Start-up robustness against resonator-Qs defects in a 2-GHz FBAR VCO

The root locus (RL) method is used to analyze the start-up robustness of a two-stage dual-resonator high-Q VCO. The VCO includes a parallel LC tank and an above-IC FBAR (f_s = 2.15 GHz, Q_s = 515) that is prone to contact defects during above-IC post-processing. Results obtained after careful circuit modeling explain the VCO´s start-up on f₁ before transitioning to and settling on the desired frequency f₀. The RL approach is shown to be effective in obtaining the constraints on resonator Q_s and revealing VCO failure modes. Only severe fabrication defects (Q_s <; 100) inhibit proper start-up on f₀.