{"id":"https://openalex.org/W3139122155","doi":"https://doi.org/10.1109/tcsi.2021.3063206","title":"Spur Immunity in MASH-Based Fractional-N CP-PLLs With Polynomial Nonlinearities","display_name":"Spur Immunity in MASH-Based Fractional-N CP-PLLs With Polynomial Nonlinearities","publication_year":2021,"publication_date":"2021-03-10","ids":{"openalex":"https://openalex.org/W3139122155","doi":"https://doi.org/10.1109/tcsi.2021.3063206","mag":"3139122155"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2021.3063206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3063206","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","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/A5037688288","display_name":"Valerio Mazzaro","orcid":"https://orcid.org/0000-0002-2512-550X"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Valerio Mazzaro","raw_affiliation_strings":["School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland"],"raw_orcid":"https://orcid.org/0000-0002-2512-550X","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058028927","display_name":"Michael Peter Kennedy","orcid":"https://orcid.org/0000-0003-3242-1056"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Michael Peter Kennedy","raw_affiliation_strings":["School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland"],"raw_orcid":"https://orcid.org/0000-0003-3242-1056","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":null,"apc_paid":null,"fwci":1.8686,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.85351127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"68","issue":"6","first_page":"2295","last_page":"2306"},"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/T10299","display_name":"Photonic and Optical Devices","score":0.9958000183105469,"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":0.9932000041007996,"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/noise-immunity","display_name":"Noise immunity","score":0.7593786120414734},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.6831889152526855},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6265446543693542},{"id":"https://openalex.org/keywords/phase-noise","display_name":"Phase noise","score":0.5793023109436035},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5675340294837952},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5653704404830933},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.5644987225532532},{"id":"https://openalex.org/keywords/noise-shaping","display_name":"Noise shaping","score":0.4958392083644867},{"id":"https://openalex.org/keywords/phase-locked-loop","display_name":"Phase-locked loop","score":0.4899734556674957},{"id":"https://openalex.org/keywords/spur","display_name":"Spur","score":0.487679123878479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45871856808662415},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.42377540469169617},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32305508852005005},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.29596662521362305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2741495966911316},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20292019844055176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19530674815177917},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18771260976791382},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1572589874267578},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07618439197540283},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07241910696029663}],"concepts":[{"id":"https://openalex.org/C2988494973","wikidata":"https://www.wikidata.org/wiki/Q179448","display_name":"Noise immunity","level":3,"score":0.7593786120414734},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.6831889152526855},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6265446543693542},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"score":0.5793023109436035},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5675340294837952},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5653704404830933},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5644987225532532},{"id":"https://openalex.org/C9083635","wikidata":"https://www.wikidata.org/wiki/Q2133535","display_name":"Noise shaping","level":2,"score":0.4958392083644867},{"id":"https://openalex.org/C12707504","wikidata":"https://www.wikidata.org/wiki/Q52637","display_name":"Phase-locked loop","level":3,"score":0.4899734556674957},{"id":"https://openalex.org/C2779821383","wikidata":"https://www.wikidata.org/wiki/Q7581537","display_name":"Spur","level":2,"score":0.487679123878479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45871856808662415},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.42377540469169617},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32305508852005005},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.29596662521362305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2741495966911316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20292019844055176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19530674815177917},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18771260976791382},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1572589874267578},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07618439197540283},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07241910696029663},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","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},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2021.3063206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2021.3063206","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1578627687","display_name":null,"funder_award_id":"TC-2015-0019","funder_id":"https://openalex.org/F4320320834","funder_display_name":"Enterprise Ireland"},{"id":"https://openalex.org/G5272196377","display_name":null,"funder_award_id":"13/IA/1979","funder_id":"https://openalex.org/F4320320847","funder_display_name":"Science Foundation Ireland"}],"funders":[{"id":"https://openalex.org/F4320320834","display_name":"Enterprise Ireland","ror":"https://ror.org/023z51242"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W371546939","https://openalex.org/W605564925","https://openalex.org/W629945696","https://openalex.org/W1492984241","https://openalex.org/W1500373038","https://openalex.org/W1566916904","https://openalex.org/W1965174157","https://openalex.org/W1983278401","https://openalex.org/W2010437213","https://openalex.org/W2030258400","https://openalex.org/W2062998260","https://openalex.org/W2108340203","https://openalex.org/W2117873004","https://openalex.org/W2125257617","https://openalex.org/W2133676222","https://openalex.org/W2134962970","https://openalex.org/W2145232736","https://openalex.org/W2145830629","https://openalex.org/W2157470323","https://openalex.org/W2182756325","https://openalex.org/W2501462716","https://openalex.org/W2560251435","https://openalex.org/W2740751239","https://openalex.org/W2758621295","https://openalex.org/W2801062342","https://openalex.org/W2960457490","https://openalex.org/W2969117469","https://openalex.org/W2977196623","https://openalex.org/W3014376599","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W3134374554","https://openalex.org/W2237480245","https://openalex.org/W2519167559","https://openalex.org/W2326560183","https://openalex.org/W1525844853","https://openalex.org/W2100729707"],"abstract_inverted_index":{"Spurious":[0],"tones":[1],"appear":[2],"in":[3,18,84],"the":[4,19,26,29,32,36,43,48,85],"output":[5],"phase":[6],"noise":[7,60],"spectrum":[8],"of":[9,51,64,72,87],"a":[10,70],"fractional-N":[11,55],"frequency":[12],"synthesizer":[13],"when":[14],"nonlinearities":[15,53],"are":[16,23],"present":[17],"loop.":[20],"These":[21],"spurs":[22,75],"generated":[24],"by":[25],"interaction":[27],"between":[28],"nonlinearity":[30],"and":[31],"quantization":[33],"error":[34],"that":[35],"digital":[37],"\u03a3":[38],"modulator":[39],"(DDSM)":[40],"introduces":[41],"into":[42],"system.":[44],"This":[45,67],"paper":[46],"analyzes":[47],"spurious":[49],"effect":[50],"polynomial":[52,89],"on":[54,79],"CP-PLLs":[56],"equipped":[57],"with":[58],"multi-stage":[59],"shaping":[61],"(MASH)":[62],"DDSMs":[63],"different":[65],"orders.":[66],"leads":[68],"to":[69],"proof":[71],"immunity":[73],"from":[74],"for":[76],"PLLs":[77],"based":[78],"higher":[80],"order":[81],"MASH":[82],"modulators":[83],"case":[86],"certain":[88],"nonlinearities.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}