Catalog Description: Numerical modelling and analysis techniques are widely used in scientific and engineering practice; they are also an excellent vehicle for understanding and concretizing theory. This course covers topics important for a proper understanding of nonlinearity and noise: periodic steady state and envelope ("RF") analyses; oscillatory systems; nonstationary and phase noise; and homotopy/continuation techniques for solving "difficult" equation systems. An underlying theme of the course is relevance to different physical domains, from electronics (e.g., analog/RF/mixed-signal circuits, high-speed digital circuits, interconnect, etc.) to optics, nanotechnology, chemistry, biology and mechanics. Hands-on coding using the MATLAB-based Berkeley Model

Units: 4

Course Objectives: Using MAPP for fast/convenient modelling and analysis, Homotopy techniques for robust nonlinear equation solution, RF (nonlinear, nonstationary) noise concepts and their application - cyclostationary noise analysis - concepts of phase noise in oscillators, Modelling and analysis of oscillatory systems - harmonic, ring and relaxation oscillators - oscillator steady state analysis - perturbation analysis of amplitude-stable oscillators, RF (nonlinear periodic steady state) analysis - harmonic balance and shooting - Multi-time PDE and envelope methods - perturbation analysis of periodic systems (Floquet theory)

Student Learning Outcomes: Students will develop a facility in the above topics and be able to apply them widely across science and engineering.

Prerequisites: Consent of Instructor

Spring: 4.0 hours of lecture per week

Grading basis: letter

Final exam status: No final exam

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