Stability and Transient Dynamics of PLLs in Theory and Experiments

Riaz, Rabia; Prousalis, Dimitrios A.; Hoyer, Christian; Wagner, Jens; Ellinger, Frank; Jülicher, Frank; Wetzel, Lucas

doi:10.1109/ecctd49232.2020.9218377

Cited by 2 publications

(3 citation statements)

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“…In the linear model [6] the loop gain is constant and equal to the yellow dashed line. In the entrainment case the loop gain depends on the steady state phase relations between the reference and the PLL [50]. These compensate for the time delay dependence and render the loop gain constant, see Fig.…”

Section: B Network Stability and The Role Of State-dependent Loop Gainmentioning

confidence: 99%

“…First, we revisit the case of an oscillator that is being entrained by a reference oscillator [50]. The reference oscillator has index R and receives no input from other oscillators in the network, i.e., all c Rl = 0.…”

Section: A Entrainment Of a Pll By A Reference Signalmentioning

confidence: 99%

“…How network topology affects which synchronized states can exist has been addressed in [39]. Mutual synchronization and entrainment in the presence of cross-coupling time delay at microwave frequencies has been addressed in [2], [43]- [45], [50]. Questions related to phase noise and the stability of synchronized states against large perturbations have been addressed or are subject to ongoing research [59].…”

Section: H Experiments On Mutual Synchronizationmentioning

confidence: 99%

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Network Synchronization Revisited: Time Delays in Mutually Coupled Oscillators

et al. 2022

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Coordinated and efficient operation in large, complex systems requires the synchronization of the rhythms of spatially distributed components. Such systems are the basis for critical infrastructure such as satellite navigation, mobile communications, and services like the precision time protocol and Universal Coordinated Time. Different concepts for the synchronization of oscillator networks have been proposed, in particular mutual synchronization without and hierarchical synchronization from a reference clock. Established network synchronization models in electrical engineering address the role of inevitable crosscoupling time delays for network synchronization. Mutual synchronization has been studied using linear approximations of the coupling functions of these models. We review previous work and present a general model in which we study synchronization taking into account nonlinearities and finite time delays. As a result, dynamical phenomena in networks of coupled electronic oscillators induced by time delays, such as the multistability and stabilization of synchronized states can be predicted and observed. We study the linear stability of nonlinear states and predict for which system parameters synchronized states can be stable. We use these results to discuss the implementation of mutual synchronization for complex system architectures. A key finding is that mutual synchronization can result in stable in-and anti-phase synchronized states in the presence of large time delays. We provide the condition for which such synchronized states are guaranteed to be stable.

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Section: B Network Stability and The Role Of State-dependent Loop Gainmentioning

confidence: 99%

Section: A Entrainment Of a Pll By A Reference Signalmentioning

confidence: 99%