On the Phase Noise Performance of Transformer-Based CMOS Differential-Pair Harmonic Oscillators

The white noise to phase noise conversion of one- and two-port CMOS differential-pair harmonic oscillators with transformer-based resonators is addressed in this paper. First, the operation of double-tuned transformer resonators is reviewed and design guidelines are proposed to maximize the quality factor. A rigorous approach is then employed to approximate the transformer network with a second order RLC model near the resonances, greatly simplifying the problem of handling the complex equations of a higher order resonator. The results are applied to phase noise calculations, leading to simple, yet accurate, closed-form 1/f² phase noise expressions in excellent agreement with the simulation results. It is formally proved, in a general case, that high-order resonators do not provide any fundamental advantage in comparison with simple LC-tanks. The two-port transformer based oscillator may be exploited to limit the phase noise contribution of the core transistors through optimization of the bias point and by leveraging the transformer voltage gain.