Algorithms Supporting Driver/Receiver Design for Multi-Conductor Interconnects
Design of packaging for high speed circuits requires modeling of transmission properties of interconnecting lines. In particular the evaluation of characteristic admittance matrix of interconnections is a basic computation needed for design of CMOS drivers and bipolar receivers. When interconnections are made out of good conductors and substrates are good insulators as it is for example in the case of printed wire boards it is often assumed that both conductor and substrate losses are negligible and interconnections are then modeled as lossless transmission lines described by the capacitance C and inductance L matrices. The admittance matrix is constant in such a case and modeling of signal transmission is relatively simple. The computation of characteristic admittance matrix is typically based on eigenanalysis. However, the numerical problems may be quite challenging in particular when the product, LC, of inductance and capacitance matrices has multiple eigenvalues. We shall present here new algorithms that simplify the computation of characteristic admittance matrix and associated diagonally matched load impedances. The simplification of admittance matrix computation is particularly significant in cases of multiple eigenvalues because determination of the orthonormal set of eigenvectors is not required.
KeywordsMultiple Eigenvalue Printed Wire Board Admittance Matrix Capacitance Matrice High Speed Circuit
Unable to display preview. Download preview PDF.
- 1.Amemiya H., “Time Domain Analysis of Multiple Parallel Transmission Lines” RCA Review 28 (1967), pp. 241–276.Google Scholar
- 2.Beyene, W. T. and J. Schutt-Aine, Analysis of Frequency-dependent Transmission Lines Using Rational Approximation and Recursive Convolution, Intl. Workshop-Signal Propagation on Interconnects, May 14–16, 1997, Travemuende, Germany.Google Scholar
- 3.Datta, B. N, Numerical Linear Algebra and Applications, Brooks/Cole Publishing Company, ITP, pp. 435–451.Google Scholar
- 4.T. C. Lee and J. Cong „The New Line in IC Design”, IEEE Spectrum, March 1997, pp. 52–58.Google Scholar
- 5.Reiss, K, “Homogeneous line systems and modal decomposition”, Univ. of Karlsruhe, private communication, 1997.Google Scholar
- 7.Szidarovszky, F. and A. T. Bahill, Linear System Theory, CRC Press, Boca Raton/London, pp. 27–28.Google Scholar
- 8.Szidarovszky, F. and O. A. Palusinski, “A Special Matrix Equation and Its Application in Microelectronics,” Applied Mathematics and Computation, Elsevier Science Inc., Dec. 1994, pp. 115–119.Google Scholar
- 9.Wiesel, M., “Automated Routing of IC and PCB are Merging”, Das ITM unter der Leitung von Professor Dieter A. M.ynski (Proceedings of Colloquium at the University of Karlsruhe, K. Reiss Editor), University of Karlsruhe Press, January 31, 1997.Google Scholar