Generation of sequential symbolic network functions for large-scale networks by circuit reduction to two-port

Abstract

The major stumbling block in symbolic analysis of large-scale circuits is the exponential growth of expression complexity with the circuit size. Sequential techniques, introduced more than a decade ago, reduced that growth to quasi-linear. The fundamental assumption in all sequential methods developed so far was that the circuit must be decomposed in order to reduce the complexity of the final expression. In this paper we will show conclusively that this is not the case. We describe a new algebraic approach to symbolic analysis of large-scale networks, based on the reduction of the compacted modified node admittance matrix to a two-port matrix. No circuit partitioning is required. Internal variables are suppressed one by one using Gaussian elimination. To minimise the number of symbolic operations we employ a locally optimal pivoting strategy. Formula complexity is estimated to grow quasi-linearly with circuit size. The technique is conceptually very simple and produces sequential formulae of significantly lesser complexity than any exact method published to date.

Efficient DDD-based symbolic analysis of linear analog circuits

“…The latter problem was completely avoided by the introduction of an error criterion in the device parameter elimination step of the sifting approach used in the SIFTER tool by Hsu and Sechen [17]. The differences die to omitted elements of the numerator or denominator matrix are multiplied with sensitivities derived from the Laplace determinant expansion rule (6) to obtain a ranking for each difference. All element eliminations are then attempted in order of increasing absolute ranking.…”

“…The first is the so-called sequence-of-expressions (SOEs) format, which represents a network function with a nested expression while making reuse of the subexpressions. Several techniques have been developed to generate SOEs [4]- [6], with generation times approximately linear to the number of circuit nodes. However, the SOE format does not give much insight into the circuit behavior, while expanding it to a more interpretable flat format results in very long expressions with many common factors in numerator and denominator.…”

Modified Nodal Analysis-Based Determination of Transfer Functions for Multi-Inputs Multi-Outputs Linear Circuits

“…1) are given in s-domain, (1) and (2). The nodal and output equations together are called the system model.…”

“…A graph-based approach is presented for the generation of exact symbolic network functions in the form of rational polynomials of the complex variable (s) in [1]. A symbolic method for generating a compact sequence of expressions for network functions of large-scale circuits is described in [2]. A unified approach to the approximate symbolic analysis of analog integrated circuits is given in [3].…”

Symbolic analysis of analog circuits containing voltage mirrors and current mirrors

“…Elsewhere, we can formulate a much reduced system of equations in a nullor network, because it also allows us to apply circuit reduction methods [6,16,21,24].…”