An in-depth investigation of oscillation modes in free-running oscillators loaded with multi-resonance networks is presented. It focuses on the mechanisms leading to the coexistence of stable oscillation modes, which may give rise to uncertainty in the physical behaviour. The multiple periodic and quasi-periodic solutions are detected and related to the stability properties of the dc solution and each of the periodic modes. Two different types of Hopf-bifurcation loci enable a global understanding of the circuit operation. The investigation is initially carried out with an analytical formulation and then extended to harmonic-balance simulations. The results have been experimentally validated through their application to a HEMT-based cross-coupled oscillator, at 0.65 and 2.4 GHz.

This work has been supported by the Spanish Ministry of Economy and Competitiveness under project TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069). The authors would like to thank S. Pana, University of Cantabria, for her assistance with the manufacturing process.