UC Santa Cruz
A Low Phase Noise Oscillator: Rotary Traveling Wave Oscillator
- Author(s): Chen, Yulin
- Advisor(s): Pedrotti, Kenneth
- et al.
Increasing demand for bandwidth in the digital communications, wired or wireless, requires integrated circuits operating at ever higher frequencies. Design and fabrication of low cost transmitter/receiver circuits remains increasingly challenging. With scaling, advances in complementary metal-oxide-semiconductor (CMOS) technologies have proven a serious competitor to the traditional SiGe, GaAs and bipolar technologies which have proven to be high power and expensive with a relatively low yield.
Voltage-controlled oscillators (VCOs) are essential building blocks for frequency synthesizers and clock-and-data recovery loops. Monolithic ring and LC oscillators have been commonly used as VCOs in such systems. Digital ring oscillators have inferior noise performance but can readily generate multiphase signals, while LC VCOs offer better phase noise for a given power dissipation. It remains challenging to achieve all the desired VCO specifications simultaneously as the frequency of operation approaches the self-resonance frequency of the on-chip inductors and the cutoff frequency of transistors.
The Rotary Traveling Wave Oscillator (RTWO) proposed by John wood in 2001 is a distributed oscillator that can be viewed as originating from distributed amplifiers. The RTWO operates by creating a rotating traveling wave within a closed-loop differential transmission line that serves as the resonant structure. Distributed CMOS inverters act as amplifiers to compensate line loss, and latches, to reduce amplitude variation. Amplifier gate and drain capacitance is absorbed into the transmission-line enabling energy to be recirculated adiabatically and results in a maximum frequency limited only by Fmax of the integrated circuit technology used. These oscillators were initially proposed for distributed clock generation in digital systems. Subsequently it has been realized that they are not only capable of very high frequency operation but also of multiphase operation ,with lithographically defined phase precision, and with lower phase noise compared to alternate approaches.
Here the fundamental physics and phase noise of RTWO are studied. First we investigate the connection between the distributed amplifier and the RTWO and the implications of lossy and periodically loaded transmission lines on its operation. This leads to the consideration of the inherently multi-mode nature of the resonator, which provides additional degrees of freedom relative to traditional designs and can be use to significantly decrease the rise and fall times of the oscillations leading to reduced phase noise. Operation is investigated in three different regions of operation: quasi-linear, critical oscillation and strongly nonlinear. In the weakly nonlinear region, a Duffing-van der Pol differential equation is developed to describe the oscillators' behavior. By using the elliptic perturbation method, a Jacobian Elliptic function type solution is derived that provides us with a more accurate calculation of the oscillating frequency relative to the first order estimates to date.
Subsequently and more importantly the novel aspects of phase noise in the RTWO is investigated. Two separate but closely related models of oscillator phase noise are introduced. The first is proposed by Leeson and the other one is by Lee and Hajimiri are investigated as relevant to these oscillators. For thermally induced white phase noise using Abidi's sampling mechanism a theoretical frame work is developed for the effect of broadband white noise on RTWOs.
Following this and most importantly the upconversion of flicker noise is studied on its impact on close-in phase noise. Several upconversion mechanisms are introduced and investigated that are unique to RTWOs. The interaction of line dispersion with amplifier nonlinearity is shown to lead to the upconversion of 1/f noise to close-in phase noise in the weakly nonlinear regime. Dispersion is implicated more generally in the creation of drive transistor asymmetries that can also lead to device 1/f noise upconversion in the strongly nonlinear large signal regime. Asymmetries in the integrated contribution of transistor gm variations to 1/f noise are further shown to arise from the latency of the amplifier response.
Most importantly we develop a novel technique we term "Gate Offset" to provide a compensatory phase alteration at the amplifiers that can not only remove the 1/f contribution due to amplifier delay but also compensate for dispersion induced delays.
Lastly, a widely tunable monolithic integrated rotary traveling wave oscillator based on the design intuition developed from this theory is designed, fabricated and measured. Results are presented that show a doubling of performance relative to the state of the art.