Piece-wise approximations of RLCK circuit responses using moment matching

ABSTRACT

Capturing RLCK circuit responses accurately with existing model order reduction (MOR) techniques is very expensive. Direct metrics for fast analysis of RC circuits exist but there is no such technique for RLCK circuits. This paper introduces a new family of MOR techniques based on piece-wise functions to capture RLCK circuit responses accurately using only four or five moments. The time-domain response is approximated using a piece-wise function whose pieces are simple polynomials. The proposed method is fast and guaranteed stable and it avoids the calculation of poles and residues associated with existing model order reduction techniques. Results for many different industrial netlists indicate that delay and transition time can be captured within 5% error using only four moments. To the authors' knowledge, there is no existing method that can extract as much information about RLCK circuits with only four or five moments.

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids
          Subjects: Simulation

General Terms:
Algorithms, Performance

Keywords:
RC, RLC, RLCK circuits, interconnect timing analysis, moments