Abstruct-A hierarchical approach to the problem of symbolic circuit analysis of large-scale circuits is presented in this paper. The methodology has been implemented in a computer program called SCAPP (Symbolic Circuit Analysis Program with Partitioning). The method solves the problem by utilizing a hierarchical network approach and the sequence of expressions concept rather than a topological approach and the single expression idea which have dominated symbolic analysis in the past. The result is a linear growth (for real circuits) in the number of terms in the symbolic solutions for the network approach versus the exponential growth exhibited by traditional methods. The analysis methodology uses a Reduced Modified Nodal Analysis (RMNA) techdque that allows the characterization of symbolic networks in terms of only a small subset of the network variables (external variables). The analysis algorithm is most efficient when network partitioning is used. Partitioning results in a reduction in the number of terms in the symbolic solutions.

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This paper presents an event-driven algorithm and its symbolic implementation for the analysis of power and ground (P/G) bus networks. The algorithm uses frequency-domain techniques and moment matching approaches based on Padé approximants to estimate the transfer function at each node in the P/G network. Afterwards, the transient waveforms are extracted for each node. The process requires repetitive simulation of a linear and time-variant (from one time event to the next) circuit model for the P/G network which is the reason a symbolic implementation was produced. The P/G network is modeled by a hierarchical combination of mesh and tree structures that are composed of a collection of RC--segments and pulldown (or pullup) switches. The switches are symbolically represented by Boolean variables and a compiled symbolic code is generated only once for each P/G network. The transient waveforms are then produced by repetitive evaluation of the symbolic output. The results show that the symbolic implementation is an order of magnitude faster, with reasonably good accuracy, than using a traditional analog circuit simulator like SPICE.Index Terms-Padé approximants, power/ground networks, symbolic analysis, VLSI.