  This paper introduces a conversion matrix method for linear periodically
time-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling that
offers precise and computationally efficient results to enable rapid design
iteration and optimization. Unlike many previous studies, which either assume
linear time-invariance (LTI) and therefore overlook phase noise aliasing
effects, or solve LPTV systems with noise folding and multiple sampling rate
conversions that heightens modeling and computational complexity, the proposed
conversion matrix method allows the designer to represent LPTV systems using
intuitive LTI-like transfer functions with excellent accuracy. Additionally,
the uncorrelated upsampling method addresses the cross-correlated spectrum of
cyclostationary noise sources by a simple matrix multiplication. This
eliminates the need to consider the beat frequency of the upsampled noise
source and the system with different sampling rates, thus improving
computational efficiency. The proposed algorithm is applied to modeling a
integer-N DPLL with time-varying proportional loop gain, and the modeling
accuracy is validated with Simulink transient simulations.
