Generiic RF passive device modeling
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Transcript of Generiic RF passive device modeling
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Generic Model Fitting of
Passive RF Devices
Tao-Yi Lee
Advisor: Yu-Jiu Wang
RFVLSI LAB @ NCTU
2014/4/18 Tao-Yi Lee @ RFVLSILAB 1
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Outline
• The Model Fitting Design Flow
• Examples
– Model Fitting Of Inductors
– Model Fitting Of Center Tapped Inductors
– Model Fitting Of Transmission Lines
– Model Fitting Of Transformers
• Conclusion and Future Works
• References
2014/4/18 Tao-Yi Lee @ RFVLSILAB 2
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Design Flow of Modeling Fitting
2014/4/18 Tao-Yi Lee @ RFVLSILAB 3
Start
Propose passive lumped equivalent model for an arbitrary high-frequency structure
Solve Y parameter matrix [Y] of the lumped equivalent network
Rum EM simulations of the desired structures, obtain [YEM]
Program the Ycost(R1, L1, C1)=[Y]-[YEM] matrix into MATLAB script as cost functions in numerical analysis
Solve values for lumped component, i.e. find R1, L1, C1,…, such that Ycost is minimized
Stop
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Passive Lumped Equivalent Model For
Arbitrary High-frequency Structure
2014/4/18 Tao-Yi Lee @ RFVLSILAB 4
Propose passive lumped equivalent model for an arbitrary high-frequency structure
PORT1 PORT3
C13
C12 C23
C33C22C11
L12 L23R12 R23
Model #1
PORT2
Mi2i1
PORT1
PORT2
PORT3
Si Substrate
IMD
Cox Cox
• Main lumped elements• Skin effect• Loss
• Substrate• Eddy current
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Modeling Skin Effect
• Skin effect: 𝑅𝑐𝑜𝑛𝑑 ∝ 𝑓; 𝐿𝑐𝑜𝑛𝑑 ≈ 𝑐𝑜𝑛𝑠𝑡.
– A non-linear effect
– Consider substrate coupling and proximity effect
2014/4/18 Tao-Yi Lee @ RFVLSILAB 5
• T. Kamgaing, T. Myers, M. Petras, And M. Miller, "Modeling Of Frequency Dependent Losses In Two-port And Three-port Inductors On Silicon," Radio Frequency Integrated Circuits Symposium, Pp. 307-310, 2002.
• C.-S. Yen, Z. Fazarinc, and R. L. Wheeler, “Time-Domain Skin-Effect Model for Transient Analysis of Lossy Transmission Lines,” Proceedings of the IEEE, vol. 70, pp. 750-757, 982• S. Kim and D. P..N eikirk, “Compact Equivalent Circuit Model for the Skin Effect”
Rm
Rf1
Lf1
Rf2
Lf2
Rf3
Lf3
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Modeling Eddy Current
• Complex Image Method
2014/4/18 Tao-Yi Lee @ RFVLSILAB 6
• D. Melendy and A. Weisshaar, “A New Scalable Model for Spiral Inductors on Lossy Silicon Substrate,” in 2003 MTT-S Symposium, June 2003, pp. 1007 – 1010• Melendy, D.; Francis, P.; Pichler, C.; Kyuwoon Hwang; Srinivasan, G.; Weisshaar, A.; , "A new wideband compact model for spiral inductors in RFICs," Electron Device Letters,
IEEE , vol.23, no.5, pp.273-275, May 2002• Kai Kang; Jinglin Shi; Wen-Yan Yin; Le-Wei Li; Zouhdi, S.; Rustagi, S.C.; Mouthaan, K.; , "Analysis of Frequency- and Temperature-Dependent Substrate Eddy Currents in On-Chip
Spiral Inductors Using the Complex Image Method ," Magnetics, IEEE Transactions on , vol.43, no.7, pp.3243-3253, July 2007
PORT1 PORT2Meddy
Rs,eddy
PORT1
PORT2
PORT3
Si Substrate
IMD
Image inductor on
lossy substrate
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Modeling Oxide Capacitance and
Substrate Loss
• Model silicon substrate and IMD (oxides) as a 2D mesh
• Semi-empirical formula accounting for fringing and proximity effects (s: spacing, w: line width, ℎ𝑜𝑥: height above oxide)
𝐶𝑜𝑥 = 1 −𝑠
𝑠 + 𝑤
1.16 𝜖0𝜖𝑜𝑥 ∙ 𝑤 ∙ 𝑙
ℎ𝑜𝑥
2014/4/18 Tao-Yi Lee @ RFVLSILAB 7
CoxCox Cox
RsubCsubRsubCsubRsubCsub
Rnon-uniform Rnon-uniform
OptionalOptional
• Kai Kang; Jinglin Shi; Wen-Yan Yin; Le-Wei Li; Zouhdi, S.; Rustagi, S.C.; Mouthaan, K.; , "Analysis of Frequency- and Temperature-Dependent Substrate Eddy Currents in On-Chip Spiral Inductors Using the Complex Image Method ," Magnetics, IEEE Transactions on , vol.43, no.7, pp.3243-3253, July 2007
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Modeling Substrate
• Modeling of substrate extrinsic is generally difficult, but some closed form solution are found in micro-strip transmission line researches (ℎ𝑠𝑢𝑏:height of the substrate, 𝜖𝑠𝑢𝑏,𝑒𝑓𝑓: effective dielectric constant)
– 𝐶𝑠𝑢𝑏 =
𝑤
ℎ𝑠𝑢𝑏+1.393+0.667 ln
𝑤
ℎ𝑠𝑢𝑏+1.444
120𝜋𝑐∙
𝑙
2𝜖𝑠𝑢𝑏,𝑒𝑓𝑓
• In reference 2, shunt resistance 𝑅𝑠𝑢𝑏 in silicon can be determined using relaxation time constant
𝜖0𝜖𝑆𝑖
𝜎𝑆𝑖
– 𝑅𝑠𝑢𝑏 =𝜖0𝜖𝑆𝑖
𝐶𝑆𝑖𝜎𝑆𝑖
• Consider circuit optimization to look for practical design values
2014/4/18 Tao-Yi Lee @ RFVLSILAB 8
• Ref. 1 :M. Kirschning and R. H. Jansen, “Accurate wide-range design equations for the frequency-dependent characteristics of parallel coupled microstrip lines,” IEEE Trans. Microwave Theory and Tech., vol. MTT-32, pp. 83–90, Jan. 1984.
• Ref.2 :J. Zheng, Y.-C. Hahm, V. K. Tripathi, and A. Weisshaar, “CAD-oriented equivalent circuit modeling of on-chip interconnects on lossy silicon substrate,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1443–1451, Sept. 2000
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Solve Y Parameter Matrix 𝑌 of The
Lumped Equivalent Network• Definition of Y parameters
– Yij = Ii
Vj Vk=0 for k≠j
–
𝐼1𝐼2𝐼3
𝑌11 𝑌12 𝑌13
𝑌21 𝑌22 𝑌23
𝑌31 𝑌32 𝑌33
𝑉1
𝑉2
𝑉3
– Short all other terminals to ground reference and write down 𝑌𝑖𝑗 as function of lumped elements
– Simple; Can be done by inspection
– Matrix symmetry of passive networks
2014/4/18 Tao-Yi Lee @ RFVLSILAB 9
Solve Y parameter matrix [Y] of the lumped equivalent network
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Solve Y Parameter Matrix 𝑌 of The
Lumped Equivalent Network
• 2-port 𝜋 model
2014/4/18 Tao-Yi Lee @ RFVLSILAB 10
Y11+Y21
-Y12
Y21+Y22
PORT1 PORT2PORT1
C12
C22C11
L12 R12
PORT2i1
simple 2 port inductor model
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Solve Y Parameter Matrix 𝑌 of The
Lumped Equivalent Network
• 2-port shunt model
2014/4/18 Tao-Yi Lee @ RFVLSILAB 11
Y11+Y21
-Y12
Y21+Y22
PORT1
Y11+Y21
PORT1
-Y12
Y11PORT1
-Y12
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Solve Y Parameter Matrix 𝑌 of The
Lumped Equivalent Network
• 2-port differential model
2014/4/18 Tao-Yi Lee @ RFVLSILAB 12
Y11+Y21
-Y12
Y21+Y22
PORT1PORT2
-Y12PORT1 PORT2
Y11+Y21 Y21+Y22
-Y12
Y11//Y22+Y21/2 Y11//Y22-Y21/2
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Run EM Simulations Of The Desired
Structures, Obtain 𝑌𝐸𝑀
• Convert S-parameters to
Y-parameters via post-
processing
2014/4/18 Tao-Yi Lee @ RFVLSILAB 13
Rum EM simulations of the desired structures, obtain [YEM]
YEMSEM
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Define The Minimization Problem In
MATLAB
∀i, j, minimizeR1,R2,…,L1,L2,…,C1,C2,…
ΔYij
= minimizeR1,R2,…,L1,L2,…,C1,C2,…
𝐘 − 𝐘𝐄𝐌
subject to all passive elements ≥ 0
2014/4/18 Tao-Yi Lee @ RFVLSILAB 14
Program the Ycost(R1, L1, C1)=[Y]-[YEM] matrix into MATLAB script as cost functions in numerical analysis
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Solve Component Values Using Non-linear
Least-square Solvers
• “lsqnolin” function in
MATLAB
– trust-region-reflective
– levenberg-marquardt
• Computational intensive
2014/4/18 Tao-Yi Lee @ RFVLSILAB 15
Solve values for lumped component, i.e. find R1, L1, C1,…, such that Ycost is minimized
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MODEL FITTING OF INDUCTORS
2014/4/18 Tao-Yi Lee @ RFVLSILAB 16
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Inductor 1 Port Model #1
Y11 = 𝑠𝐶𝑠1 +1
𝑠𝐿1 + 𝑅1
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 17
Model#11R1L
1SC
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Inductor 1 Port Model #2
𝑌11 =𝐶𝑆1𝐶𝑆5
(𝐶𝑆1 + 𝐶𝑆5)⋅
𝑠 ⋅ (𝑠 +1
𝑅𝑆5𝐶𝑆5)
𝑠 +1
𝑅𝑆5 𝐶𝑆1 + 𝐶𝑆5
+1
𝑠𝐿1 + 𝑅1
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 18
Model#2
1SC
5SC
5SR
1R1L
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Inductor 1 Port Model #3
• 𝑌11 = 𝑠𝐶𝑓 +1
𝐿0⋅
𝑠+𝑅0+𝑅1
𝐿1
𝑠2+𝑠 𝑅0𝐿0+𝑅1𝐿0+𝑅0𝐿1
𝐿0𝐿1+
𝑅0𝑅1𝐿0𝐿1
+𝐶𝑆1𝐶𝑆2
(𝐶𝑆1+𝐶𝑆2)⋅
𝑠⋅(𝑠+1
𝑅𝑆2𝐶𝑆2)
𝑠+1
𝑅𝑆2 𝐶𝑆1+𝐶𝑆2
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 19
2R2LModel#3
1SC
5SC
5SR
1R1L
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EM Setup – Symmetrical Inductor
• Inductor@M9, UTM = 3.4𝜇𝑚, 2 turns
• IMD Simplification
• Localized Excitation
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 20
Name Thickness (nm) Rel Permittivity Z
FOXEQ 300 3.9 1
ILDEQ 310 4.2 2
IMD_1aEQ 4100 3.523395 3
IMD_9aEQ 725 4.2 4
IMD_9bEQ 110 8.1 5
IMD_9cEQ 3230 4.2 6
PASS1EQ 1800 5.254054 7
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MODEL FITTING OF CENTER-TAPPED
INDUCTORS
2014/4/18 Tao-Yi Lee @ RFVLSILAB 21
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Center Tapped Inductor 3 Port Model #1
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 22
PORT1 PORT3
C13
C12 C23
C33C22C11
L12 L23R12 R23
Model #1
PORT2
Mi2i1
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Center Tapped Inductor 3 Port Model #1
• 𝜇 =𝑠𝑀
𝑠𝐿12+𝑅12 𝑠𝐿23+𝑅23 −𝑠2𝑀2
• A =𝑠𝐿23+𝑅23
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿23𝑅12 +𝑅12𝑅23
• 𝐵 =𝑠𝐿12+𝑅12
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿23𝑅12 +𝑅12𝑅23
• 𝐴′ = −𝑠𝐿23+𝑅23+𝑠𝑀
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿23𝑅12 +𝑅12𝑅23
• 𝐵′ = −𝑠𝐿12+𝑅12+𝑠𝑀
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿23𝑅12 +𝑅12𝑅23
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 23
Self Mutual
Y11 = sC11 + sC12 + sC13 + A 𝑌13 = 𝑌31 = −𝑠𝐶13 + 𝜇
Y22 = sC22 + sC12 + sC23 − A′ − B′ 𝑌12 = 𝑌21 = −𝑠𝐶12 + 𝐴′
Y33 = sC33 + sC23 + sC13 + B 𝑌23 = 𝑌32 = −𝑠𝐶23 − 𝐵′
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Center Tapped Inductor 3 Port Model #2
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 24
PORT1
PORT2
PORT3
C13
C12 C23
C33C22C11
L12 L23R12 R23
Model #2
CS2RS2 CS3RS3CS1RS1
Mi2i1
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Center Tapped Inductor 3 Port Model #2
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 25
Ys1
=sC11 sRS1CS1 + 1
sRS1 C11 + CS1 + 1
Ys2
=sC22 sRS2CS2 + 1
sRS2 C22 + CS2 + 1
Ys3
=sC33 sRS3CS3 + 1
sRS3 C33 + CS3 + 1
Self Mutual
Y11 = sC12 + sC13 + Ys1 + A 𝑌13 = 𝑌31 = −𝑠𝐶13 + 𝜇
Y22 = sC13 + sC23 + Ys2 − A′ − B′ 𝑌12 = 𝑌21 = −𝑠𝐶12 + 𝐴′
Y33 = sC13 + sC23 + Ys3 + B 𝑌23 = 𝑌32 = −𝑠𝐶23 + 𝐵′
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Center Tapped Inductor 3 Port Model #3
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 26
PORT1
PORT2
PORT3
C13
C12 C23
C33C22C11
L12 L23R12 R23
Model #3
CS2RS2 CS3RS3CS1RS1
L12i R12i L23iR23i
M
i2i1
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Center Tapped Inductor 3 Port Model #3
• C =sL23+R23
′
s2L12L23−s2M2+s L12R23′ +L23R12
′ +R12′ R23
′
• D =sL12+R12
′
s2L12L23−s2M2+s L12R23′ +L23R12
′ +R12′ R23
′
• 𝐶′ = −𝑠𝐿23+𝑅23
′ +𝑠𝑀
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23′ +𝐿23𝑅12
′ +𝑅12′ 𝑅23
• 𝐷′ = −𝑠𝐿12+𝑅12
′ +𝑠𝑀
𝑠2𝐿12𝐿23−𝑠2𝑀2+𝑠 𝐿12𝑅23′ +𝐿23𝑅12
′ +𝑅12′ 𝑅23
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 27
Self Mutual
Y11 = sC12 + sC13 + Ys1 + C 𝑌13 = 𝑌31 = −𝑠𝐶13 + 𝜇′
Y22 = sC12 + sC23 + Ys2 − C′ − D′ 𝑌12 = 𝑌21 = −𝑠𝐶12 + 𝐶′
Y33 = sC13 + sC23 + Ys3 + D 𝑌23 = 𝑌32 = −𝑠𝐶23 + 𝐷′
R12′ =
R12 sL12i + R12i
R12 + R12i + sL12iR23
′ =R23 sL23i + R23i
R23 + R23i + sL23i
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Center Tapped Inductor 3 Port Model #4
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 28
PORT1
PORT2
PORT3
C13
C12 C23
C33C22
C11
L12 L23R12 R23
Model #4
CS2RS2 CS3RS3CS1RS1
L12i R12i L23iR23i
RS4 RS4
M
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Quality of Fitting
• Good from 1GHz thru 30 GHz
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 29
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EM Setup –
Symmetrical Center-Tapped Inductor• Inductor@M9, UTM = 3.4𝜇𝑚, 2 turns
• IMD Simplification
• Localized Excitation
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 30
Name Thickness (nm) Rel Permittivity Z
FOXEQ 300 3.9 1
ILDEQ 310 4.2 2
IMD_1aEQ 4100 3.523395 3
IMD_9aEQ 725 4.2 4
IMD_9bEQ 110 8.1 5
IMD_9cEQ 3230 4.2 6
PASS1EQ 1800 5.254054 7
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MODEL FITTING OF 4 PORT CENTER-
TAPPED INDUCTORS
2014/4/18 Tao-Yi Lee @ RFVLSILAB 31
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Center Tapped Inductor 4 Port Model #1
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 32
PORT1 PORT3
C14
C12
C34
C44C33C11
L12 L34R12 R34
Model #1
PORT2
M i2i1
PORT3C22
C23PORT4
C24C13
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Center Tapped Inductor 3 Port Model #1
• 𝜇 =𝑠𝑀
𝑠𝐿12+𝑅12 𝑠𝐿34+𝑅34 −𝑠2𝑀2
• A =𝑠𝐿34+𝑅34
𝑠2𝐿12𝐿34−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿34𝑅12 +𝑅12𝑅34
• 𝐵 =𝑠𝐿12+𝑅12
𝑠2𝐿12𝐿34−𝑠2𝑀2+𝑠 𝐿12𝑅34+𝐿34𝑅12 +𝑅12𝑅34
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 33
Self
𝑌11 = 𝑠𝐶11 + 𝑠𝐶12 + 𝑠𝐶13 + 𝑠𝐶14 + 𝐴
𝑌22 = 𝑠𝐶12 + 𝑠𝐶22 + 𝑠𝐶23 + 𝑠𝐶24 + 𝐴
𝑌33 = 𝑠𝐶14 + 𝑠𝐶23 + 𝑠𝐶33 + 𝑠𝐶34 + 𝐵
𝑌44 = 𝑠𝐶14 + 𝑠𝐶24 + 𝑠𝐶34 + 𝑠𝐶44 + 𝐵
Mutual
𝑌12 = 𝑌21 = −𝑠𝐶13 − A
𝑌13 = 𝑌31 = −𝑠𝐶12 − 𝜇
𝑌14 = 𝑌41 = −𝑠𝐶23 + 𝜇
𝑌23 = 𝑌32 = −𝑠𝐶13 + 𝜇
𝑌24 = 𝑌42 = −𝑠𝐶12 − 𝜇
𝑌34 = 𝑌43 = −𝑠𝐶23 − 𝐵
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Center Tapped Inductor 4 Port Model #2
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 34
PORT1
PORT2
PORT4
C14
C12 C34
C44C33C11
L12 L34R12 R34
Model #2
CS2
RS2 CS4RS4CS1RS1
Mi2i1
CS3
RS3
C22
C23
PORT3
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Center Tapped Inductor 3 Port Model #2
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 35
Ys1
=sC11 sRS1CS1 + 1
sRS1 C11 + CS1 + 1
Ys2
=sC22 sRS2CS2 + 1
sRS2 C22 + CS2 + 1
Ys3
=sC33 sRS3CS3 + 1
sRS3 C33 + CS3 + 1
Ys𝟒
=sC𝟒𝟒 sRS𝟒CS𝟒 + 1
sRS𝟒 C𝟒𝟒 + CS𝟒 + 1
Self
𝑌11 = Ys1 + 𝑠𝐶12 + 𝑠𝐶13 + 𝑠𝐶14 + 𝐴
𝑌22 = Ys2 + 𝑠𝐶12 + 𝑠𝐶23 + 𝑠𝐶24 + 𝐴
𝑌33 = Ys3 + 𝑠𝐶13 + 𝑠𝐶23 + 𝑠𝐶34 + 𝐵
𝑌44 = Ys1 + 𝑠𝐶14 + 𝑠𝐶24 + 𝑠𝐶34 + 𝐵
Mutual
𝑌12 = 𝑌21 = −𝑠𝐶13 − A
𝑌13 = 𝑌31 = −𝑠𝐶12 − 𝜇
𝑌14 = 𝑌41 = −𝑠𝐶23 + 𝜇
𝑌23 = 𝑌32 = −𝑠𝐶13 + 𝜇
𝑌24 = 𝑌42 = −𝑠𝐶12 − 𝜇
𝑌34 = 𝑌43 = −𝑠𝐶23 − 𝐵
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Center Tapped Inductor 4 Port Model #3
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 36
PORT1
PORT2
PORT4
C14
C12 C34
C44
C22C11
L12 L34R12 R34
Model #3
CS3RS2
CS4RS4CS1RS1
L12i R12i L34iR34i
M
i2i1
C33
RS3CS2
C23
PORT3
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Center Tapped Inductor 3 Port Model #3
• 𝜇′ =𝑠𝑀
𝑠𝐿12+R12′ 𝑠𝐿34+R𝟑𝟒
′ −𝑠2𝑀2
• C =𝑠𝐿34+R𝟑𝟒
′
𝑠2𝐿12𝐿34−𝑠2𝑀2+𝑠 𝐿12𝑅23+𝐿34R12′ +R12
′ R𝟑𝟒′
• 𝐷 =𝑠𝐿12+R12
′
𝑠2𝐿12𝐿34−𝑠2𝑀2+𝑠 𝐿12R𝟑𝟒′ +𝐿34R12
′ +R12′ R𝟑𝟒
′
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 37
R12′ =
R12 sL12i + R12i
R12 + R12i + sL12iR𝟑𝟒
′ =R𝟑𝟒 sL𝟑𝟒𝐢 + R𝟑𝟒𝐢
R𝟑𝟒 + R𝟑𝟒𝐢 + sL𝟑𝟒𝐢
Self
𝑌11 = Ys1 + 𝑠𝐶12 + 𝑠𝐶13 + 𝑠𝐶14 + 𝐶
𝑌22 = Ys2 + 𝑠𝐶12 + 𝑠𝐶23 + 𝑠𝐶24 + 𝐶
𝑌33 = Ys3 + 𝑠𝐶13 + 𝑠𝐶23 + 𝑠𝐶34 + 𝐷
𝑌44 = Ys1 + 𝑠𝐶14 + 𝑠𝐶24 + 𝑠𝐶34 + 𝐷
Mutual
𝑌12 = 𝑌21 = −𝑠𝐶13 − C
𝑌13 = 𝑌31 = −𝑠𝐶12 − 𝜇′
𝑌14 = 𝑌41 = −𝑠𝐶23 + 𝜇
𝑌23 = 𝑌32 = −𝑠𝐶13 + 𝜇
𝑌24 = 𝑌42 = −𝑠𝐶12 − 𝜇
𝑌34 = 𝑌43 = −𝑠𝐶23 − 𝐷
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Center Tapped Inductor 3 Port Model #4
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 38
PORT1
PORT2
PORT4
C14
C12 C34
C44
C22
C11
L12 L34R12 R34
Model #4
CS3RS2
CS4RS4CS1RS1
L12i R12i L34iR34i
M
i2i1
C33
RS3CS2
C23
PORT3
Rs12 Rs34
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EM Setup –
Symmetrical Center-Tapped Inductor• Inductor@M9, UTM = 3.4𝜇𝑚, 2 turns
• IMD Simplification
• Localized Excitation
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 39
Name Thickness (nm) Rel Permittivity Z
FOXEQ 300 3.9 1
ILDEQ 310 4.2 2
IMD_1aEQ 4100 3.523395 3
IMD_9aEQ 725 4.2 4
IMD_9bEQ 110 8.1 5
IMD_9cEQ 3230 4.2 6
PASS1EQ 1800 5.254054 7
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Quality of Fitting
• Good from 1GHz thru 30 GHz
2014/4/18 (C) RFVLSI LAB Confidential TYLEE 40
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Future Works
• Accuracy of transformer models
• Accuracy in higher frequencies
2014/4/18 Tao-Yi Lee @ RFVLSILAB 41
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2014/4/18 Tao-Yi Lee @ RFVLSILAB 42
Thank you for listening!
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References
• Sung-gi Yang, Gi-hyon Ryu, And Kwang-seok Seo, "Fully Symmetrical, Diff Erential-pair Type Floating Active Inductors," International Symposium On Circuits And Systems, Pp. 93-96, Jun. 1997.
• Kenichi Okada And Kazuya Masu, "Modeling Of Spiral Inductors," In Advanced Microwave Circuits And Systems, April 1, 2010, P. 291.
• C. Patrick Yue, Changsup Ryu, Jack Lau, Thomas H. Lee, And S. Simon Wong, "A PHYSICAL MODEL FOR PLANAR SPIRAL INDUCTORS ON SILICON".
• T. Kamgaing, T. Myers, M. Petras, And M. Miller, "Modeling Of Frequency Dependent Losses In Two-port And Three-port Inductors On Silicon," Radio Frequency Integrated Circuits Symposium, Pp. 307-310, 2002.
• J. R. Long And M. A. Copeland, "Modeling, Characterization And Design Of Monolithic Inductors For Silicon Rfics.," Custom Integrated Circuits Conference, 1996.
• Sunderarajan S. Mohan, Maria Del Mar Hershenson, Stephen P. Boyd, And Thomas H. Lee, "Simple Accurate Expressions For Planar Spiral Inductances," JOURNAL OF SOLID-STATE CIRCUITS, Vol. 34, No. 10, Oct. 1999.
2014/4/18 Tao-Yi Lee @ RFVLSILAB 43