IMPLICATIONS OF THE ABOVE HOLISTIC UNDERSTANDING OF HARMONY ON PROFESSIONAL E...
Generiic RF passive device modeling
1. 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
2. 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
3. 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
4. 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
C33
C22C11
L12 L23R12 R23
Model #1
PORT2
M
i2i1
PORT1
PORT2
PORT3
Si Substrate
IMD
Cox Cox
• Main lumped elements
• Skin effect
• Loss
• Substrate
• Eddy current
5. Modeling Skin Effect
• Skin effect: 𝑅 𝑐𝑜𝑛𝑑 ∝ 𝑓; 𝐿 𝑐𝑜𝑛𝑑 ≈ 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
6. 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 PORT2
Meddy
Rs,eddy
PORT1
PORT2
PORT3
Si Substrate
IMD
Image inductor on
lossy substrate
7. 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, ℎ 𝑜𝑥: height above oxide)
𝐶 𝑜𝑥 = 1 −
𝑠
𝑠 + 𝑤
1.16 𝜖0 𝜖 𝑜𝑥 ∙ 𝑤 ∙ 𝑙
ℎ 𝑜𝑥
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
8. Modeling Substrate
• Modeling of substrate extrinsic is generally difficult, but some
closed form solution are found in micro-strip transmission line
researches (ℎ 𝑠𝑢𝑏:height of the substrate, 𝜖 𝑠𝑢𝑏,𝑒𝑓𝑓: effective
dielectric constant)
– 𝐶𝑠𝑢𝑏 =
𝑤
ℎ 𝑠𝑢𝑏
+1.393+0.667 ln
𝑤
ℎ 𝑠𝑢𝑏
+1.444
120𝜋𝑐
∙
𝑙
2
𝜖 𝑠𝑢𝑏,𝑒𝑓𝑓
• In reference 2, shunt resistance 𝑅 𝑠𝑢𝑏 in silicon can be determined
using relaxation time constant
𝜖0 𝜖 𝑆𝑖
𝜎 𝑆𝑖
– 𝑅 𝑠𝑢𝑏 =
𝜖0 𝜖 𝑆𝑖
𝐶 𝑆𝑖 𝜎 𝑆𝑖
• 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
9. Solve Y Parameter Matrix 𝑌 of The
Lumped Equivalent Network
• Definition of Y parameters
– Yij =
Ii
Vj Vk=0 for k≠j
–
𝐼1
𝐼2
𝐼3
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
10. 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 PORT2
PORT1
C12
C22C11
L12 R12
PORT2i1
simple 2 port inductor model
11. 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
Y11
PORT1
-Y12
12. 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
PORT1
PORT2
-Y12
PORT1 PORT2
Y11+Y21 Y21+Y22
-Y12
Y11//Y22+Y21/2 Y11//Y22-Y21/2
13. 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
14. Define The Minimization Problem In
MATLAB
∀i, j, minimize
R1,R2,…,L1,L2,…,C1,C2,…
ΔYij
= minimize
R1,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
15. 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
43. 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
