{"id":"https://openalex.org/W2514488892","doi":"https://doi.org/10.1109/tcsi.2016.2573119","title":"Modeling nonlinear wave digital elements using the Lambert function","display_name":"Modeling nonlinear wave digital elements using the Lambert function","publication_year":2016,"publication_date":"2016-08-01","ids":{"openalex":"https://openalex.org/W2514488892","doi":"https://doi.org/10.1109/tcsi.2016.2573119","mag":"2514488892"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2016.2573119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2016.2573119","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11311/1003022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088704369","display_name":"Alberto Bernardini","orcid":"https://orcid.org/0000-0001-7973-0134"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Bernardini","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7973-0134","affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000698721","display_name":"Kurt James Werner","orcid":"https://orcid.org/0000-0003-0635-0258"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kurt James Werner","raw_affiliation_strings":["Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051897828","display_name":"Augusto Sarti","orcid":"https://orcid.org/0000-0002-5803-1702"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Augusto Sarti","raw_affiliation_strings":["Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015837093","display_name":"Julius O. Smith","orcid":"https://orcid.org/0000-0002-5251-2935"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julius Orion Smith","raw_affiliation_strings":["Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2411,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.91848212,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"63","issue":"8","first_page":"1231","last_page":"1242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12677","display_name":"Sports Dynamics and Biomechanics","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12677","display_name":"Sports Dynamics and Biomechanics","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11349","display_name":"Music Technology and Sound Studies","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diode","display_name":"Diode","score":0.681007444858551},{"id":"https://openalex.org/keywords/bipolar-junction-transistor","display_name":"Bipolar junction transistor","score":0.6163325309753418},{"id":"https://openalex.org/keywords/lambert-w-function","display_name":"Lambert W function","score":0.6049585938453674},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6025175452232361},{"id":"https://openalex.org/keywords/describing-function","display_name":"Describing function","score":0.5235057473182678},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49727872014045715},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4954262971878052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49105262756347656},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.47104477882385254},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4608243703842163},{"id":"https://openalex.org/keywords/amplifier","display_name":"Amplifier","score":0.4574235677719116},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.34200581908226013},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.3401482105255127},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3262503147125244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3211085796356201},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.2642343044281006},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2501673400402069},{"id":"https://openalex.org/keywords/transistor","display_name":"Transistor","score":0.21628135442733765},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17155370116233826},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1431310772895813},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13530904054641724},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.08300080895423889}],"concepts":[{"id":"https://openalex.org/C78434282","wikidata":"https://www.wikidata.org/wiki/Q11656","display_name":"Diode","level":2,"score":0.681007444858551},{"id":"https://openalex.org/C23061349","wikidata":"https://www.wikidata.org/wiki/Q188946","display_name":"Bipolar junction transistor","level":4,"score":0.6163325309753418},{"id":"https://openalex.org/C130924491","wikidata":"https://www.wikidata.org/wiki/Q429331","display_name":"Lambert W function","level":2,"score":0.6049585938453674},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6025175452232361},{"id":"https://openalex.org/C147317941","wikidata":"https://www.wikidata.org/wiki/Q1925419","display_name":"Describing function","level":3,"score":0.5235057473182678},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49727872014045715},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4954262971878052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49105262756347656},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.47104477882385254},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4608243703842163},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.4574235677719116},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.34200581908226013},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.3401482105255127},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3262503147125244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3211085796356201},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.2642343044281006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2501673400402069},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.21628135442733765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17155370116233826},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1431310772895813},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13530904054641724},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.08300080895423889},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcsi.2016.2573119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2016.2573119","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"},{"id":"pmh:oai:pure.qub.ac.uk/portal:publications/55476d39-0685-4fa0-a603-9ef3bf379606","is_oa":false,"landing_page_url":"https://pure.qub.ac.uk/portal/en/publications/modeling-nonlinear-wave-digital-elements-using-the-lambert-function(55476d39-0685-4fa0-a603-9ef3bf379606).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402319","display_name":"Research Portal (Queen's University Belfast)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126231945","host_organization_name":"Queen's University Belfast","host_organization_lineage":["https://openalex.org/I126231945"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:re.public.polimi.it:11311/1003022","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1003022","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:re.public.polimi.it:11311/1003022","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1003022","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1486298633","https://openalex.org/W1515104269","https://openalex.org/W1547021691","https://openalex.org/W1547850816","https://openalex.org/W1557314559","https://openalex.org/W1571071896","https://openalex.org/W1972580129","https://openalex.org/W1988562736","https://openalex.org/W1989846871","https://openalex.org/W1996432748","https://openalex.org/W1996630910","https://openalex.org/W1998589219","https://openalex.org/W2011192352","https://openalex.org/W2031866318","https://openalex.org/W2042882368","https://openalex.org/W2056225453","https://openalex.org/W2067922464","https://openalex.org/W2068728923","https://openalex.org/W2078140934","https://openalex.org/W2090561099","https://openalex.org/W2096727144","https://openalex.org/W2098988753","https://openalex.org/W2099587991","https://openalex.org/W2112545765","https://openalex.org/W2119212591","https://openalex.org/W2121108042","https://openalex.org/W2144751081","https://openalex.org/W2145694954","https://openalex.org/W2153293927","https://openalex.org/W2156899537","https://openalex.org/W2166546105","https://openalex.org/W2180490775","https://openalex.org/W2197480006","https://openalex.org/W2207604102","https://openalex.org/W2468306622","https://openalex.org/W2582057770","https://openalex.org/W2614441919","https://openalex.org/W4285719527","https://openalex.org/W4299802695","https://openalex.org/W6629189680","https://openalex.org/W6633347134","https://openalex.org/W6634325903","https://openalex.org/W6676950288","https://openalex.org/W6688334366","https://openalex.org/W6719896775","https://openalex.org/W6737689262"],"related_works":["https://openalex.org/W2100396057","https://openalex.org/W2164591582","https://openalex.org/W2076985060","https://openalex.org/W1849061327","https://openalex.org/W2131888264","https://openalex.org/W2360723056","https://openalex.org/W1568882526","https://openalex.org/W1607514316","https://openalex.org/W2115987671","https://openalex.org/W2098307246"],"abstract_inverted_index":{"A":[0],"large":[1],"class":[2],"of":[3,82,100,108,110,142,164],"transcendental":[4],"equations":[5],"involving":[6],"exponentials":[7],"can":[8],"be":[9],"made":[10],"explicit":[11,68,80,125],"using":[12],"the":[13,18,46,49,56,65,74,87,98,106,111,115,165],"Lambert":[14],"W":[15,50,112],"function.":[16],"In":[17,159],"last":[19],"fifteen":[20],"years,":[21],"this":[22],"powerful":[23],"mathematical":[24],"tool":[25],"has":[26],"been":[27],"extensively":[28],"used":[29],"to":[30,96,122],"find":[31],"closed-form":[32],"expressions":[33],"for":[34,70,124,128,170],"currents":[35],"or":[36],"voltages":[37],"in":[38,52,64,73,86,94,114],"circuits":[39,72],"containing":[40,134],"diodes.":[41,135],"Until":[42],"now":[43],"almost":[44],"all":[45],"studies":[47],"about":[48],"function":[51,113],"circuit":[53],"analysis":[54],"concern":[55],"Kirchhoff":[57],"(K)":[58],"domain,":[59],"while":[60],"only":[61],"few":[62],"works":[63],"literature":[66],"describe":[67],"models":[69,81],"diode":[71],"Wave":[75],"Digital":[76],"(WD)":[77],"domain.":[78],"However":[79],"NonLinear":[83],"Elements":[84],"(NLEs)":[85],"WD":[88,116,136],"domain":[89],"are":[90,157],"particularly":[91],"desirable,":[92],"especially":[93],"order":[95],"avoid":[97],"use":[99],"iterative":[101],"algorithms.":[102],"This":[103],"paper":[104],"explores":[105],"range":[107],"action":[109],"domain;":[117],"it":[118],"describes":[119],"a":[120,148],"procedure":[121],"search":[123],"wave":[126],"mappings,":[127],"both":[129],"one-port":[130],"and":[131,145,152],"multi-port":[132],"NLEs":[133],"models,":[137],"describing":[138],"an":[139,161],"arbitrary":[140],"number":[141],"different":[143],"parallel":[144],"anti-parallel":[146],"diodes,":[147],"transformerless":[149],"ring":[150],"modulator":[151],"some":[153],"BJT":[154,166],"amplifier":[155],"configurations,":[156],"derived.":[158],"particular,":[160],"extended":[162],"version":[163],"Ebers-Moll":[167],"model,":[168],"suitable":[169],"implementing":[171],"feedback":[172],"between":[173],"terminals,":[174],"is":[175],"introduced.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}