Piet Vanassche
ABSTRACT
A new approach is presented for the construction of behavioral models for harmonic oscillators and sets of coupled harmonic oscillators. The models can be used for system-level simulations and trade-off analysis. Besides the steady state behavior, the model also takes the transient behavior of the oscillation amplitudes and phase differences into account. This behavior is modeled using a set of linear differential equations. Their extraction from a netlist description is based upon the ideas of perturbation analysis and stochastic averaging. The modeling equations are valid in the neighbourhood of the oscillator's steady-state operating point and can be evaluated at very low computational cost. Another major advantage of the approach is that it explicitely separates the fast-varying steady-state behavior and the slow varying transient behavior. This allows for straightforward application of multi-rate simulation techniques, greatly boosting simulation speeds. The technique is illustrated for a quadrature oscillator.
- N.N. Bogoliubov and Y.A. Mitropolsky,phAsymptotic methods in the theory of non-linear oscillations, Hindustan Pulishing Corp., Delhi, 1961Google Scholar
- J. Crols and M. Steyaert,phCMOS Wireless Transceiver, Kluwer Academic Publishers, June 1997 Google ScholarDigital Library
- A. Demir et al., "Behavioral Simulation Techniques for Phase/Delay-Locked Systems", InphProc. IEEE CICC, pp. 21.3.1--4, 1994Google Scholar
- A. Demir, A. Mehrotra and J. Roychowdhury, "Phase Noise in Oscillators: A Unifying Theory and Numerical Methods for Characterization", InphIEEE Trans. Circ. and Syst.-I, vol. 47, no. 5, pp. 655--674, May 2000Google ScholarCross Ref
- M.I. Freidlin and A.D. Wentzell,phRandom perturbations of dynamical systems, 2nd ed., Springer, 1998Google Scholar
- A. Hadjimiri and T.H. Lee, "A General Theory of Phase Noise in Electrical Oscillators", InphIEEE J. Solid-State Circuits, vol. 33, no. 2, pp. 179--194, February 1998Google ScholarCross Ref
- F.X. Kaertner, "Analysis of White and f-α Noise in Oscillators", InphInt. J. Circuit Theory Appl., vol. 18, pp 485--519, 1990Google ScholarCross Ref
- J. Kevorkian and J.D. Cole,phPerturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981Google ScholarCross Ref
- N. Kryloff and N. Bogoliubov,phIntroduction to non-linear mechanics, Princeton University Press, New York, 1947Google Scholar
- M.F. Mar, "An Event-Driven PLL Behavioral Model with Applications to Design Driven Noise Modeling", InphProc. BMAS, Session 1.1, 1999Google Scholar
- O. Narayan and J. Roychowdhury, "Multi-Time Simulation of Voltage Controlled Oscillators", InphProc. IEEE DAC, Session 36, 1999 Google ScholarDigital Library
- M. Steyaert et al., "A 2-V CMOS Cellular Transceiver Front-End", In phIEEE Journ. Solid-State Circ., vol. 35, no. 12, pp. 1895--1907, December 2000Google ScholarCross Ref
- F. Verhulst,phNonlinear Differential Equations and Dynamical Systems, 2nd ed., Springer 1996 Google ScholarDigital Library
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- Behavioral modeling of (coupled) harmonic oscillators
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