Computing phase noise eigenfunctions directly from harmonic balance/shooting matrices

A prerequisite for computing phase noise is finding the Perturbation Projection Vector (PPV), a periodic vector function that encapsulates the “transfer function” between individual noise sources and the phase noise of the oscillator. In this paper, we illustrate a novel technique for calculating the PPV that has several advantages over the monodromy matrix method currently used. The new method can be applied in the context of both frequency- and time-domain steady-state computations, and involves only a single linear solution of the appropriate Jacobian matrix. It also removes the need for applying heuristics in choosing the correct PPV from a potentially large set of choices, a feature particularly useful for high-Q oscillators. We compare PPVs obtained with the new method with those from the monodromy matrix method