Linearization of S-Parameter Cascading for Analysis of Multiple Reflections
Keywords:
Inter-symbol interference (ISI), networks and circuits, scattering parameters, signal integrity, signal processing, transmission line matrixAbstract
This paper develops a method to derive intuitive understanding of the root causes of reflective interference created by the many impedance discontinuities between the packages, PCBs and connectors. Scattering parameters are cascaded to describe the system response and linearized to analyze the multiple reflections. An upper error bound of the linearization is derived and is validated with Monte Carlo studies.
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References
B. Casper, “Electrical interconnect potential and limits,” in Optical Interconnects Conference, 2014 IEEE, 2014.
T. Liang, S. Hall, H. Heck, and G. Brist, “A practical method for modeling PCB transmission lines with conductor surface roughness and wideband dielectric properties,” in Microwave Symposium Digest, 2006. IEEE MTT-S International, pp. 1780-1783, 2006.
I. Bardi, E. Bracken, M. Commens, and R. Petersson, “Finite Element Method Practices to Result in Accurate and Causal Broad Band Frequency Sweeps in Simulating PCBs and Interconnects,” 28th Annual Review of Progress in Applied Computational Electromagnetics, 2012.
“OIF2010.404.04: CEI-28G-VSR draft IA,” 2010.
D. M. Pozar, Microwave Engineering. John Wiley & Sons, 2009.
J. Frei, X.-D. Cai, and S. Muller, “Multiport Sparameter and T-parameter conversion with symmetry extension,” IEEE Transactions on Microwave Theory and Techniques, vol. 56, no. 11, pp. 2493-2504, 2008.
D. Telian, S. Camerlo, K. Matta, M. Steinberger, B. Katz, and W. Katz, “Moving Higher Data Rate Serial Links into Production - Issues & Solutions,” Presented at the DesignCon 2014 Conference, Santa Clara CA, 2014.
D. Telian, S. Camerlo, M. Steinberger, B. Katz, and W. Katz, “Simulating Large Systems with Thousands of Serial Links,” Presented at the DesignCon 2012 Conference, Santa Clara CA, 2012.
C.-W. Huang, C. E. Smith, A. Z. Elsherbeni, and B. Hammond, “A novel simplified four-port scattering parameter model for design of fourpair twisted-pair cabling systems for local area networks,” IEEE Transactions on Microwave Theory and Techniques, vol. 48, no. 5, pp. 815-821, 2000.
W. T. Beyene, N. Cheng, and C. Yuan, “Design and analysis of multi-gigahertz parallel bus interfaces of low-cost and band-limited channels,” in Electrical Performance of Electronic Packaging, 2003.
J. Lu and D. Thiel, “EMC Computer Modeling and Simulation Techniques,” 22nd Annual Review of Progress in Applied Computational Electromagnetics, 2006.
H. Yordanov, M. T. Ivrlac, A. Mezghani, J. A. Nossek, and P. Russer, “Computation of the Impulse Response and Coding Gain of a Digital Interconnection Bus,” 24th Annual Review of Progress in Applied Computational Electromagnetics, 2008.
M. Schneider, “Computation of impedance and attenuation of TEM-lines by finite difference methods,” IEEE Transactions on Microwave Theory and Techniques, vol. 13, no. 6, pp. 793-800, 1965.
“Quantum Channel Designer User Manual,” Signal Integrity Software, Inc., 2018.
“I/O Buffer Information Specification (IBIS) Version 6.1.,” 2015.
P. Triverio, S. Grivet-Talocia, M. S. Nakhla, F. G. Canavero, and R. Achar, “Stability, causality, and passivity in electrical interconnect models,” IEEE Transactions on Advanced Packaging, vol. 30, no. 4, pp. 795-808, 2007.
Z. N. Yong, et al., “Main cause of resonance appeared around 7.5 GHz on the frequency response of S-parameters of PWB,” in Electronic Packaging Technology and High Density Packaging (ICEPT-HDP), 2011 12th International Conference on, 2011.
S. J. Mason, “Feedback theory: Further properties of signal flow graphs,” Proceedings of the IRE, vol. 44, no. 7, pp. 920-926, 1956.
R. J. Allred, B. Katz, and C. Furse, “Ripple analysis: Identify and quantify reflective interference through ISI decomposition,” in Signal and Power Integrity (SPI), 2016 IEEE 20th Workshop on, 2016.
IEEE Standard for Ethernet, Amendment 2: Physical Layer Specifications and Management Parameters for 100 Gb/s Operation Over Backplanes and Copper Cables, IEEE Std 802.3bj2014, 2014.
“Proposal for a causal transmission line model,” IEEE P802.3bj Task Force, http://www.ieee802. org/3/bj/public/mar14/healey_3bj_01_0314.pdf, March 2014.
R. J. Allred, “System and method for signal integrity waveform decomposition analysis,” U.S. Patent 9,633,164, issued April 25, 2017.
