Matrix computations (3rd ed.)
Symbolic modeling of periodically time-varying systems using harmonic transfer matrices
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Operator-based model-order reduction of linear periodically time-varying systems
Proceedings of the 42nd annual Design Automation Conference
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This paper presents a new, frequency-domain based method for modeling and analysis of phase-locked loop (PLL) small-signal behavior, including time-varying aspects. Focus is given to PLLs with sampling phase-frequency detectors (PFDs) which compute the phase error only once per period of the reference signal. Using the harmonic transfer matrix (HTM) formalism, the well-known continuous-time, linear time-invariant (LTI) approximations are extended to take the impact of time-varying behavior, arising from the sampling nature of the PFD, into account. Especially for PLLs with a fast feedback loop, this time-varying behavior has severe impact on, for example, loop stability and cannot be neglected. Contrary to LTI analysis, our method is able to predict and quantify these difficulties. The method is verified for a typical loop design.