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Application of the tree‐cotree splitting for improving matrix conditioning in the full‐wave finite‐element analysis of high‐speed circuits
Author(s) -
Lee ShihHao,
Jin JianMing
Publication year - 2008
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.23403
Subject(s) - electronic circuit , decoupling (probability) , finite element method , broadband , electronic engineering , reduction (mathematics) , matrix (chemical analysis) , solver , engineering , microwave , algorithm , topology (electrical circuits) , computer science , electrical engineering , mathematics , mathematical optimization , telecommunications , materials science , geometry , structural engineering , control engineering , composite material
In this study the tree‐cotree splitting technique is applied for improving the finite‐element matrix conditioning for the analysis of high‐speed circuits. A well‐known issue is that at low frequencies a full‐wave solver yields less accurate solutions and may even breakdown due to ill‐conditioned system matrices. To enhance the capability and reliability of the conventional finite element method in broadband full‐wave analyses, we apply the tree‐cotree splitting to edge elements to account for the decoupling between the electric and magnetic fields at low frequencies, which is the main reason for the low‐frequency problem. The algorithm for finding a minimum spanning tree when there exist wave ports, lumped ports, or for a PEC‐free structure are described. Besides, a model order reduction method, called the solution space projection, is applied for a fast broadband analysis. We further propose an expansion to available solution bases for a better approximation to low‐frequency fields, so that a simulation can be extended to extremely low frequencies. The application is focused on the simulation of high‐speed circuits, of which both low and high frequency characteristics are of equal importance. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1476–1481, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23403