Limitations of PLL simulation: Hidden oscillations in MatLab and SPICE

Bianchi, G.; Kuznetsov, Nikolay V.; Леонов, Г. А.; Yuldashev, M. V.; Yuldashev, R. V.

doi:10.1109/icumt.2015.7382409

Cited by 23 publications

(19 citation statements)

References 42 publications

(25 reference statements)

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“…Note that in this case a numerical simulation may give wrong estimates and should be used very carefully. For example, in [40] the SIMetrics SPICE model for a twophase PLL with a lead-lag filter gives two essentially different results of simulation with default "auto" sampling step (acquires lock) and minimum sampling step set to 1m (does not acquire lock -such behaviour agrees with the theoretical analysis). The same problems are also observed in MatLab Simulink [20], [21], [49], see, e.g.…”

Section: By the Design Of The Circuit (Eg Capacitors Have Limited Msupporting

confidence: 64%

“…Note that the corresponding initial states in SPICE (e.g. capacitor's initial charge) are zero by default but can be changed manually [40]. 10 In general (when the stable equilibria coexist and some of them may appear or disappear), the stable equilibria can be considered as a multiple-valued function of variable ω free ∆ , in which case the existence of its continuous singlevalue branch for |ω free …”

Section: Definition 1 a Set Of All Frequency Deviations |ω Free ∆ | mentioning

confidence: 99%

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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory

Леонов

Kuznetsov

Yuldashev

et al. 2015

IEEE Trans. Circuits Syst. I

118

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Abstract-The terms hold-in, pull-in (capture), and lock-in ranges are widely used by engineers for the concepts of frequency deviation ranges within which PLL-based circuits can achieve lock under various additional conditions. Usually only non-strict definitions are given for these concepts in engineering literature. After many years of their usage, F. Gardner in the 2nd edition of his well-known work, Phaselock Techniques, wrote "There is no natural way to define exactly any unique lock-in frequency" and "despite its vague reality, lock-in range is a useful concept". Recently these observations have led to the following advice given in a handbook on synchronization and communications "We recommend that you check these definitions carefully before using them" [1, p.49]. In this survey an attempt is made to discuss and fill some of the gaps identified between mathematical control theory, the theory of dynamical systems and the engineering practice of phase-locked loops. It is shown that, from a mathematical point of view, in some cases the hold-in and pull-in "ranges" may not be the intervals of values but a union of intervals and thus their widely used definitions require clarification. Rigorous mathematical definitions for the hold-in, pullin, and lock-in ranges are given. An effective solution for the problem on the unique definition of the lock-in frequency, posed by Gardner, is suggested.Index Terms-Phase-locked loop, nonlinear analysis, analog PLL, high-order filter, local stability, global stability, stability in the large, cycle slipping, hold-in range, pull-in range, capture range, lock-in range, definition, Gardner's problem on unique lock-in frequency, Gardner's paradox on lock-in range.

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Section: By the Design Of The Circuit (Eg Capacitors Have Limited Msupporting

confidence: 64%

Section: Definition 1 a Set Of All Frequency Deviations |ω Free ∆ | mentioning

confidence: 99%

Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory

Леонов

Kuznetsov

Yuldashev

et al. 2015

IEEE Trans. Circuits Syst. I

118

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“…The following article is further development of Bianchi et al (2015), which considers two-phase PLL. (project 6.38.505.2014, s.…”

Section: Introductionmentioning

confidence: 99%

“…The following article is further development of Bianchi et al (2015), which considers two-phase PLL. In our work the two-phase Costas loop is studied and corresponding examples, where simulation leads to unreliable results, is demonstrated in SPICE.…”

Section: Introductionmentioning

confidence: 99%

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Hidden oscillations in SPICE simulation of two-phase Costas loop with non-linear VCO

et al. 2016

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Simulation is widely used for analysis of Costas loop based circuits. However it may be a non-trivial task, because incorrect choice of integration parameters may lead to qualitatively wrong conclusions. In this work the importance of choosing appropriate parameters and simulation model is discussed. It is shown that hidden oscillations may not be found by simulation in SPICE, however it can be predicted by analytical methods.

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Analysis of Orbital Stability of Self-excited Periodic Motions in Lure System

Boiko

2020

Studies in Systems, Decision and Control

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Limitations of PLL simulation: Hidden oscillations in MatLab and SPICE

Cited by 23 publications

References 42 publications

Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory

Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory

Hidden oscillations in SPICE simulation of two-phase Costas loop with non-linear VCO

Analysis of Orbital Stability of Self-excited Periodic Motions in Lure System

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