Modeling, optimization and control of rotary traveling-wave oscillator

Rotary traveling-wave oscillator (RTWO) is a recently proposed transmission-line approach for multi-gigahertz rate clock generation. RTWO has the characteristics of both conventional LC tank oscillator and ring oscillator. Thus, it is difficult to be analyzed by a general-purpose method. This paper presents a systematic and efficient method for RTWO modeling and optimization. Equations for frequency, power dissipation, die area, loop gain and phase noise are formulated in posynomial forms. The resulting optimization problem is relaxed to be a Geometric Programming (GP) and can be efficiently solved with a convex optimization solver. A novel scheme to control the rotation direction is also suggested for skew control. Experimental results show that our method can rapidly compute the globally optimal trade-off and reduce the power by up to 85% for a 11.8 GHz RTWO design. Compared to a recently reported low-power methodology, the proposed design scheme can save about 50% of die area and achieve lower power dissipation as well as faster rise/fall time.