Phase Transition Analysis of Dual-Mode Standing-Rotary Traveling-Wave Oscillator.

In this paper, a dual-mode standing-rotary traveling-wave oscillator (S-RTWO) is analyzed. In order to force the conventional RTWO to oscillate in the standing wave mode, an ideal switch is used for shorting two differential nodes of the RTWO circuit. The closed-form equations, which describe the transitions of phases between the standing wave mode and the rotary traveling wave mode of the oscillator, are derived, and the delays of transitions between two modes of the oscillator are extracted by using these equations. Besides, the oscillation start-up delay is analyzed, and the closed-form equation for the start-up delay is obtained in terms of circuit elements. Finally, our theoretical results are compared with appropriate and accurate simulations to evaluate the validity of the delays analysis and the accuracy of the closed-form equations. Simulations of the dual-mode oscillator have been done in a 0.18- $\mu \text{m}$ CMOS technology with a 1.8-V supply voltage. The evaluations show very good agreement between analytical equations and simulation results, and confirm the validity and accuracy of the delays analysis. [ABSTRACT FROM AUTHOR]