A three-stage coupled ring oscillator with quadrature outputs

Modeling and analysis of a coupled three-stage ring oscillator is presented in this paper. The oscillator consists of two ordinary three-stage ring oscillators, which are coupled to each other and oscillate with the same frequency, but with 30 degree phase difference resulting in three sets of quadrature outputs. A simple and insightful technique for modeling coupled oscillators is proposed here. This technique is then used to analyze the coupled oscillator. It has been proven analytically that the coupled two rings, oscillate with the same frequency, but with 30 degree phase shift. It has also been shown that for small transistor sizes, the coupled ring oscillator has an inherent capability of oscillating with frequencies as high as 1.577 times that of a single ring. The accuracy of the proposed linearized model is verified with SPICE simulations.