Simulation and sensitivity of linear analog circuits under parameter variations by Robust interval analysis

An interval-mathematic approach is presented for frequency-domain simulation and sensitivity analysis of linear analog circuits under parameter variations. With uncertain parameters represented as intervals, bounding frequency-domain responses is formulated as the problem of solving systems of linear interval equations. The formulation is based on a variant of modified nodal analysis, and is particularly amenable to interval analysis. Some characterization of the solution sets of systems of linear interval equations are derived. With these characterizations, an elegant and efficient algorithm is proposed to solve systems of linear interval equations. While the widely used Monte Carlo approach requires many circuit simulations to achieve even moderate accuracy, the computational cost of the proposed approach is about twice that of one circuit simulation. The computed response bounds contain provably, or are usually very close to, the actual response bounds. Further, sensitivity under parameter variations can be computed from the response bounds at minor computational cost. The algorithms are implemented in SPICE3F5, using sparse-matrix techniques and tested on several practical analog circuits.

[1]  A. Hoffman,et al.  A theorem on inverses of convex sets of real matrices with application to the worst case dc problem , 1977 .

[2]  Randal E. Bryant,et al.  Intractability in linear switch-level simulation , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  Daniel P. Lopresti,et al.  Interval methods for modeling uncertainty in RC timing analysis , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  A. Householder.  A Survey of Some Closed Methods for Inverting Matrices , 1957 .

[5]  Xieting Ling,et al.  Novel methods for circuit worst-case tolerance analysis , 1996 .

[6]  C.-J.R. Shi,et al.  Worst-case analysis of linear analog circuits using sensitivity bands , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[7]  Keith Baker,et al.  Mixed signal test-techniques, applications and demands , 1996 .

[8]  Charles A. Zukowski.  VLSI Circuit Simulation , 1986 .

[9]  Bozena Kaminska,et al.  LIMSoft: automated tool for design and test integration of analog circuits , 1996, Proceedings International Test Conference 1996. Test and Design Validity.

[10]  Eldon Hansen,et al.  Bounding the solution of interval linear equations , 1992 .

[11]  Robert Spence,et al.  Tolerance Design of Electronic Circuits , 1997 .

[12]  Anil Pahwa,et al.  Band faults: Efficient approximations to fault bands for the simulation before fault diagnosis of linear circuits , 1982 .

[13]  Valeri Mladenov,et al.  Interval mathematics algorithms for tolerance analysis , 1988 .

[14]  C.-J. Richard Shi,et al.  Rapid frequency-domain analog fault simulation under parameter tolerances , 1997, DAC.

[15]  Fumihiko Kajiya,et al.  Compartmental system analysis: Realization of a class of linear systems with physical constraints , 1977 .

[16]  Mohammed Ismail,et al.  Statistical Modeling for Computer-Aided Design of Mos VLSI Circuits , 1993 .

[17]  S. Skelboe,et al.  True worst-case analysis of linear electrical circuits by interval arithmetic , 1979 .

[18]  Wojciech Maly,et al.  VLSI Design for Manufacturing: Yield Enhancement , 1989 .

[19]  V. A. Barker.  Sparse Matrix Techniques , 1977 .

[20]  C.-J. Richard Shi,et al.  Non-Monte Carlo Simulation and Sensitivity of Linear(ized) Analog Circuits under Parameter Variations* , 1997 .

[21]  Charles A. Zukowski.  The Bounding Approach to VLSI Circuit Simulation , 1986 .

[22]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[23]  Albert E. Ruehli,et al.  The modified nodal approach to network analysis , 1975 .