A System of Two Coupled Oscillators With a Continuously Controllable Phase Shift

We present a novel generalization of quadrature oscillators (QVCO) which we call “arbitrary phase oscillator” or APO for short. In contrast to a QVCO which generates only quadrature phases, the APO is capable of continuously generating any desired phase at its output. The proposed structure employs a novel coupling mechanism to generate arbitrary phase shifts between two coupled oscillators without the need for an explicit phase shifter. A rigorous nonlinear dynamic analysis is presented to give a closed-form formula for the generated phase shifts, and the theory is verified by numerical simulation as well as measurement results of a prototype chip fabricated in 130-nm CMOS technology. The prototype APO has a frequency tuning range of 4.90-5.65 GHz and is continuously phase tunable from 0° to 360° across the entire frequency range. The APO structure can be used in designing novel coupled-oscillator-based phased arrays for 5G wireless communications.