Efficient DDD-based symbolic analysis of linear analog circuits

Abstract

The general framework of a symbolic analysis environment for linear time-invariant circuits is presented. Such a framework consists of two major parts: a simplification at circuit level and a simplifying expression-generation. An overview of the known techniques for both circuit simplification and expression generation is given, and in addition a new nonhierarchical expression generation technique based on the concept of determinant decision diagrams (DDDs) is presented. The DDD-based technique is evaluated on a set of benchmark circuits together with a known fast symbolic analysis algorithm, and turns out to be the most efficient. The DDD-based expression generation algorithm is, therefore, the best solution for nonhierarchical linear symbolic expression generation to the authors' knowledge.

Pathological Element-Based Active Device Models and Their Application to Symbolic Analysis

“…Note that (2) and (3) are special cases of (4). Based on (4), the determinant of (1) can be represented with compact graphs by using the Determinant Decision Diagrams (DDDs) concept [12]- [14]. Each non-zero coefficient of the matrix is considered as one distinct symbol and each of them is represented into DDDs as one non-terminal vertex.…”

Symbolic analysis of (MO)(I)CCI(II)(III)‐based analog circuits

“…Using nullors, one is able to formulate a system of equations by only applying NA [72][73][74][75][76], because all non-NA compatible elements can be transformed as NA compatible ones [73]. Further, the solution can be performed by applying determinant decision diagrams [64,65].…”

Symbolic formulation method for mixed-mode analog circuits using nullors

“…The evaluation of the Cartesian product between ROW×COL leads us to the formulation given by (1). For example: since g1 is floating, the Cartesian product between ROW [5]×COL [3] leads us to the combination (11,5), so -g1 is added into the admittance matrix in the position (5,3) in (1). Finally, the solution is given by (2), where the parasitic resistance at terminal X of each current conveyor has been added, since it is in series connection with R1 and R2.…”

“…As already shown in [3], the main advantage of transforming an analog circuit to a nullorbased equivalent is to use Nodal Analysis (NA) to formulate the system of equations. This paper introduces a new formulation method at the circuit level, whose solution can be performed by determinant decision diagrams [4], [5]. For large circuits, however, the solution can be performed by applying Boolean logic operations [6].…”