A Rigorous Phase Noise Analysis of Tuned Ring Oscillators

Tuned ring oscillators have found numerous applications due to their ability to generate multiple phases at high frequencies of operation while maintaining high signal purity. However, a comprehensive phase noise theory that explains the phase noise performance of tuned rings as a function of design parameters such as the number of elements and inter element phase shift is lacking. This paper rigorously builds such a theory and demonstrates that the phase noise improves by a factor of 10log₁₀N as the number of elements (N) is increased. Further, the phase noise deteriorates (by a factor of 40log₁₀cosDeltaPhi at least) when the inter element phase shift DeltaPhi is increased. In the context of multiple phase generation, under a fixed current budget, we demonstrate that it is beneficial to use a larger ring sizes. Extensive GHz-range simulations as well as measurements of prototype oscillators validate these claims