Analytical formulation of transient oscillation amplitude in rotary traveling wave oscillators

Abstract

This paper presents an accurate analysis for deriving transient oscillation amplitude of Rotary Traveling Wave Oscillators (RTWOs) as a transmission-line based and high frequency circuit. The procedure of the paper is based on considering the nonlinear behavior of negative transconductors that are used for loss compensation of the transmission line. Finally, a closed-form expression for the time-domain amplitude of the RTWOs is obtained. The proposed useful and accurate expression could be used for designing the RTWOs for high performance-high speed systems. Also, it enables us to analyze and synthesize the oscillators with the desired transient behavior. This aspect of the RTWOs is not studied in previous works. The proposed theoretical results are then compared with accurate simulations. Simulations have been done in 0.18 μm CMOS technology with 1.8 V supply voltage. Results show less than 10% difference in steady state oscillation amplitude of theoretical expression and simulations. Considering the nonlinear equation of the RTWOs amplitude, complicated type of solving, simplifications and its numerical solution, the proposed derived expression has a good agreement with simulations.