A Time-Variant Analysis of Fundamental $1/f^{3}$ Phase Noise in CMOS Parallel $LC$ -Tank Quadrature Oscillators

This paper presents a rigorous time-variant analysis of the 1/f MOS device noise upconversion into 1/
f
phase noise for two of the most popular parallel-coupled quadrature CMOS harmonic oscillators. Simple closed-form equations for the fundamental 1/f
³
phase-noise spectrum are derived and validated through SpectreRF simulations, proving that the two topologies display remarkably different sensitivities to the low-frequency noise sources. Based on the developed analysis, useful general design insights are also presented.