Jaijeet Roychowdhury University of Minnesota

Novel Numerical Simulation Methods and Design Formulae for Oscillatory Systems

The design, analysis and numerical simulation of oscillators presents challenges as well as unique opportunities.  In this talk, we will provide an overview of several threads of our recent work on oscillators, as time permits:

- Automated oscillator macromodelling and applications: The lack of fast yet accurate oscillator and PLL simulation methods has constituted a serious bottleneck in mixed-signal, RF and digital design flows. We will describe methods that, given differential equations for any oscillator (i.e., equivalent to, e.g., a SPICE-level circuit), will extract a simple nonlinear phase macromodel. We will show how such nonlinear phase Macromodels are capable of capturing a variety of important effects, including jitter and phase noise, injection locking, PLL lock and capture phenomena, cycle slipping, etc., while being faster by several orders of magnitude than SPICE-level simulation. We will also show how this nonlinear phase macromodel, when applied to large systems of networked biochemical and nanoelectronic oscillators, correctly predicts spontaneous pattern formation and edge detection.

- Analytical phase macromodel for 3-stage ring oscillator: In a non-numerical application of the theory behind the numerical macromodelling methods above, we obtain a closed-form equation for determining phase errors in an idealized 3 stage ring oscillator. The equation, which prominently features the famous Golden Ratio, provides direct design insight regarding the response of ring oscillators to perturbations and noise.

- Nonlinear feedback analysis of injection locking: We will present a rigorous, yet simple and graphical, procedure to understand and predict injection locking in negative-resistance LC oscillators.

- Fast envelope and multitime analysis simulation of oscillators: Finally, we will describe advanced numerical methods for fast but robust envelope simulation of oscillatory systems. If time permits, we will also outline a novel technique for correct, nonlinear, AC analysis of oscillators.

Bio:

Jaijeet Roychowdhury received the Bachelor's degree in Electrical Engineering from the Indian Institute of Technology, Kanpur, India, in 1987, and the Ph.D.  degree in Electrical Engineering and Computer Science from the University of California at Berkeley, in 1993. From 1993 to 1995, he was with the Computer-Aided Design (CAD) Laboratory, AT&T Bell Laboratories, Allentown, PA. From 1995 to 2000, he was with the Communication Sciences Research Division, Bell Laboratories, Murray Hill, NJ.  From 2000 to 2001, he was with CeLight Inc. (an optical networking startup), Silver Spring, MD. Since 2001, he has been with the Electrical and Computer Engineering Department and the Digital Technology Center, University of Minnesota, Minneapolis.