A Study of the Design Criteria for 4-Stage, Pseudo-Differential Ring Oscillators to Self-Start From Any Initial State

This paper is a study of the minimum set of sufficient conditions that allow a 4-stage pseudo-differential ring oscillator to self-start from any initial state and the corresponding design criteria that allow these conditions to be met. First, a mathematical model that describes all the possible points of equilibrium is derived by exploiting the symmetry and regularity of the chain of gain stages that form the ring oscillator. The analysis then proceeds to determine the set of minimum conditions that guarantee that the ring oscillator can self-start. The result is a collection of equations that provides the proper design criteria to avoid any start-up failure. These criteria are only a function of the supply, the devices threshold voltage and the ratio between the forward and cross-coupled inverters. No further process technology or system parameters need be known. A graphic representation of the equations allows us to determine at a glance the region of guaranteed oscillations. Simulations that cover process and temperature corners of several 4-stage pseudo-differential ring oscillators built with different device sizes in a 7nm FinFET technology confirm the validity of the mathematical analysis, and the equations thereby derived.