Global stability analysis of nonlinear microwave circuits based on numerical implementation of bifurcation theory

The principal aim of the talk is to explain to a non-specialized audience the fundamentals of bifurcation theory and of its implementation in a microwave CAD environment in order to develop a self-consistent approach to the global stability analysis of nonlinear microwave circuits. The applications are intended to demonstrate that this technique allows a simple understanding of many difficult microwave design problems. The numerical implementation of Nyquist’s analysis for the detection of the natural frequencies of a large-signal steady state is first addressed, and the differences between forced and autonomous circuits are examined in depth. The numerically efficient construction of solution paths in the state space of a parametrized circuit is then considered, and an automatic switching-parameter algorithm for automatically overcoming the turning points is introduced. The automatic search of the solution path for bifurcations and the development of a global stability pattern for the circuit under consideration is demonstrated, and the relationships between stability and noise are high-lighted. Several practical examples of application are provided, including the search and sup-pression of spurious tones in microwave oscillators and VCO’s, the stability analysis of MEMS switching circuits under very large-signal drive, and the determination of the complex stability patterns of MEMS-reconfigurable microstrip antennas.