q=30.48mm (~0.5λ@2.46GHz)

• D=4mm, S=2mm (~0.25λ@18GHz)

• VNA: Agilent 8510B

Stripline

S = 2 mm

D = 4mm

Vias

t=17.78 μm

H=

728.98 μm

W=150 μm

d=406.4 μm

T1

T=17.78 μmH=

728.98 μm

W=150 μm

d=101.6 μm

T2

L

Reference Plane

|Γ|=0 |Γ|=0

p

VNA

port 1

VNA

port 2

q

R. B. Wu 56

Measured S-parameters

• Resonance suppressing is design to 18 GHz but the

results stay valid only until 14GHz

R. B. Wu 57

Measured Phase and Attenuation

• Use loss ratio to split conductive attenuation and

dielectric attenuation Kappa=1.67,

error amp. =4

Conductive

att. =1.2

Conductive

att. =2

R. B. Wu 58

Experimental Result

• The slight difference in

dielectric constant

attributes to error of

internal inductance

estimation

• Increase in loss tangent

implies loss growth with

frequency more than 1

degree, making it

unsuitable at high

frequencies

R. B. Wu 59

Conclusions (1/2)

• A characterization method using stripline with via fence is

presented. It is suitable for investigate multi-layer PCBs

properties

• Via fence design should satisfy

but

while S is as small as possible

• Internal inductance effect in phase constant can be eliminated

as

rm

m

f

cD

2

1

2

D

S

H

W

y

x

z

WD 3

HD 3

ca 2

00

1

r

R. B. Wu

60

Conclusions (2/2)

• The smaller substrate thickness and line width, the lager

internal inductance and corresponding effect in dielectric

constant. It is small, but may be no longer negligible in

advanced process

• Calculating attenuation by simulating loss ratio is

applicable in material under special process or treatment

aaa

1

21d

a d2

tan

dc aaa 11

dc aaa 22

2

1

c

c

a

a