Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory
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 l...
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| Autor*in: |
Leonov, Gennady A [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
Gardner's problem on unique lock-in frequency |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on circuits and systems / 1 - New York, NY : Institute of Electrical and Electronics Engineers, 1992, 62(2015), 10, Seite 2454-2464 |
|---|---|
| Übergeordnetes Werk: |
volume:62 ; year:2015 ; number:10 ; pages:2454-2464 |
| Links: |
|---|
| DOI / URN: |
10.1109/TCSI.2015.2476295 |
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| 520 | |a 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." 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, pull-in, 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. | ||
| 650 | 4 | |a definition | |
| 650 | 4 | |a global stability | |
| 650 | 4 | |a capture range | |
| 650 | 4 | |a hold-in range | |
| 650 | 4 | |a lock-in range | |
| 650 | 4 | |a Gardner's problem on unique lock-in frequency | |
| 650 | 4 | |a local stability | |
| 650 | 4 | |a high-order filter | |
| 650 | 4 | |a nonlinear analysis | |
| 650 | 4 | |a phase-locked loop | |
| 650 | 4 | |a pull-in range | |
| 650 | 4 | |a Analog PLL | |
| 650 | 4 | |a stability in the large | |
| 650 | 4 | |a cycle slipping | |
| 650 | 4 | |a Gardner's paradox on lock-in range | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Dynamical Systems | |
| 650 | 4 | |a Mathematics | |
| 700 | 1 | |a Kuznetsov, Nikolay V |4 oth | |
| 700 | 1 | |a Yuldashev, Marat V |4 oth | |
| 700 | 1 | |a Yuldashev, Renat V |4 oth | |
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10.1109/TCSI.2015.2476295 doi PQ20160617 (DE-627)OLC1959253204 (DE-599)GBVOLC1959253204 (PRQ)a1559-dca7858ca282402e69d8ea10ed236988ba345cbc2b33b08f003c4e57619ff3530 (KEY)0213966920150000062001002454holdinpullinandlockinrangesofpllcircuitsrigorousma DE-627 ger DE-627 rakwb eng 000 620 DNB Leonov, Gennady A verfasserin aut Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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." 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, pull-in, 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. definition global stability capture range hold-in range lock-in range Gardner's problem on unique lock-in frequency local stability high-order filter nonlinear analysis phase-locked loop pull-in range Analog PLL stability in the large cycle slipping Gardner's paradox on lock-in range Control theory Dynamical Systems Mathematics Kuznetsov, Nikolay V oth Yuldashev, Marat V oth Yuldashev, Renat V oth Enthalten in IEEE transactions on circuits and systems / 1 New York, NY : Institute of Electrical and Electronics Engineers, 1992 62(2015), 10, Seite 2454-2464 (DE-627)131043080 (DE-600)1100194-X (DE-576)02804679X 1549-8328 nnns volume:62 year:2015 number:10 pages:2454-2464 http://dx.doi.org/10.1109/TCSI.2015.2476295 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7277189 http://search.proquest.com/docview/1729175442 http://arxiv.org/abs/1505.04262 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2059 AR 62 2015 10 2454-2464 |
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10.1109/TCSI.2015.2476295 doi PQ20160617 (DE-627)OLC1959253204 (DE-599)GBVOLC1959253204 (PRQ)a1559-dca7858ca282402e69d8ea10ed236988ba345cbc2b33b08f003c4e57619ff3530 (KEY)0213966920150000062001002454holdinpullinandlockinrangesofpllcircuitsrigorousma DE-627 ger DE-627 rakwb eng 000 620 DNB Leonov, Gennady A verfasserin aut Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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." 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, pull-in, 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. definition global stability capture range hold-in range lock-in range Gardner's problem on unique lock-in frequency local stability high-order filter nonlinear analysis phase-locked loop pull-in range Analog PLL stability in the large cycle slipping Gardner's paradox on lock-in range Control theory Dynamical Systems Mathematics Kuznetsov, Nikolay V oth Yuldashev, Marat V oth Yuldashev, Renat V oth Enthalten in IEEE transactions on circuits and systems / 1 New York, NY : Institute of Electrical and Electronics Engineers, 1992 62(2015), 10, Seite 2454-2464 (DE-627)131043080 (DE-600)1100194-X (DE-576)02804679X 1549-8328 nnns volume:62 year:2015 number:10 pages:2454-2464 http://dx.doi.org/10.1109/TCSI.2015.2476295 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7277189 http://search.proquest.com/docview/1729175442 http://arxiv.org/abs/1505.04262 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2059 AR 62 2015 10 2454-2464 |
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10.1109/TCSI.2015.2476295 doi PQ20160617 (DE-627)OLC1959253204 (DE-599)GBVOLC1959253204 (PRQ)a1559-dca7858ca282402e69d8ea10ed236988ba345cbc2b33b08f003c4e57619ff3530 (KEY)0213966920150000062001002454holdinpullinandlockinrangesofpllcircuitsrigorousma DE-627 ger DE-627 rakwb eng 000 620 DNB Leonov, Gennady A verfasserin aut Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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." 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, pull-in, 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. definition global stability capture range hold-in range lock-in range Gardner's problem on unique lock-in frequency local stability high-order filter nonlinear analysis phase-locked loop pull-in range Analog PLL stability in the large cycle slipping Gardner's paradox on lock-in range Control theory Dynamical Systems Mathematics Kuznetsov, Nikolay V oth Yuldashev, Marat V oth Yuldashev, Renat V oth Enthalten in IEEE transactions on circuits and systems / 1 New York, NY : Institute of Electrical and Electronics Engineers, 1992 62(2015), 10, Seite 2454-2464 (DE-627)131043080 (DE-600)1100194-X (DE-576)02804679X 1549-8328 nnns volume:62 year:2015 number:10 pages:2454-2464 http://dx.doi.org/10.1109/TCSI.2015.2476295 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7277189 http://search.proquest.com/docview/1729175442 http://arxiv.org/abs/1505.04262 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2059 AR 62 2015 10 2454-2464 |
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10.1109/TCSI.2015.2476295 doi PQ20160617 (DE-627)OLC1959253204 (DE-599)GBVOLC1959253204 (PRQ)a1559-dca7858ca282402e69d8ea10ed236988ba345cbc2b33b08f003c4e57619ff3530 (KEY)0213966920150000062001002454holdinpullinandlockinrangesofpllcircuitsrigorousma DE-627 ger DE-627 rakwb eng 000 620 DNB Leonov, Gennady A verfasserin aut Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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." 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, pull-in, 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. definition global stability capture range hold-in range lock-in range Gardner's problem on unique lock-in frequency local stability high-order filter nonlinear analysis phase-locked loop pull-in range Analog PLL stability in the large cycle slipping Gardner's paradox on lock-in range Control theory Dynamical Systems Mathematics Kuznetsov, Nikolay V oth Yuldashev, Marat V oth Yuldashev, Renat V oth Enthalten in IEEE transactions on circuits and systems / 1 New York, NY : Institute of Electrical and Electronics Engineers, 1992 62(2015), 10, Seite 2454-2464 (DE-627)131043080 (DE-600)1100194-X (DE-576)02804679X 1549-8328 nnns volume:62 year:2015 number:10 pages:2454-2464 http://dx.doi.org/10.1109/TCSI.2015.2476295 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7277189 http://search.proquest.com/docview/1729175442 http://arxiv.org/abs/1505.04262 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2059 AR 62 2015 10 2454-2464 |
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10.1109/TCSI.2015.2476295 doi PQ20160617 (DE-627)OLC1959253204 (DE-599)GBVOLC1959253204 (PRQ)a1559-dca7858ca282402e69d8ea10ed236988ba345cbc2b33b08f003c4e57619ff3530 (KEY)0213966920150000062001002454holdinpullinandlockinrangesofpllcircuitsrigorousma DE-627 ger DE-627 rakwb eng 000 620 DNB Leonov, Gennady A verfasserin aut Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier 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." 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, pull-in, 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. definition global stability capture range hold-in range lock-in range Gardner's problem on unique lock-in frequency local stability high-order filter nonlinear analysis phase-locked loop pull-in range Analog PLL stability in the large cycle slipping Gardner's paradox on lock-in range Control theory Dynamical Systems Mathematics Kuznetsov, Nikolay V oth Yuldashev, Marat V oth Yuldashev, Renat V oth Enthalten in IEEE transactions on circuits and systems / 1 New York, NY : Institute of Electrical and Electronics Engineers, 1992 62(2015), 10, Seite 2454-2464 (DE-627)131043080 (DE-600)1100194-X (DE-576)02804679X 1549-8328 nnns volume:62 year:2015 number:10 pages:2454-2464 http://dx.doi.org/10.1109/TCSI.2015.2476295 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7277189 http://search.proquest.com/docview/1729175442 http://arxiv.org/abs/1505.04262 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2059 AR 62 2015 10 2454-2464 |
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Leonov, Gennady A ddc 000 misc definition misc global stability misc capture range misc hold-in range misc lock-in range misc Gardner's problem on unique lock-in frequency misc local stability misc high-order filter misc nonlinear analysis misc phase-locked loop misc pull-in range misc Analog PLL misc stability in the large misc cycle slipping misc Gardner's paradox on lock-in range misc Control theory misc Dynamical Systems misc Mathematics Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory |
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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory |
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hold-in, pull-in, and lock-in ranges of pll circuits: rigorous mathematical definitions and limitations of classical theory |
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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory |
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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." 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, pull-in, 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. |
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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." 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, pull-in, 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. |
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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." 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, pull-in, 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. |
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Hold-In, Pull-In, and Lock-In Ranges of PLL Circuits: Rigorous Mathematical Definitions and Limitations of Classical Theory |
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