The main effort in oscillator phase noise calculation and macromodeling lies in computing a vector function called the perturbation projection vector (PPV). Current techniques for PPV calculation use time-domain numerics to generate the system's monodromy matrix, followed by full or partial eigenanalysis. We present superior methods that find the PPV using only a single linear solution of the oscillator's time-or frequency-domain steady-state Jacobian matrix. The new methods are better suited

more »

... r implementation in existing tools with harmonic balance or shooting capabilities (especially those incorporating "fast" variants), and can also be more accurate than explicit eigenanalysis. A key advantage is that they dispense with the need to select the correct one eigenfunction from amongst a potentially large set of choices, an issue that explicit eigencalculation-based methods have to face. We illustrate the new methods in detail using LC and ring oscillators. Index Terms-Eigenvalues and eigenfunctions, iterative methods, oscillator noise, phase jitter, phase noise, reduced-order systems, timing jitter. 1 A varied and extensive literature, developed over many decades, exists on the phase noise problem. We do not provide a review of prior work here as it is not central to our contribution, but we refer the interested reader to, e.g., [4], [6] . 2 Corresponding to eigenvalue 1, existence of which is guaranteed by Floquet analysis of orbitally stable oscillators (see e.g., [5] ).