Sea Ceramics Technologies

Design, Measurement and Modeling of
LTCC Embedded Inductors and PCB
Balanced Devices
Prof. T.S. Horng (? ??)
E.E. Dept., National Sun Yat-Sen Univ.
Email: jason@ee.nsysu.edu.tw

Outline
LTCC Embedded Inductors
PCB Balanced Devices
Conclusions

Design Trend
Planar Spiral Stacked Spiral Helical
LTCC Inductor
Area
(under the same L eff )
SRF
(under the same L eff )
Q
(under the same L eff )
No. of Layers
Planar Spiral
Large
Low
Low
2
Stacked Spiral
Smaller
Higher
Higher
2
Helical
Smallest
Highest
Highest
≥ 2

Test fixture
Microstrip
line
Measurement Techniques
Test Fixture Microwave Probes
LTCC
Device
Reference plane after
TRL calibration
Electrode
Vector Network
Analyzer
SG/GS-type
probes
LTCC Device
(top view)

Spiral
inductor
The whole
LTCC device
Test-Fixture Measurement
Electrode
LTCC device
on test fixture
Microstrip line
vs. HFSS Simulation
L eff » 6 nH
dB(S21)
dB(S11)
0
-10
-20
-30
-40
-50
0 1 2 3 4 5 6 7 8 9 10
Frequency (GHz)
0
-10
-20
-30
-40
Mea#1
Mea#2
Mea#3
Sim
Mea#1
Mea#2
Mea#3
Sim
-50
0 1 2 3 4 5 6 7 8 9 10
Frequency (GHz)

Microwave-Probe Measurement
L eff » 6 nH
vs. HFSS Simulation
GS probe
�Smaller area
�Higher SRF
�Higher Q factor
�Better measured data repeatability
�Better agreement between simulation
and measurement
dB(S11)
dB(S21)
0
-10
-20
-30
-40
-50
0 1 2 3 4 5 6 7 8 9 10
Frequency (GHz)
0
-10
-20
-30
-40
Mea#1
Mea#2
Sim
Mea#1
Mea#2
Sim
-50
0 1 2 3 4 5 6 7 8 9 10
Frequency (GHz)

A New Modified-T Model for
Lossless Transmission Line
Lossless transmission line
Z 0 : Characteristic impedance
τ: Propagation delay
θ: Electrical length
θ
Z
0
,
θ = 0 → π ⇔ ω =
0 →
τ
≈ ?
ωq
�Is it possible to create an equivalent
single-stage lumped model
for a lossless transmission line
having electrical length up to π ?
Equivalent π model
Equivalent Τ model
Equivalent modified-Τ model
C p
Lm
Ls s L
Cs

Derivation of Element Values of
Equivalent Modified-T Model
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
+
−
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
−
−
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
−
+
⎥
⎦
⎤
⎢
⎣
⎡
+
−
+
+
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
p
s
m
s
m
s
s
s
p
s
m
s
m
s
s
m
p
s
m
s
m
s
s
m
p
s
m
s
m
s
s
s
C
j
C
j
L
L
j
L
L
j
C
j
L
j
C
j
C
j
L
L
j
L
L
j
C
j
L
j
C
j
C
j
L
L
j
L
L
j
C
j
L
j
C
j
C
j
L
L
j
L
L
j
C
j
L
j
Z
j
Z
j
Z
j
Z
j
2
)
(
)
(
1
2
)
(
)
(
1
2
)
(
)
(
1
2
)
(
)
(
1
cot
c s c
c s c
cot
0
0
0
0
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
ω
θ
θ
θ
θ
≈
⇒ (F)
(F),
(H)
)
1
4
1
(
(H),
)
1
4
1
(
2
0
0
2
0
2
0
π
τ
τ
π
τ
π
τ
Z
C
Z
C
Z
L
Z
L
p
s
m
s
≈
≈
−
≈
+
≈

S 11 (dB)
S11(dB)
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
Comparison of Bandwidth among
Equivalent Models
Modified-T model
Lossless_TL
Modified-T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
q = p q = 2p q = 3p
Transmission-line circuit
50 Ω Z = 1 0 0 Ω , τ =
1 0 0
p s
5 0
Ω
0
S 11 (dB)
S 11 (dB)
S11(dB)
S11(dB)
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
π model
Lossless_TL
Pi_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
T model
Lossless_TL
T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)

S 11 (phase)
S11(phase)
200
150
100
50
-100
-150
-200
0
-50
Comparison of Bandwidth among
Equivalent Models
Modified-T model
Lossless_TL
Modified-T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
q = p q = 2p q = 3p
Transmission-line circuit
50 Ω Z = 1 0 0 Ω , τ =
1 0 0
p s
5 0
Ω
0
S 11 (phase)
S11(phase)
S11(phase)
S 11 (phase)
200
150
100
50
0
-50
-100
-150
-200
0 2 4 6 8 10 12 14 16
200
150
100
50
0
-50
-100
-150
π model
Freq(GHz)
T model
Lossless_TL
Pi_model
Lossless_TL
T_model
-200
0 2 4 6 8
Freq(GHz)
10 12 14 16

S 21 (dB)
S21(dB)
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
Comparison of Bandwidth among
Equivalent Models
Modified-T model
Lossless_TL
Modified-T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
q = p q = 2p q = 3p
Transmission-line circuit
50 Ω Z = 1 0 0 Ω , τ =
1 0 0
p s
5 0
Ω
0
S 21 (dB)
S21(dB)
S 21 (dB)
S21(dB)
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Lossless_TL
Pi_model
-20
0 2 4 6 8
Freq(GHz)
10 12 14 16
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
π model
T model
Lossless_TL
T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)

S 21 (phase)
S21(phase)
200
150
100
50
-50
-100
-150
-200
0
Comparison of Bandwidth among
Equivalent Models
Modified-T model
Lossless_TL
Modified-T_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
q = p q = 2p q = 3p
Transmission-line circuit
50 Ω Z = 1 0 0 Ω , τ =
1 0 0
p s
5 0
Ω
0
S 21 (phase)
S 21 (phase)
S21(phase)
S21(phase)
200
150
100
50
0
-50
-100
-150
Lossless_TL
Pi_model
-200
0 2 4 6 8
Freq(GHz)
10 12 14 16
200
150
100
50
0
-50
-100
-150
π model
T model
Lossless_TL
T_model
-200
0 2 4 6 8
Freq(GHz)
10 12 14 16

Z
0
,
Distributed Modified-T Model
3π-long
transmission line
Phase(S11)
dB(S11)
-120
-180
-10
-20
-30
-40
-50
-60
120
60
-60
θ =
3π
0
0
τ
≈
C p
/
3
Lm
/
3
Ls /
3 Ls
/
3
Cs
/
3
q = p q = 2p q = 3p
Lossless_TL
3-stage modified-T_model
0 2 4 6 8 10 12 14
Frequency (GHz)
Lossless_TL
3-stage modified-T_model
0 2 4 6 8 10 12 14
Frequency (GHz)
3-stage modified-T model
Phase(S21)
dB(S21)
-0.5
-1
-1.5
-2
-2.5
180
-60
-180
-300
0
-3
60
C
p
/
3
Lm
/
3
Ls /
3 Ls
/
3
Cs
/
3
C p
/
3
Lm
/
3
Ls /
3 Ls
/
3
Cs
/
3
Lossless_TL
3-stage modified-T_model
0 2 4 6 8 10 12 14
Frequency (GHz)
Lossless_TL
3-stage modified-T_model
0 2 4 6 8 10 12 14
Frequency (GHz)

loss
Shunt
Cap
L eff » 6 nH
Cp
Modified-T Models
for Spiral Inductors
Modified-T model
R
p
C p1
Lp
1
Lm
Lp
Ls Ls
Cs
Lg
Cg
dB(S21)
0
-5
-10
-15
-20
-25
-30
Conventional p model
Cs
zero
Rs
Cp
Leff
1 st by-pass 2 nd by-pass
Ground
Resonance
s C
-35
0 2 4 6 8 10 12 14
Frequency (GHz)

S 11 (dB)
S22(dB)
S 11 (phase)
S22(phase)
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
200
150
100
50
-50
-100
-150
-200
0
Comparison of Bandwidth
between Two Inductor Models
Modified-T model
measurement measurement
Modified-T_model
modeling
0 2 4 6 8 10 12 14 16
Freq(GHz)
measurement
Modified-T_model
measurement
modeling
0 2 4 6 8 10 12 14 16
Freq(GHz)
S 11 (dB)
S11(dB)
S 11 (phase)
S11(phase)
-100
-150
-200
0
-5
-10
-15
-20
-25
-30
-35
200
150
100
50
0
-50
Conventional π model
measurement
pi_model Pi_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
measurement
pi_model Pi_model
0 2 4 6 8 10 12 14 16
Freq(GHz)

S 21 (dB)
S21(dB)
S 21 (phase)
S21(phase)
0
-5
-10
-15
-20
-25
-30
200
150
100
50
0
-50
-100
-150
Comparison of Bandwidth
between Two Inductor Models
Modified-T model
measurement
Modified-T_model
measurement
modeling
0 2 4 6 8 10 12 14 16
Freq(GHz)
measurement measurement
Modified-T_model
modeling
0 2 4 6 8 10 12 14 16
Freq(GHz)
S 21 (dB)
S21(dB)
S 21 (phase)
S21(phase)
0
-5
-10
-15
-20
-25
-30
200
150
100
50
0
-50
-100
-150
-200
Conventional π model
measurement
pi_model Pi_model
0 2 4 6 8 10 12 14 16
Freq(GHz)
measurement
Pi_model pi_model
0 2 4 6 8 10 12 14 16
Freq(GHz)

Outline
LTCC Embedded Inductors
PCB Balanced Devices
Conclusions

Measurement Systems for Multiport
and Mixed-Mode S-Parameters
�Pure Mode Network Analyzer
�Multiport Network Analyzer Using
Full-N Port Calibration
�Two-Port Network Analyzer Using
Renormalization Techniques

Port Termination Problem
DUT
Port 3
terminated
1
a
1
b
2
a
2
b
3
a 3
b
Port 1 Port 2
Port 3
3
33
2
32
1
31
3
3
23
2
22
1
21
2
3
13
2
12
1
11
1
a
S
a
S
a
S
b
a
S
a
S
a
S
b
a
S
a
S
a
S
b
+
+
=
+
+
=
+
+
=
Three-port Network Three-port S parameters
Reflection due to port
termination
3
3
3
b
a
=
Γ
Measured two-port S
parameters
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
Γ
−
Γ
+
Γ
−
Γ
+
Γ
−
Γ
+
Γ
−
Γ
+
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
3
33
3
32
23
22
3
33
3
31
23
21
3
33
3
32
13
12
3
33
3
31
13
11
p3t
22
p3t
21
p3t
12
p3t
11
p3t
1
1
1
1
]
[
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S

Partial Renormalization
a
1
a
2
Zo1 Z
2
b
1
Port 1 Port 2
Port 3
[ S′
] = ( [ U ] − [ S]
) ( [ S]
− [ Γ]
) ( [ U ] − [ S][
Γ]
) ( [ U ] − [ S]
)
where
G
o o1
[S DUT
]
[ DUT S
]
a 3
3 b
Port 3
terminated
k
=
ζ
ζ
− 1
0k
0k
−
+
b
2
Zo
3
Z
Z
0k
0k
⇒
,
a
1
a
2
ζ ζo
2
for
k
b
1
=
Port 1 Port 2
1,
2
Port 3
a 3
3 b
Port 3
terminated
− 1
'
b
2
ζo
3

Renormalization Transforms
�Three partial 2-port S-parameter measurements
⎡
p 3 t
p 3 t⎤
⎡
p 3 t S
= ⎢
1 1 S1
2 ⎥
p 2 t S
[ S
]
,
[ S
] = ⎢
p 3 t
p 3 t
⎢
⎣S
⎥
⎦
⎢
2 1 S2
2 ⎣
S
�After partial renormalizations
[ S
m1
⎡S
] = ⎢
⎢⎣
S
⎡S
⎢
⎢
⎢
⎢⎣
S
m1
11
m1
21
m1
11
S
S
m1
12
m1
22
⎤
⎥
,
⎥⎦
[ S
m2
⎡S
] = ⎢
⎢⎣
S
p 2 t
1 1
p 2 t
3 1
m2
11
m2
31
S
S
S
S
p 2 t
1 3
p 2 t
3 3
m2
13
m2
33
⎤
⎥
,
[ S
⎥
⎦
⎤
⎥
,
[ S
⎥⎦
p 1 t
m3
⎡S
] = ⎢
⎢
⎣
S
⎡S
] = ⎢
⎢⎣
S
�Construct the S matrix of the three-port network normalized
to [ζ 0 ] and then transform it back to the S matrix normalized
to [Z0 ] :
p 1 t
2 2
p 1 t
3 2
m3
22
m3
32
m1
m1
m3
[ S′ ] = S S S
⇒
[ S]
21
m2
31
S
S
m1
12
22
m3
32
S
S
m2
13
23
m2
33
⎤
⎥
⎥
⎥
⎥⎦
renormalized to
S
S
S
S
p 1 t
2 3
p 1 t
3 3
m3
23
m3
33
⎤
⎥
⎥
⎦
⎤
⎥
⎥⎦

Determination of [ζ 0 ]
� Use TRL Calibration
�
ζ
=
0i
Z
0
1+
1−
Γ
Γ
i
i

DC-Block Branch-Line Coupler
Design guide Photo of component
Z
a a
0e − Z
0o
=
2Z
0
Port 1 Port 2
Port 4 Port 3
Z
a a
0e − Z
0o
=
2Z
0

S11 (dB)
S31 (dB)
0
-5
-10
-15
-20
-25
Comparison between Ensemble
Simulation and Measurement
-30
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
0
-5
-10
-15
-20
-25
-30
-35
-40
Frequency
Ensemble
Measured
-45
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
Frequency
Ensemble
Measured
S21 (dB)
S41 (dB)
0
-5
-10
-15
-20
-25
-30
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
0
-5
-10
-15
-20
-25
-30
Frequency
Ensemble
Measured
-35
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
Frequency
Ensemble
Measured

Impedance Transform
Branch-Line Coupler
Design guide Photo of component
Port 1
Z
1
[ S
] ⇒
[ Z
]
:
[ Z
] ⇒
[ S
λ
Z 4
1
2
λ
4
Z
'
]
:
[ Z
] =
[ S
'
]
=
[ Z
0
[ ξ
]
(
[ U
] −
[ S
]
)
0
]
-
1
(
[ Z
] −
[ ξ
Port 2
Port 4 Port 3
Z
1
Z
1
Z
Z
2
50O 25O
Generalized S-parameter Transform
2
Z
1Z
2
2
2
Z
2
−1
0
(
[ U
] +
[ S
]
)
]
)
(
[ Z
] +
[ ξ
0
]
)
[ Z
−1
0
]
−1
[ ξ
0
]

S21 (dB)
S11 (dB)
0
-5
-10
-15
-20
-25
-30
-35
Comparison between Ensemble
Simulation and Measurement
-40
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
0
-5
-10
-15
-20
-25
Frequency
-30
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
Frequency
Ensemble
Measured Before transform
Measured After transform
Ensemble
Measured Before transform
Measured After transform
S41 (dB)
S22 (dB)
0
-5
-10
-15
-20
-25
-30
-35
-40
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
Frequency
-50
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009
Frequency
Ensemble
Measured Before transform
Measured After transform
Ensemble
Measured Before transform
Measured After transform

Mixed-Mode S parameters
Mixed-Mode S Matrix
Response
⎡
⎢
⎣
Different ial-Mode
Port 2
Port 1
Common-Mode
Port 4
Port 3
[ bD
]
[ b ]
C
⎤ ⎡
⎥ = ⎢
⎦ ⎣
D i f f e r e n t i a l-M o d e C o m m o n- M o d e
Port 1 Port 2 Port 1 Port 2
S DD
11 S DD
12
S DD
21 S DD
22
S CD
11 S CD
12
S CD
21 SCD
22
[ SDD
] [ SDC
]
[ S ] [ S ]
CD
CC
⎤⎡
⎥⎢
⎦⎣
S t i m u l u s
[ aD
]
[ a ]
C
⎤
⎥
⎦
S DC
11 S DC
12
S DC
21 S DC
22
S CC
11 S CC
12
S CC
21 SCC
22
=
mm [ S ]
⎡
⎢
⎣
[ ]
[ ] ⎥ aD
⎤
aC
⎦
Common-Mode Rejection Ratio
CMRR
=
S
S
DD
2 1
CC
2 1

Mixed-Mode Transform
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
4
3
2
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
2
1
a
a
a
a
a
a
a
a
C
C
D
D
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
4
3
2
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
2
1
b
b
b
b
b
b
b
b
C
C
D
D
]
][
[
]
[
se
mm
a
M
a =
]
][
[
]
[
se
mm
b
M
b =
1
]
][
][
[
]
[
−
= M
S
M
S
se
mm

Design guide
Input
C
=
(
Lange-Type Marchand Balun
1+
λ
2
Output
[ M ]
=
⎡
⎢
⎢
⎢
⎣
Input
0 ⎤
⎥
−
1⎥
1 ⎥
⎦
Port 1
Response
Balanced Port 2
Common Differential
Lange
Coupler
Output
Planar type Lange type
2Z
Z
o u t
0 −1
)
in
0
Photo of component
,
1
2
⇒
0
0
2
0
1
1
Port 1
S
11
S D
1
Lange
Coupler
Mixed-mode [S]
S
DD
S C
1 S CD
Stimulus
Balanced Port 2
Differential Common
S 1 D
S 1 C
S
S
DC
CC

S11 (dB)
SCC (dB)
S11 (dB)
0
-5
-10
-15
-20
Comparison between HFSS
Simulation and Measurement
-25
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
0
-0.5
-1
-1.5
-2
Frequency
-2.5
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
Frequency
Simulated
Measured
Simulated
Measured
SC1 & S1C (dB)
SD1 & S1D (dB)
0
-5
-10
-15
-20
-25
-30
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
0
-5
-10
-15
-20
-25
-30
Frequency
Simulated
Measure
-35
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
Frequency
Simulated
Measured

SDD (dB)
CMRR
30
20
10
0
-10
-20
Comparison between HFSS
Simulation and Measurement
-30
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
5
0
-5
-10
-15
-20
Frequency
Simulated
Measured
SD1
-25
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
Frequency
Simulated
Measured
SCC (dB)
SCD & SDC (dB)
0
-0.5
-1
-1.5
-2
-2.5
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
-10
-15
-20
-25
-30
-35
-40
Frequency
Simulated
Measured
-45
1E+009 2E+009 3E+009 4E+009 5E+009 6E+009 7E+009 8E+009
Frequency
Simulated
Simulated

VNA setup via Vee
Measure, renormalize
and Transform
Semi-Automatic
Measurement System
Single-ended S parameters
Mixed-Mode
S Parameters

Application to On-Wafer
91$
$JLOHQW $JLOHQW $JLOHQW
Measurement
Our proposed System System made by NIST

Conclusions
� Various types of LTCC Embedded Inductors have been
designed and measured. Simulated results agree with
measurements quite well.
� A new modified-T equivalent circuit has been
proposed to model LTCC inductors over an extremely
large bandwidth successfully.
� Very cost-effective multiport network analyzer system
based on renormalization techniques has been
developed to measure balanced devices.
� Several examples of multiport and balanced devices
on PCB have been designed and measured.
Comparison between simulation and measurement
shows excellent agreement.

References
1. K. Lim, et. al., “RF-system-on-package (SOP) for wireless
communications,” IEEE Microwave Magazine, pp. 88-99,
March 2002.
2. J.C. Tippet and R.A. Speciale, “A rigorous technique for
measuring the scattering matrix of a multiport device with a
2-port network analyzer, ” IEEE Transactions on Microwave
Theory and Techniques, pp. 661-666, May 1982.
3. L.-Q. Yang, Design and modeling of embedded inductors and
capacitors in low-temperature cofired ceramic technology,
Master ’s Thesis, National Sun Yat-Sen University at Kaohsiung
Taiwan, 2002.
4. D.-C. Tsai, Measurement of balanced devices using vector
network analyzers, Master ’s Thesis, National Sun Yat-Sen
University at Kaohsiung, Taiwan, 2002.