An efficient linear-time variant simulation technique of oscillator phase sensitivity function

This paper presents a fast and accurate simulation technique to evaluate the impulse sensitivity function (ISF) of an oscillator. The proposed method, based on the linear-time variant (LTV) analysis of oscillators, computes the impulse phase response by means of periodic steady-state (PSS) and periodic transfer function (PXF) simulations available in commercial simulators (Spectre, Eldo, etc.). This technique overwhelms the classical simulation method based on transient analysis and injection of charge pulses along the oscillator period in terms of speed, precision and ease of use. The good accuracy of the proposed method has been verified in two oscillator topologies, namely a Van der Pol and a ring oscillator.

I. Introduction

Phase noise of VCOs (Voltage Controlled Oscillators) and PLLs (Phase Locked Loops) is still a major issue in the design of wireless communication systems limiting the maximum achievable data transfer rate [1]. Since bit-rates keep increasing with time, this results in more stringent requirements of the transceiver and a deep insight of phase noise generation mechanism is necessary to perform an optimum design. In the framework of linear time variant (LTV) model, which is the most suitable for circuits with a periodically varying operating point such as oscillators, the impulse sensitivity function (ISF) introduced by Hajimiri and Lee [2] provides a very useful tool for the analysis of the oscillator system dynamics under small signal excitations, such as MOSFET current noise, and thus for evaluating the oscillator phase noise. The above mentioned sensitivity function is also adopted to analyze injection locking mechanism in oscillators [3]. This phenomenon is observed when an oscillator is perturbed by a weak external signal whose frequency is close enough but not equal to that of the unperturbed oscillator and has been exploited to realize quadrature oscillators or oscillators with finer phase separation [4] and low-power frequency dividers [5]. At the present time, the ISF cannot be directly computed by commercially available circuit simulators, thus requiring ad hoc simulations. The traditional technique, proposed in [2] and adopted by RF designers, is based on the definition of impulse phase response of an oscillator. By means of time-domain transient simulations, current pulses are injected in an oscillator node and the phase response of the system is evaluated. This technique basically trades accuracy off against implementation simplicity and simulation speed. In this paper, a frequency-domain simulation method for the ISF is pre-sented, based on a small-signal time-varying analysis, namely the periodic transfer function (PXF) simulation available in Cadence environment [6]. It overwhelms the transient analysis-based method in terms of both accuracy and speed.