期刊名称：Lecture Notes in Engineering and Computer Science
印刷版ISSN：2078-0958
电子版ISSN：2078-0966
出版年度：2019
卷号：2241
页码：78-83
出版社：Newswood and International Association of Engineers
摘要：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.
Index Terms—large scale circuits, poles and zeros, general
eigenvalue problem, numerical precision, 128-bit arithmetics.
关键词：large scale circuits; poles and zeros; general;
eigenvalue problem; numerical precision; 128-bit arithmetics.
