## Canonical Symbolic Analysis of Large Analog Circuits with Determinant Decision Diagrams (2000)

Venue: | IEEE TRANS. ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS |

Citations: | 17 - 5 self |

### BibTeX

@ARTICLE{Shi00canonicalsymbolic,

author = {C.-J. Richard Shi and Xiangdong Tan},

title = {Canonical Symbolic Analysis of Large Analog Circuits with Determinant Decision Diagrams},

journal = {IEEE TRANS. ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS},

year = {2000},

volume = {19},

pages = {1--18}

}

### OpenURL

### Abstract

Symbolic analog-circuit analysis has many applications, and is especially useful for analog synthesis and testability analysis. Existing approaches rely on two forms of symbolic expression representation: expanded sum-of-product form or arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit, and approximation has to be used. Nested form is not canonical, i.e., many representations exist for a symbolic expression, and manipulations with the nested form are often complicated. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. It consists of representing the symbolic determinant of a circuit matrix by a graph---called determinant decision diagram (DDD)---and performing symbolic analysis by graph manipulations. We showed that DDD construction, as well as many symbolic analysis algorithms, can be performed in time complex...