An Accurate and Efficient Computation of Zeros and Poles of Transfer Function for Large Scale Circuits

conference paper

English

The zeros and poles of a circuit transfer function are computed solving a general eigenvalue problem, which could be transformed to a standard eigenvalue task to be solved by a suitably modified QR algorithm. Both reduction of the general eigenvalue problem to the standard form and the iterative procedures of the QR algorithm are very sensitive to the numerical precision of all calculations. The numerical accuracy is especially critical for two kinds of circuits: the microwave ones characterized by huge differences among magnitudes of the zeros and poles, and the large scale circuits, where the errors of the zeros and poles are increased by an extreme number of arithmetic operations. In the paper, an illustrative example of the reduction of the general eigenvalue problem and using the QR algorithm is shown first. After that, three circuits of various sizes are analyzed: simpler microwave low noise amplifier, larger power operational amplifier, and the most complex example with a 272 integrated operational amplifier. A meticulous comparison of obtained results shows that a usage of newly implemented 128-bit arithmetics in GNU Fortran or C compilers with partial pivoting can assure both efficient and enough accurate procedures for computing the zeros and poles.

large scale circuits; poles and zeros; general eigenvalue problem; numerical precision; 128-bit arithmetics

DOBEŠ, J.; MÍCHAL, J.; VEJRAŽKA, F.; BIOLKOVÁ, V.

28. 10. 2019

IEEE

San Francisco, USA

978-988-14048-7-9

Proceedings of the World Congress on Engineering and Computer Science 2019

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http://www.iaeng.org/publication/WCECS2019/