Stability and bifurcation analysis based on harmonic balance

Prof. Almudena Suárez, University of Cantabria

The harmonic-balance method is mostly used for the nonlinear analysis of high-frequency circuits, often containing distributed elements. Due to the Fourier series representation of the variables, only steady states are simulated and convergence to either stable or unstable solutions can be obtained. Thus, the stability analysis is essential. The talk presents techniques for stability and bifurcation analysis, based on harmonic balance. Different approaches for the local-stability analysis of nonlinear regimes will be shown, with emphasis on pole-zero identification, using the conversion matrix. Techniques will also be shown presented for the detection of the most common types of bifurcations from constant, periodic and quasi-periodic solutions and for obtaining the bifurcation loci, in the plane defined by two system parameters. The techniques have been extended to the detection of the initial bifurcations taking place in common routes to chaos, like the period-doubling and quasi-periodic routes. Finally, the envelope-transient method and its application to bifurcation analysis will be discussed.

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BIOGRAPHY

Almudena Suárez was born in Santander, Spain.  She received the degree in Electronic Physics from the University of Cantabria (Spain) in June 1987, and the Ph.D. degree from the same University in July 1992.  In 1987 she joined the Electronics Department of the University of Cantabria, working on nonlinear simulation. She received the Ph.D. degree in Electronics from the University of Limoges in February 1993. From 1995 she has been an associate professor at the University of Cantabria, and a member of its Communications Engineering Department. Her areas of interest include the nonlinear design of microwave circuits and, specially, the nonlinear stability analysis, the phase noise analysis and the investigation of chaotic regimes. She is a senior member of IEEE. She has written a book on nonlinear stability analysis for the publisher Artech House.