{"id":"https://openalex.org/W2906575168","doi":"https://doi.org/10.1109/tvlsi.2018.2878665","title":"Timing Jitter Distribution and Power Spectral Density of a Second-Order Bang\u2013Bang Digital PLL With Transport Delay Using Fokker\u2013Planck Equations","display_name":"Timing Jitter Distribution and Power Spectral Density of a Second-Order Bang\u2013Bang Digital PLL With Transport Delay Using Fokker\u2013Planck Equations","publication_year":2018,"publication_date":"2018-12-18","ids":{"openalex":"https://openalex.org/W2906575168","doi":"https://doi.org/10.1109/tvlsi.2018.2878665","mag":"2906575168"},"language":"en","primary_location":{"id":"doi:10.1109/tvlsi.2018.2878665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2018.2878665","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054231284","display_name":"Pratheep Bondalapati","orcid":"https://orcid.org/0000-0002-8864-8324"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pratheep Bondalapati","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-8864-8324","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020170250","display_name":"Won Namgoong","orcid":null},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Won Namgoong","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-3047-2888","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054231284"],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":null,"apc_paid":null,"fwci":0.1309,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51930877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"2","first_page":"398","last_page":"406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11417","display_name":"Advancements in PLL and VCO Technologies","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11417","display_name":"Advancements in PLL and VCO Technologies","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jitter","display_name":"Jitter","score":0.7725911140441895},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.6903797388076782},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.5976404547691345},{"id":"https://openalex.org/keywords/phase-locked-loop","display_name":"Phase-locked loop","score":0.5761716961860657},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4823129177093506},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4742771089076996},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.459003210067749},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.442943811416626},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4149875342845917},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.41382503509521484},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.382824182510376},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.24062368273735046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20647183060646057},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11350992321968079},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10898205637931824},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09859123826026917}],"concepts":[{"id":"https://openalex.org/C134652429","wikidata":"https://www.wikidata.org/wiki/Q1052698","display_name":"Jitter","level":2,"score":0.7725911140441895},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.6903797388076782},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.5976404547691345},{"id":"https://openalex.org/C12707504","wikidata":"https://www.wikidata.org/wiki/Q52637","display_name":"Phase-locked loop","level":3,"score":0.5761716961860657},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4823129177093506},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4742771089076996},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.459003210067749},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.442943811416626},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4149875342845917},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.41382503509521484},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.382824182510376},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.24062368273735046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20647183060646057},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11350992321968079},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10898205637931824},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09859123826026917},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvlsi.2018.2878665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2018.2878665","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5522873551","display_name":null,"funder_award_id":"1310279","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1981447218","https://openalex.org/W1991414111","https://openalex.org/W2023401960","https://openalex.org/W2036186630","https://openalex.org/W2094135260","https://openalex.org/W2101241604","https://openalex.org/W2103897641","https://openalex.org/W2107327405","https://openalex.org/W2111977069","https://openalex.org/W2123892792","https://openalex.org/W2127115683","https://openalex.org/W2129429105","https://openalex.org/W2144581882","https://openalex.org/W2151100180","https://openalex.org/W2155323511","https://openalex.org/W2160320241","https://openalex.org/W2163117858"],"related_works":["https://openalex.org/W2121182846","https://openalex.org/W2315668284","https://openalex.org/W2155789024","https://openalex.org/W2109491806","https://openalex.org/W3213608175","https://openalex.org/W2058044441","https://openalex.org/W2139484866","https://openalex.org/W2140560482","https://openalex.org/W2048978945","https://openalex.org/W4249485354"],"abstract_inverted_index":{"In":[0],"this":[1,49],"paper,":[2,50],"a":[3],"second-order":[4],"bang-bang":[5],"digital":[6],"phase-locked":[7],"loop":[8,103],"(BBPLL)":[9],"with":[10,76],"dominant":[11],"random":[12],"walk":[13],"phase":[14],"noise":[15],"and":[16,38,60],"transport":[17],"delay":[18],"is":[19,55,71,74,94,97,111],"analyzed":[20],"using":[21],"Fokker-Plank":[22],"equations.":[23],"Explicit":[24],"closed-form":[25],"expressions":[26,110],"are":[27,82],"derived":[28,69,109],"for":[29,100],"the":[30,44,51,68,87,91,98,108],"timing":[31,52],"error":[32,53],"probability":[33],"distribution":[34,54],"function,":[35],"jitter":[36],"variance,":[37],"power":[39],"spectral":[40],"density":[41],"(psd).":[42],"For":[43],"type-II":[45],"BBPLL":[46,92],"considered":[47],"in":[48],"shown":[56],"to":[57],"be":[58],"Laplacian":[59],"not":[61],"Gaussian":[62],"distributed":[63],"as":[64,84,86,96],"previously":[65],"assumed,":[66],"while":[67],"psd":[70],"Lorentzian,":[72],"which":[73],"consistent":[75],"earlier":[77],"works.":[78],"The":[79,105],"analytical":[80],"solutions":[81],"valid":[83],"long":[85],"continuous-time":[88],"approximation":[89],"of":[90,107],"dynamics":[93],"accurate":[95],"case":[99],"typical":[101],"operating":[102],"bandwidths.":[104],"accuracy":[106],"validated":[112],"via":[113],"simulation.":[114]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}