An algorithm for simulating power/ground networks using padé approximants and its symbolic implementation

Jatan C. Shah, Ahmed A. Younis, Sachin S. Sapatnekar, Marwan M. Hassoun

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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-π-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.

Original languageEnglish (US)
Pages (from-to)1372-1382
Number of pages11
JournalIEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Issue number10
StatePublished - 1998

Bibliographical note

Funding Information:
Manuscript received November 30, 1997; revised April 19, 1998. This work was supported in part by the National Science Foundation under Grant MIPS-9502556, by the Semiconductor Research Corporation (SRC) under Contract DJ-98-609, by the National Science Foundation under Award CCR-9800992, and by a grant from Texas Instruments Incorporated. This paper was recommended by Guest Editor G. G. E. Gielen.


  • Approximants
  • Ground networks
  • Padé
  • Power
  • Symbolic analysis
  • VLSI


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