Phase noise reduction by resistor abutment in differential ring VCOs

In this work, a differential ring VCO architecture and its phase noise are inspected. Resistor bridges are added between the stages that, as evident through theory and simulation, are capable of reducing flicker and thermal noise upconversion. A differential two-stage ring VCO is considered operating at 2.5 GHz for simulation in 180 nm CMOS technology which show phase noise reduction by 4 dBc/Hz and 6.5 dBc/Hz at 10 kHz offset frequency for resistor values of 11 kΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega }$$\end{document} and 5 kΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega }$$\end{document} respectively with similar power dissipation compared to the unmodified architecture. Similar reduction in phase noise also observed in a three-stage structure operating at 1.5 GHz.