{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:33:21Z","timestamp":1773815601037,"version":"3.50.1"},"reference-count":80,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"10","license":[{"start":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T00:00:00Z","timestamp":1443657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Circuits Syst. I"],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1109\/tcsi.2015.2476295","type":"journal-article","created":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T19:03:27Z","timestamp":1443207807000},"page":"2454-2464","source":"Crossref","is-referenced-by-count":119,"title":["Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory"],"prefix":"10.1109","volume":"62","author":[{"given":"Gennady A.","family":"Leonov","sequence":"first","affiliation":[]},{"given":"Nikolay V.","family":"Kuznetsov","sequence":"additional","affiliation":[]},{"given":"Marat V.","family":"Yuldashev","sequence":"additional","affiliation":[]},{"given":"Renat V.","family":"Yuldashev","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref73","author":"dyer","year":"2004","journal-title":"Wiley Survey of Instrumentation and Measurement"},{"key":"ref72","author":"de muer","year":"2003","journal-title":"CMOS Fractional-N Synthesizers Design for High Spectral Purity and Monolithic Integration"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2870-5"},{"key":"ref70","author":"irwin","year":"1997","journal-title":"The Industrial Electronics Handbook"},{"key":"ref76","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06728-4","author":"meyer-baese","year":"2004","journal-title":"Digital Signal Processing with Field Programmable Gate Arrays"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2015.09.272"},{"key":"ref74","author":"shu","year":"2005","journal-title":"CMOS PLL Synthesizers Analysis and Design"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/NORCHP.2009.5397821"},{"key":"ref75","author":"baker","year":"2011","journal-title":"CMOS circuit design layout simulation"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1002\/9780470021804"},{"key":"ref78","doi-asserted-by":"crossref","DOI":"10.1007\/978-81-322-2041-1","author":"purkayastha","year":"2015","journal-title":"A Digital Phase Locked Loop Based Signal and Symbol Recovery System for Wireless Channel"},{"key":"ref79","first-page":"730","article-title":"Pull-in range of the pll-based circuits with proportionally-integrating filter","author":"alexandrov","year":"2015","journal-title":"1st IFAC Conf Modelling Identification Control Nonlinear Syst IFAC Proc Vol (IFAC-PapersOnline)"},{"key":"ref33","author":"blanchard","year":"1976","journal-title":"Phase-Locked Loops"},{"key":"ref32","author":"bakshi","year":"2009","journal-title":"Linear ICs and Applications"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68030-9"},{"key":"ref30","first-page":"2086","article-title":"Asymptotic stability of an equilibrium position of a family of systems of differential equations","volume":"14","author":"kharitonov","year":"1978","journal-title":"Differentsialnye Uravneniya"},{"key":"ref37","author":"zucchelli","year":"2007","journal-title":"?Phase locked loop tutorial?"},{"key":"ref36","first-page":"475","article-title":"Top-down PLL design methodology combining block diagram, behavioral transistor-level simulators","author":"nicolle","year":"2007","journal-title":"Proc IEEE Radio Freq Integr Circuits (RFIC) Symp"},{"key":"ref35","first-page":"1081","article-title":"Modeling of fractional-N division frequency synthesizers with SIMULINK and MATLAB","volume":"2","author":"brigati","year":"0","journal-title":"Proc 8th IEEE Int Conf Electron Circuits Syst (ICECS 2001)"},{"key":"ref34","author":"brendel","year":"2013","journal-title":"Millimeter-Wave Radio-over-Fiber Links Based on Mode-Locked Laser Diodes"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0193-3"},{"key":"ref62","author":"suarez","year":"2003","journal-title":"Stability Analysis of Nonlinear Microwave Circuits"},{"key":"ref61","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-01676-9","author":"tranter","year":"2010","journal-title":"Basic Simulation Models of Phase Tracking Devices Using MATLAB"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1982.1095423"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2012.2188953"},{"key":"ref64","first-page":"600","article-title":"Frequency estimates of the number of cycle slidings in phase control systems","volume":"44","author":"ershova","year":"1983","journal-title":"Avtomat Remove Control"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cds.2013.0438"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1142\/7260"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1002\/9780470178737"},{"key":"ref29","author":"gelig","year":"0","journal-title":"Stability of Nonlinear Systems with Nonunique Equilibrium States"},{"key":"ref67","author":"best","year":"1984","journal-title":"Phase-Locked Loops Design Simulation and Applications"},{"key":"ref68","author":"wolaver","year":"1991","journal-title":"Phase-Locked Loop Circuit Design"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1109\/41.544547"},{"key":"ref2","author":"lindsey","year":"1973","journal-title":"?A bibliography of the theory and application of the phase-lock principle ?"},{"key":"ref1","author":"kihara","year":"2002","journal-title":"Digital Clocks for Synchronization and Communications"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS.2015.7168688"},{"key":"ref22","first-page":"704","article-title":"Nonlinear models of BPSK Costas loop","volume":"1","author":"kudryasoha","year":"0","journal-title":"Proc 11th Int Conf Informat Control Autom Robot (ICINCO 2014)"},{"key":"ref21","first-page":"1296","article-title":"A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis","author":"best","year":"2015","journal-title":"Proc IEEE Amer Control Conf (ACC)"},{"key":"ref24","first-page":"83","article-title":"BPSK Costas loop: Simulation of nonlinear models in MATLAB Simulink","volume":"2015 january","author":"kuznetsov","year":"2014","journal-title":"Proc IEEE 6th Int Congr Ultra Modern Telecommun Control Syst Workshops (ICUMT)"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/ICUMT.2014.7002080"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2014.2356873"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-014-0846-x"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"5445","DOI":"10.3182\/20140824-6-ZA-1003.02501","article-title":"Hidden attractors in dynamical systems: Systems with no equilibria, multistability and coexisting attractors","volume":"19","author":"kuznetsov","year":"2014","journal-title":"IFAC Proc Volumes (IFAC-PapersOnline)"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2015-02470-3"},{"key":"ref59","doi-asserted-by":"crossref","DOI":"10.1142\/2638","author":"leonov","year":"1996","journal-title":"Frequency-Domain Methods for Nonlinear Analysis Theory and Applications"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-12261-6"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2003.1243434"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/26.64662"},{"key":"ref55","first-page":"513","article-title":"Stability and dynamical properties of astatic frequency synchronization system","volume":"8","author":"bakaev","year":"1963","journal-title":"Radiotekhnika i Elektronika"},{"key":"ref54","author":"goldman","year":"2007","journal-title":"Phase-Locked Loops Engineering Handbook for Integrated Circuits"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.07.005"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1997.652491"},{"key":"ref10","author":"davis","year":"2011","journal-title":"Radio Frequency Circuit Design"},{"key":"ref11","author":"leonov","year":"2014","journal-title":"Nonlinear Mathematical Models Of Phase-Locked Loops Stability and Oscillations"},{"key":"ref40","author":"bianchi","year":"2015","journal-title":"?Limitations of PLL simulation Hidden oscillations in SPICE analysis ?"},{"key":"ref12","doi-asserted-by":"crossref","DOI":"10.1007\/b95399","author":"margaris","year":"2004","journal-title":"Theory of the Non-linear Analog Phase Locked Loop"},{"key":"ref13","author":"suarez","year":"2009","journal-title":"Analysis and Design of Autonomous Microwave Circuits"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2002.1024769"},{"key":"ref15","year":"2004","journal-title":"Method for Guaranteeing Stable Non-Linear PLLs"},{"key":"ref16","author":"krylov","year":"1947","journal-title":"Introduction to Non-Linear Mechanics"},{"key":"ref17","doi-asserted-by":"crossref","DOI":"10.1142\/6580","author":"kudrewicz","year":"2007","journal-title":"EQUATIONS of PHASE-LOCKED LOOPS Dynamics Oncircle Torus and Clinder"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2012.2213362"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2014.08.033"},{"key":"ref80","doi-asserted-by":"crossref","DOI":"10.1201\/9781420041408","author":"chen","year":"2002","journal-title":"The Circuits and Filters Handbook"},{"key":"ref4","author":"viterbi","year":"1966","journal-title":"Principles of Coherent Communications"},{"key":"ref3","author":"gardner","year":"1966","journal-title":"Phase-Lock Techniques"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/0471732699"},{"key":"ref5","author":"shakhgil'dyan","year":"1966","journal-title":"Fazovaya avtopodstroika chastoty"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/9781118310144"},{"key":"ref7","author":"best","year":"2007","journal-title":"Phase-Locked Loops Design Simulation and Applications"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"8253","DOI":"10.3182\/20140824-6-ZA-1003.02772","article-title":"Nonlinear analysis of classical phase-locked loops in signal's phase space","volume":"19","author":"kuznetsov","year":"2014","journal-title":"IFAC Proc Volumes (IFAC-PapersOnline)"},{"key":"ref9","author":"gardner","year":"1979","journal-title":"Phase-Lock Techniques"},{"key":"ref46","first-page":"1415","article-title":"Study of a piecewise-linear system of phase-locked frequency control","author":"shakhtarin","year":"1969","journal-title":"Radiotech &Electr (in Russian)"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/682318"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300024"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1007\/BF01030651"},{"key":"ref42","first-page":"1","article-title":"Integrazione di unequazione differenziale presentatasi in elettrotechnica","volume":"2","author":"tricomi","year":"1933","journal-title":"Annali della Scuola Normale Superiore di Pisa"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1002\/9781118383285"},{"key":"ref44","author":"stensby","year":"1997","journal-title":"Phase-Locked Loops Theory and Applications"},{"key":"ref43","author":"andronov","year":"1937","journal-title":"Theory of Oscillators"}],"container-title":["IEEE Transactions on Circuits and Systems I: Regular Papers"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8919\/7277125\/07277189.pdf?arnumber=7277189","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T15:19:43Z","timestamp":1692026383000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7277189\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":80,"journal-issue":{"issue":"10"},"URL":"https:\/\/doi.org\/10.1109\/tcsi.2015.2476295","relation":{},"ISSN":["1549-8328","1558-0806"],"issn-type":[{"value":"1549-8328","type":"print"},{"value":"1558-0806","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]}}}