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 minimize 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.
