Physical processes of phase noise in differential LC oscillators

Abstract

There is an unprecedented interest among circuit designers today to obtain insight into the mechanisms of phase noise in LC oscillators. For only with this insight is it possible to optimize oscillator circuits using low-quality integrated resonators to comply with the exacting phase noise specifications of modern wireless systems. In this paper we concentrate on an understanding of the popular differential LC oscillator. We introduce simple models to capture the nonlinear processes that convert voltage or current thermal noise in resistors or transistors into phase noise in the oscillator. The analysis does not require hypothetical elements, such as limiters or amplitude control loops, to fully explain phase noise. A simple expression at the end accurately specifies thermally induced phase noise, and lends substance to Leeson's original hypothesis. Next, the upconversion of flicker noise into phase noise is traced to mechanisms first identified in the 1930's, but apparently since forgotten. Unlike thermally induced phase noise, which appears as phase modulation sidebands, flicker noise is shown to upconvert by bias-dependent frequency modulation. The results are validated against SpectreRF simulations and measurements on two differential CMOS oscillators tuned by resonators with very different Q's.