A COMPLETE VARIATIONAL METHOD FOR CAPACITANCE EXTRACTIONS

In the past, coupling capacitances between conductors was extracted using charge distributions directly. In this paper a set of new generalized variational formulas are derived. They are complete since they are valid not only for self-capacitances, but also for mutual capacitances. As for the realistic numerical implementation, elastance matrices become asymmetrical because of numerical method used. Then a more general variational formula is derived to account for the asymmetrical elastance matrix case. By these novel formulas the computational accuracy can be significantly improved compared to the conventional capacitance extraction method.

[1]  Weng Cho Chew,et al.  Effects of Fringing Fields on the Capacitance of Circular Microstrip Disk , 1980 .

[2]  Weng Cho Chew,et al.  Asymptotic formula for the capacitance of two oppositely charged discs , 1981, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Yong Wang,et al.  A surface-based integral-equation formulation for coupled electromagnetic and circuit simulation , 2002 .

[4]  T. Itoh,et al.  A New Method for Calculating the Capacitance of a Circular Disk for Microwave Integrated Circuits (Short Papers) , 1973 .

[5]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

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

[7]  S. Borkar,et al.  Capacitance of a Circular Disk for Applications in Microwave Integrated Circuits (Short Papers) , 1975 .

[8]  Weng Cho Chew,et al.  A fast multipole-method-based calculation of the capacitance matrix for multiple conductors above stratified dielectric media , 2001 .

[9]  F. G. Leppington,et al.  On the capacity of the circular disc condenser at small separation , 1970, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  Y. Nomura The Electrostatic Problems of Two Equal Parallel Circular Plates , 1941 .

[11]  S. Kim,et al.  Fast capacitance extraction of general three-dimensional structures , 1991, [1991 Proceedings] IEEE International Conference on Computer Design: VLSI in Computers and Processors.

[12]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[13]  Y. L. Le Coz,et al.  Performance of random-walk capacitance extractors for IC interconnects: A numerical study , 1998 .

[14]  Weng Cho Chew,et al.  MICROSTRIP CAPACITANCE FOR A CIRCULAR DISK THROUGH MATCHED ASYMPTOTIC EXPANSIONS. , 1982 .

[15]  G. Pólya,et al.  Isoperimetric inequalities in mathematical physics , 1951 .

[16]  Weng Cho Chew,et al.  Approximate Formulas for Line Capacitance and Characteristic Impedance of Microstrip Line , 1981 .

[17]  Weng Cho Chew,et al.  A hierarchical fast-multipole method for stratified media , 2000 .

[18]  G. Temple Static and Dynamic Electricity , 1940, Nature.

[19]  Susann J. N. Shaw Circular‐Disk Viscometer and Related Electrostatic Problems , 1970 .

[20]  Weiping Shi,et al.  A fast hierarchical algorithm for 3-D capacitance extraction , 1998, DAC.