Stability and oscillation analysis at circuit level and through semi-analytical formulations

Abstract

Harmonic balance provides steady-state solutions only and has significant shortcomings when addressing oscillatory regimes. As a result, complementary methodologies are required both to ensure the stability of the solution obtained and to design/simulate oscillator circuits. The complexity of the stability analysis increases with the number of active elements and the intricacy of the topology, so there can be uncertainties in the case of complex structures. On the other hand, as recently demonstrated oscillators enable a compact and low-cost implementation of RFID readers and radar systems, which comes at the expense of a more complex performance, very difficult/impossible to simulate with commercial HB. This work presents a review of recent advances on stability and oscillation analysis at circuit level and through semi-analytical formulations. At circuit level, a method for the stability analysis of complex microwave systems is presented, based on the calculation of the characteristic determinant, extracted from the commercial simulator through a judicious partition of the system into simpler blocks. This determinant will be used for the first time to obtain the stability boundaries through a contour-intersection method, able to provide multivalued and disconnected curves. At a semi-analytical level, a realistic numerical model of the standalone oscillator, extracted from HB simulations, is introduced in an analytical formulation that describes the oscillator interaction with other elements. Here it will be applied to a self-injection locked radar, in which the oscillator is injected by its own signal after this signal undergoes propagation and reflection effects. A procedure to determine the stability properties considering the time delay of the signal envelope is presented for the first time. Using the same self-injection concept, a new stabilization method to reduce the phase-noise of an existing oscillator with minimum impact on its original frequency is described.