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This paper introduces a conversion matrix method for linear periodicallytime-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling thatoffers precise and computationally efficient results to enable rapid designiteration and optimization. Unlike many previous studies, which either assumelinear time-invariance (LTI) and therefore overlook phase noise aliasingeffects, or solve LPTV systems with noise folding and multiple sampling rateconversions that heightens modeling and computational complexity, the proposedconversion matrix method allows the designer to represent the LPTV systemsusing intuitive LTI-like transfer functions with excellent accuracy.Additionally, computational efficiency is improved through the uncorrelatedupsampling method, which eliminates the need to consider beat frequency ofnoise sources with different sampling rates. The proposed algorithm is appliedto modeling a DPLL with time-varying proportional loop gain, and the modelingaccuracy is validated with Simulink transient simulations.

Computationally-Efficient Linear Periodically Time-Variant Digital PLL Modeling Using Conversion Matrices and Uncorrelated Upsampling