A Decomposition-Based Symbolic
Analysis Method for Analog Synthesis
from Behavioral Specifications
Alex Doboli and Ranga Vemuri
Digital Design Environments Laboratory, Department ofECECS
University of Cincinnati, Cincinnati, OH 45221-0030
Email: { adoboli,ranga } ececs.uc.edu
Abstract This paper discusscs a technique for symbolic analysis of largc analog systems.
The method exploits the hierarchical structure and uniformity of a system for
producing compact symbolie expressions. The technique is based on decom-
posing a system through the method of tcaring [5] as opposed to traditional
symbolic methods that llse nodal analysis. After producing the symbolic model
ora system, a set ofredLlction rules is applied to the model. RedLlctions attempt 10
dccrease the number of arithmetic operations perronned for numetically evalu-
ating the symbolic model. The discLlssed technique is useful for synthesis, inside
an exploration-Ioop, as it avoids repeatedly computing the symbolic models.
1. INTRODUCTION
Symbolic analysis is the task of automatically deducing relationships be-
tween overall parameters of a system and parameters ofthe composing elements
of the system [6] [3]. For example, a symbolic expression can describe the
transfer-function of a filter in terms of parameters of its building elements, i.e.
op amps, resistors, and capacitors. Analysis techniques include determinant-
based methods and signal-flow graph methods [6]. Determinant-based methods
use Cramer's rule for solving the set of linear equations implied by symbolic
analysis [3]. Signal-flow graph methods represent a set oflinear equations as a
weighted graph, and use Mason's rule for solving the equations [6]. Symbolic
analysis has a wide range of applications i.e. frequency response calculation,
sensitivity analysis, hardware synthesis etc. This paper proposes on a new
symbolic analysis technique for analog synthesis.
The main challenge for symbolic analysis is the exponential growth of
the produced symbolic expressions (10
11
terms for an op amp [4]). Current
research considers two ways ofhandling this aspect: approximation and hierar-
The original version of this chapter was revised: The copyright line was incorrect. This has been
corrected. The Erratum to this chapter is available at DOI:
© IFIP International Federation for Information Processing 2000
L. M. Silveira et al. (eds.), VLSI: Systems on a Chip
10.1007/978-0-387-35498-9_57