Stability Analysis of Oscillation Modes in Quadruple-Push and Rucker's Oscillators

Oscillator systems composed by
N
sub-oscillators coupled through a symmetric linear network enable the combination of output power at the first or
N
th harmonic component of the oscillation frequency of each sub-oscillator. However, they have the drawback of a possible coexistence of different oscillation modes, which limits their practical application. This paper presents an in-depth stability analysis of coexisting steady-state solutions in Rucker's oscillator and
N
-push oscillators. Criteria are provided to avoid undesired oscillation modes. The coupled system is described by means of a semianalytical formulation based on numerical models of the active subcircuits, extracted from harmonic-balance (HB) simulations. Each active subcircuit is composed by the transistor(s), feedback elements, and termination load. The use of the HB numerical models allows a realistic prediction of the behavior of the globally coupled oscillator. Alternatively, a graphical technique is provided to obtain the different oscillation modes using full HB simulations. The perturbation of the reduced-order nonlinear system enables the stability and phase-noise analysis of the steady-state oscillatory solutions. In the derived formulation for phase-noise analysis, both flicker- and white-noise perturbations are considered. The different techniques have been applied to a Rucker's oscillator at 3.9 GHz and a quadruple-push oscillator at 15.6 GHz.