Continuation Analysis of a Phase/quadrature Electronic oscillator

An RF phase-quadrature oscillator is analyzed. The designer "ensured" the phase-quadrature working condition through a suitable cross-coupled electrical connection between the two parts composing the complete oscillator. Through a detailed analysis of the dynamics of this oscillator, we show that device mismatch can lead to an unexpected stable working mode where the oscillator does not operate in a phase-quadrature condition. The proposed analysis has been first performed on a simplified model of the oscillator to allow the use of software packages for numerical continuation. The results of the analysis of the simplified oscillator dynamics have been then checked by means of accurate device models from a 65 nm RF technology library.