Stability of microwave and electronic devices: an approach from dynamical systems theory

The general problem of stability of microwave and RF devices and circuits in the presence of multifrequency or broadband signals is addressed. The problem is formulated in terms of the system of nonlinear nonautonomous differential equations for generalized coordinates in the phase space that can be attributed to, e.g., amplitudes of electric currents in circuits with lumped elements or mode amplitudes of the electromagnetic field in the distributed systems. An approach to the stability analysis is proposed that allows predicting the appearance of various kinds of instabilities including the deterministically chaotic motion. The new criterion based on the analysis of Lyapunov exponents is discussed that establishes the relation between maximal stable amplitude of oscillations and the levels of nonlinearity and damping in the system. The examples of one- and two-mode oscillators are considered in detail.