Periodic Small Signal Analysis of a Wide Class of Type-II Phase Locked Loops Through an Exhaustive Variational Model

Phase-locked loops are important building blocks for several different applications. Modern design and implementation of these circuits is largely advantaged by a mixed analog/digital simulation approach since phase locked loops are stiff systems and a full analog representation is in general too large to simulate in reasonable time. Even though current algorithms, based on a mixed analog/digital representation, lead to models characterized by outstanding properties, they do not allow efficient simulations of important periodic and small signal features such as modulation/demodulation or noise effects. In this paper a novel, reliable and efficient method is proposed that overcomes those limitations and makes possible to evaluate both modulation/demodulation and noise effects in the widely adopted class of type-II phase-locked loop circuits based on a digital three-state phase-frequency detector.

[1]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[2]  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.

[3]  Salvatore Levantino,et al.  Behavioral phase-noise analysis of charge-pump phase-locked loops , 2011, 2011 20th European Conference on Circuit Theory and Design (ECCTD).

[4]  Ian Galton,et al.  A Discrete-Time Model for the Design of Type-II PLLs With Passive Sampled Loop Filters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Giambattista Gruosso,et al.  Periodic noise analysis of electric circuits: Artifacts, singularities and a numerical method , 2010, Int. J. Circuit Theory Appl..

[6]  Salvatore Levantino,et al.  Folding of Phase Noise Spectra in Charge-Pump Phase-Locked Loops Induced by Frequency Division , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Daniele D. Caviglia,et al.  Improved Small-Signal Analysis for Circuits Working in Periodic Steady State , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Chien-Nan Jimmy Liu,et al.  Fast Statistical Analysis of Process Variation Effects Using Accurate PLL Behavioral Models , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Poras T. Balsara,et al.  Time-Domain Modeling of an RF All-Digital PLL , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Damian Giaouris,et al.  Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Jaeha Kim,et al.  Variable domain transformation for linear PAC analysis of mixed-signal systems , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[12]  Damian Giaouris,et al.  Control of Fast Scale Bifurcations in Power-Factor Correction Converters , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  A. Lacaita,et al.  Integrated Frequency Synthesizers for Wireless Systems: Noise in oscillators , 2007 .

[14]  Paolo Maffezzoni,et al.  Computation of period sensitivity functions for the simulation of phase noise in oscillators , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Hiroshi Tanimoto,et al.  A time-domain method for numerical noise analysis of oscillators , 1997, Proceedings of ASP-DAC '97: Asia and South Pacific Design Automation Conference.

[16]  Jacob K. White,et al.  Efficient AC and noise analysis of two-tone RF circuits , 1996, 33rd Design Automation Conference Proceedings, 1996.

[17]  Mark Van Paemel,et al.  Analysis of a charge-pump PLL: a new model , 1994, IEEE Trans. Commun..

[18]  Tetsuro Itakura,et al.  Numerical noise analysis for nonlinear circuits with a periodic large signal excitation including cyclostationary noise sources , 1993 .

[19]  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..

[20]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[21]  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.

[22]  F. Gardner,et al.  Charge-Pump Phase-Lock Loops , 1980, IEEE Trans. Commun..

[23]  Jiri Vlach,et al.  A piecewise harmonic balance technique for determination of periodic response of nonlinear systems , 1976 .

[24]  Luca Dieci,et al.  Fundamental matrix solutions of piecewise smooth differential systems , 2011, Math. Comput. Simul..

[25]  Miklós Farkas,et al.  Periodic Motions , 1994 .

[26]  T. Aprille,et al.  Steady-state analysis of nonlinear circuits with periodic inputs , 1972 .