An algorithm for frequency-domain noise analysis in nonlinear systems

ABSTRACT

Many mixed-technology and mixed-signal designs require the assessment of the system's performance in the presence of signals that are best characterized as having continuous frequency spectra: for instance, the simulation of a circuit's behavior in the presence of electrical noise. This paper describes an algorithm for frequency-domain simulation of nonlinear systems capable of handling signals with continuous spectra. The algorithm is based on an orthogonal series expansion of the signals in the frequency domain. Thus it is, in a sense, the dual approach to frequency-domain simulation with respect to harmonic balance, which relies on a time-domain series expansion of the signals. Signal spectra are obtained from the solution of a system of nonlinear algebraic equations whose dimension increases with the desired spectral accuracy. Numerical results obtained on an optical amplifier are presented.

REFERENCES

• 1: A. Demir, E. W. Y. Liu, and A. L. Sangiovanni-Vincentelli, "Time-domain non Monte Carlo noise simulation for nonlinear dynamic circuits with arbitrary excitations," IEEE Trans. Computer-Aided Design, vol. 15, pp. 493--505, May 1996.
• 2: M. Okumura, H. Tanimoto, T. Itakura, and T. Sugawara, "Numerical noise analysis for nonlinear circuits with a periodic large signal excitation including cyclostationary noise sources," IEEE Trans. Circuits Syst. I, vol. 40, pp. 581--590, Sept. 1993.
• 3: J. Roychowdhury, D. Long, and P. Feldmann, "Cyclostationary noise analysis of large RF circuits with multitone excitations," IEEE J. Solid-State Circuits, vol. 33, pp. 324--336, Mar. 1998.
• 4: Ricardo Telichevesky , Ken Kundert , Jacob White, Efficient AC and noise analysis of two-tone RF circuits, Proceedings of the 33rd annual conference on Design automation, p.292-297, June 03-07, 1996, Las Vegas, Nevada, United States [doi>10.1145/240518.240572]
• 5: K. S. Kundert and A. Sangiovanni-Vincentelli, "Simulation of nonlinear circuits in the frequency domain," IEEE Trans. Computer-Aided Design, vol. CAD 5, pp. 521--535, Oct. 1986.
• 6: K. S. Kundert, J. White, and A. Sangiovanni-Vincentelli, Steady-State Methods for Simulating Analog and Microwave Circuits. Norwell, MA: Kluwer Academic Publishers, 1990.
• 7: V. Rizzoli and A. Neri, "State of the art and present trends in nonlinear microwave CAD techniques," IEEE Trans. Microwave Theory Tech., vol. 36, pp. 343--365, Feb. 1988.
• 8: Alan V. Oppenheim , Ronald W. Schafer, Discrete-time signal processing, Prentice-Hall, Inc., Upper Saddle River, NJ, 1989
• 10: F. J. Harris, "On the use of windows for harmonic analysis with discrete Fourier transform," Proc. IEEE, vol. 66, pp. 51--83, Jan. 1978.
• 11: Youcef Saad , Martin H Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing, v.7 n.3, p.856-869, July 1986 [doi>10.1137/0907058]

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation

General Terms:
Algorithms, Verification

Keywords:
circuit simulation, frequency-domain analysis