Start-up and Frequency Stability Analysis using Time-Varying Root Locus

Undesired points of operation i.e. real pole in the right half of s-plane causes relaxation oscillation, especially in GHz-range of monolithic oscillators. They also prove to be 'hard' target for most of the very powerful circuit simulators, like SpecterRF for example. Since the behavior is best described by the Eigen values of characteristic polynomial, then we settle on investigating the operating points using the time varying root locus (TVRL) method. The numerical QZ algorithm has been practiced to compute the characteristic roots relative to periodic steady-state (PSS). The circuit is modified to avoid relaxation process and it confirms the proper sinusoidal operation of oscillator.