A simulation tool for the analysis and verification of the steady state of circuit designs

H. G. Brachtendorf, G. Welsch, R. Laur

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Analogue and microwave design requires accurate and reliable simulation tools and methods to meet the design specifications. System properties are often measured in the steady state. Well‐suited algorithms for calculating the steady state can be classified into shooting methods, finite difference methods and the harmonic balance (HB) technique. Harmonic balance is a frequency domain method which approaches the problem of finding the steady state by a trigonometric polynomial. Depending on the size of the circuit and the number of Fourier coefficients of the polynomial, the resulting system of non‐linear equations can become very large. These non‐linear equations are solved by using Newton's method. The sparse linear system arising from Newton's method can be solved by direct, stationary or non‐stationary iterative solvers. Iterative methods are normally easy to parallelize or vectorize. In this paper a tool for the simulation of the steady state of electronic circuits is presented. the steady state is calculated using the harmonic balance technique. Non‐linear equations are solved by Newton's method and linear equations by preconditioned non‐stationary iterative solvers (CGS, Bi‐CGSTAB, BiCGSTAB(2), TFQMR). the run time is reduced dramatically, by up to an order of magnitude.

Original languageEnglish
Pages (from-to)311-323
Number of pages13
JournalInternational Journal of Circuit Theory and Applications
Issue number4
Publication statusPublished - 1995
Externally publishedYes

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