A Passive analytical per-unit-length internal impedance matrix model for multiconductor interconnections

Based on multiconductor transmission line (MTL) theory, we describe a technique for a simple computation of the high-frequency (h.f.) current distribution in a multiconductor interconnection and of the h.f. per-unit-length (p.u.l.) resistance matrix of the interconnection. This result is used in a model for the p.u.l. internal impedance matrix of the interconnection. We show that this model is passive, hence causal.

[1]  A. Zemanian,et al.  An N-Port Realizability Theory Based on the Theory of Distributions , 1963 .

[2]  T. Sarkar,et al.  Analysis of Multiconductor Transmission Lines , 1988, 31st ARFTG Conference Digest.

[3]  A. Cangellaris.  A note on the calculation of the current distribution in lossy microstrip structures , 1991, IEEE Microwave and Guided Wave Letters.

[4]  Frédéric Broydé,et al.  A new method for the reduction of crosstalk and echo in multiconductor interconnections , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  H. A. Wheeler.  Formulas for the Skin Effect , 1942, Proceedings of the IRE.

[6]  R. Collin.  Field theory of guided waves , 1960 .

[7]  C. Johnk,et al.  Engineering Electromagnetic Fields and Waves , 1975 .

[8]  A.C. Cangellaris,et al.  Note on the Definition and Calculation of the Per-Unit-Length Internal Impedance of a Uniform Conducting Wire , 2007, IEEE Transactions on Electromagnetic Compatibility.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  Giulio Antonini,et al.  Internal impedance of conductors of rectangular cross section , 1998, 1998 IEEE EMC Symposium. International Symposium on Electromagnetic Compatibility. Symposium Record (Cat. No.98CH36253).

[11]  Howard W. Johnson,et al.  High Speed Signal Propagation: Advanced Black Magic , 2003 .

[12]  E.F. Kuester,et al.  DC Internal Inductance for a Conductor of Rectangular Cross Section , 2009, IEEE Transactions on Electromagnetic Compatibility.

[13]  R. Achar,et al.  Stability, Causality, and Passivity in Electrical Interconnect Models , 2007, IEEE Transactions on Advanced Packaging.