Accurate and Efficient PSD Computation in Mixed-Signal Circuits: A Time-Domain Approach

The aim of this brief is twofold. On one side, the time-domain technique presented by Vasudevan to obtain the average and instantaneous power-spectral density of electrical variables in analog circuits characterized by (non)stationary noise sources is rigorously extended to the wide class of analog mixed-signal circuits modeled as hybrid dynamical systems. On the other side, an efficient numerical implementation is proposed to overcome the computational effort required by the original approach. The reliability of the method is first tested through the analog ring oscillator analyzed by Vasudevan. A fractional delta-sigma phase-locked loop with dithering is then simulated and the obtained results are partially validated through experimental measurements.

[1]  Jacob K. White,et al.  Efficient AC and noise analysis of two-tone RF circuits , 1996, DAC '96.

[2]  Federico Bizzarri,et al.  Reliable and efficient phase noise simulation of mixed-mode integer-N Phase-Locked Loops , 2013, 2013 European Conference on Circuit Theory and Design (ECCTD).

[3]  James Wiegold,et al.  CIPHER SYSTEMS: The Protection of Communications , 1983 .

[4]  Evelyn Buckwar,et al.  Multistep methods for SDEs and their application to problems with small noise , 2006, SIAM J. Numer. Anal..

[5]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[6]  Alberto L. Sangiovanni-Vincentelli,et al.  Simulation of Nonlinear Circuits in the Frequency Domain , 1986, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  Leon O. Chua,et al.  Linear and nonlinear circuits , 1987 .

[8]  Federico Bizzarri,et al.  Extension of the variational equation to analog/digital circuits: numerical and experimental validation , 2013, Int. J. Circuit Theory Appl..

[9]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[10]  R. Poujois,et al.  A new approach for noise simulation in transient analysis , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[11]  Federico Bizzarri,et al.  Steady State Computation and Noise Analysis of Analog Mixed Signal Circuits , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  D. Lampard.  Generalization of the Wiener‐Khintchine Theorem to Nonstationary Processes , 1954 .

[13]  Alberto L. Sangiovanni-Vincentelli,et al.  Time-domain non-Monte Carlo noise simulation for nonlinear dynamic circuits with arbitrary excitations , 1994, ICCAD '94.

[14]  Angelo Brambilla,et al.  Frequency warping in time-domain circuit simulation , 2003 .

[15]  Tsutomu Sugawara,et al.  An efficient small signal frequency analysis method of nonlinear circuits with two frequency excitations , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Vinita Vasudevan,et al.  A time-domain technique for computation of noise-spectral density in linear and nonlinear time-varying circuits , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  G. S. Gajani,et al.  Periodic Small Signal Analysis of a Wide Class of Type-II Phase Locked Loops Through an Exhaustive Variational Model , 2012, IEEE Transactions on Circuits and Systems Part 1: Regular Papers.

[18]  Werner Römisch,et al.  Efficient transient noise analysis in circuit simulation , 2006 .

[19]  Nicolas Privault,et al.  Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales , 2009 .

[20]  Federico Bizzarri,et al.  Effects of numerical noise floor on the accuracy of time domain noise analysis in circuit simulators , 2013, 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013).

[21]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.