Electric Properties of Dielectrics -...
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Electric Properties of
Dielectrics
吳瑞北
Rm. 340, Department of Electrical Engineering
E-mail: [email protected]
url: cc.ee.ntu.edu.tw/~rbwu
S. H. Hall et al., High-Speed Digital Designs, Chap.6
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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?
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R. B. Wu
Tx-Line Losses
• Polarization of Dielectrics
• Dielectric losses
• Environmental & Localization Effects
• Measurements
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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.
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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
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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
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Polarization of Dielectrics
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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
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R. B. Wu
Other Polarizations
• Orientational (dipole)
polarization
• Ionic (molecular)
polarization
ip Ea
op Ea
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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
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Dielectric Loss
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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
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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
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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
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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
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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
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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 =
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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
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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
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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
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Environmental & Localization
Effects
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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
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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
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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
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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)
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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?
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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
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28
Measurement of Dielectric Constants
Student: Chia-Hao Chang
Adviser: Ruey-Beei Wu
Date : 06/27 2009
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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R. B. Wu 52
Internal Inductance Effect
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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
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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
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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
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R. B. Wu 56
Measured S-parameters
• Resonance suppressing is design to 18 GHz but the
results stay valid only until 14GHz
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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
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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
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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
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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