A Phase Tunable Rotary Traveling Wave Oscillator: Analysis and Calibration

Abstract

In this paper, a new phase error analysis is introduced for rotary traveling wave oscillators (RTWOs). Two new analytical approaches are used to extract closed-form equations for the RTWOs phase error arising from asymmetric resonator and inequality of negative transconductors. Derived equations show that the phase error can be cancelled and even controlled by adjusting the bias current of negative transconductors without any undesirable changing in oscillation frequency. This characteristic is then used for introducing a new phase error calibration method for RTWOs. This calibration method is not limited by the problems that limit the usage of the prior calibration technique. Our theoretical results are compared with accurate simulations to evaluate the validity of the proposed analysis and accuracy of the closed-form equations. Simulations have been done in 0. 18- $\mu$ m CMOS technology with a 1.8-V supply voltage. The evaluations show good agreement between analytical phase-error equations and simulation results. Also, appropriate simulations confirm the validity of the calibration method that is introduced in this paper.