{"id":"https://openalex.org/W2123381913","doi":"https://doi.org/10.1109/tcsi.2012.2215713","title":"Intrinsic Distortion of a Fully Differential BD-Modulated Class-D Amplifier With Analog Feedback","display_name":"Intrinsic Distortion of a Fully Differential BD-Modulated Class-D Amplifier With Analog Feedback","publication_year":2012,"publication_date":"2012-10-19","ids":{"openalex":"https://openalex.org/W2123381913","doi":"https://doi.org/10.1109/tcsi.2012.2215713","mag":"2123381913"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2012.2215713","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2215713","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://eprints.nottingham.ac.uk/1886/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026128270","display_name":"Stephen M. Cox","orcid":"https://orcid.org/0000-0002-4609-5848"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Stephen Michael Cox","raw_affiliation_strings":["School of Mathematical Sciences, University of Nottingham, Nottingham, UK","Sch. of Math. Sci., Univ. of Nottingham, Nottingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Nottingham, Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"Sch. of Math. Sci., Univ. of Nottingham, Nottingham, UK","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100313058","display_name":"Jun Yu","orcid":"https://orcid.org/0009-0007-5870-0041"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jun Yu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042682339","display_name":"Wang Ling Goh","orcid":"https://orcid.org/0000-0001-7466-8941"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Wang Ling Goh","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109435253","display_name":"Meng Tong Tan","orcid":"https://orcid.org/0000-0002-3203-5019"},"institutions":[{"id":"https://openalex.org/I4210090209","display_name":"Institute of Microelectronics","ror":"https://ror.org/009rw8n36","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I4210090209","https://openalex.org/I91275662"]},{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Meng Tong Tan","raw_affiliation_strings":["Agency for Science, Technology and Research (A*STAR), Institute of Microelectronics (IME), Singapore","Inst. of Microelectron. (IME), Agency for Sci., Technol. & Res. (A*STAR), Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Agency for Science, Technology and Research (A*STAR), Institute of Microelectronics (IME), Singapore","institution_ids":["https://openalex.org/I115228651","https://openalex.org/I4210090209"]},{"raw_affiliation_string":"Inst. of Microelectron. (IME), Agency for Sci., Technol. & Res. (A*STAR), Singapore, Singapore","institution_ids":["https://openalex.org/I115228651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026128270"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":null,"apc_paid":null,"fwci":0.982,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.7934504,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"60","issue":"1","first_page":"63","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11248","display_name":"Advanced Power Amplifier Design","score":0.9994000196456909,"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/T11248","display_name":"Advanced Power Amplifier Design","score":0.9994000196456909,"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":0.9952999949455261,"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/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.98580002784729,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/intermodulation","display_name":"Intermodulation","score":0.8280914425849915},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.6849132776260376},{"id":"https://openalex.org/keywords/total-harmonic-distortion","display_name":"Total harmonic distortion","score":0.6309183239936829},{"id":"https://openalex.org/keywords/nonlinear-distortion","display_name":"Nonlinear distortion","score":0.6127485036849976},{"id":"https://openalex.org/keywords/amplifier","display_name":"Amplifier","score":0.609989583492279},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.5839778780937195},{"id":"https://openalex.org/keywords/modulation","display_name":"Modulation (music)","score":0.5389367938041687},{"id":"https://openalex.org/keywords/pulse-width-modulation","display_name":"Pulse-width modulation","score":0.5083443522453308},{"id":"https://openalex.org/keywords/amplitude-distortion","display_name":"Amplitude distortion","score":0.5059780478477478},{"id":"https://openalex.org/keywords/modulation-index","display_name":"Modulation index","score":0.5019538402557373},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4789362847805023},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4708751440048218},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.4300330579280853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40080776810646057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21151939034461975},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.1415727138519287},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.09179115295410156},{"id":"https://openalex.org/keywords/optoelectronics","display_name":"Optoelectronics","score":0.09065261483192444},{"id":"https://openalex.org/keywords/cmos","display_name":"CMOS","score":0.07289060950279236}],"concepts":[{"id":"https://openalex.org/C11773624","wikidata":"https://www.wikidata.org/wiki/Q2142232","display_name":"Intermodulation","level":4,"score":0.8280914425849915},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.6849132776260376},{"id":"https://openalex.org/C42156128","wikidata":"https://www.wikidata.org/wiki/Q162641","display_name":"Total harmonic distortion","level":3,"score":0.6309183239936829},{"id":"https://openalex.org/C173413354","wikidata":"https://www.wikidata.org/wiki/Q7049470","display_name":"Nonlinear distortion","level":4,"score":0.6127485036849976},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.609989583492279},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.5839778780937195},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.5389367938041687},{"id":"https://openalex.org/C92746544","wikidata":"https://www.wikidata.org/wiki/Q585184","display_name":"Pulse-width modulation","level":3,"score":0.5083443522453308},{"id":"https://openalex.org/C201154478","wikidata":"https://www.wikidata.org/wiki/Q4748515","display_name":"Amplitude distortion","level":5,"score":0.5059780478477478},{"id":"https://openalex.org/C2776635522","wikidata":"https://www.wikidata.org/wiki/Q11883093","display_name":"Modulation index","level":4,"score":0.5019538402557373},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4789362847805023},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4708751440048218},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.4300330579280853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40080776810646057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21151939034461975},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.1415727138519287},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.09179115295410156},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.09065261483192444},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.07289060950279236},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcsi.2012.2215713","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2215713","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:eprints.nottingham.ac.uk:1886","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/1886/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:1003780","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/1003780","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:eprints.nottingham.ac.uk:1886","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/1886/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W140525707","https://openalex.org/W1485634462","https://openalex.org/W1501948856","https://openalex.org/W1538652127","https://openalex.org/W1600063698","https://openalex.org/W1971568424","https://openalex.org/W1980552189","https://openalex.org/W1988430741","https://openalex.org/W1997550144","https://openalex.org/W1997707771","https://openalex.org/W2002009081","https://openalex.org/W2030191971","https://openalex.org/W2033831006","https://openalex.org/W2059418378","https://openalex.org/W2095687975","https://openalex.org/W2098653732","https://openalex.org/W2101304967","https://openalex.org/W2108527821","https://openalex.org/W2129379462","https://openalex.org/W2140612368","https://openalex.org/W2160569614","https://openalex.org/W2168548626","https://openalex.org/W2596323328","https://openalex.org/W6628941933","https://openalex.org/W6632276586","https://openalex.org/W6636022663"],"related_works":["https://openalex.org/W1986100960","https://openalex.org/W2516432655","https://openalex.org/W4231827520","https://openalex.org/W2537863327","https://openalex.org/W2007917446","https://openalex.org/W2765243463","https://openalex.org/W2967636963","https://openalex.org/W2119085274","https://openalex.org/W1980329671","https://openalex.org/W2142683138"],"abstract_inverted_index":{"This":[0,57],"paper":[1],"presents":[2],"a":[3,7,19,90,95,125,134],"mathematical":[4],"analysis":[5],"of":[6,35,97,100,112],"fully":[8],"differential":[9],"BD-modulated":[10,121],"Class-D":[11,122],"amplifier":[12,123],"with":[13,23],"analog":[14],"feedback,":[15],"i.e.,":[16],"one":[17],"having":[18],"bridge-tied-load":[20],"output":[21,47],"configuration":[22],"negative":[24],"feedback":[25],"and":[26,51,71,104],"ternary":[27],"PWM":[28,82],"signal.":[29],"Notwithstanding":[30],"the":[31,36,45,85,98,101,109,113,120],"highly":[32],"nonlinear":[33],"nature":[34],"amplifier's":[37],"operation,":[38],"an":[39],"extremely":[40],"accurate":[41],"closed-form":[42],"expression":[43,58],"for":[44,74,79,129,138],"audible":[46],"signal":[48,103,115,132],"is":[49,116],"derived":[50],"verified":[52],"based":[53],"on":[54],"computer":[55],"simulations.":[56],"demonstrates":[59],"that":[60,78],"there":[61],"exist":[62],"larger":[63,126],"high-order":[64],"intrinsic":[65,127,136],"distortions":[66],"(e.g.,":[67],"5th-order":[68],"harmonic":[69,87],"distortion":[70,88,128,137],"intermodulation":[72],"distortion)":[73],"BD-modulation,":[75],"compared":[76,142],"to":[77,143],"AD-modulation":[80],"(binary":[81],"signal).":[83],"Furthermore,":[84],"3rd-order":[86],"has":[89,124],"roughly":[91],"parabolic":[92],"response":[93],"as":[94],"function":[96],"magnitude":[99],"input":[102,114,131,140],"reaches":[105],"its":[106],"peak":[107],"when":[108],"modulation":[110],"index":[111],"around":[117],"0.7.":[118],"Overall,":[119],"small":[130],"but":[133],"smaller":[135],"large":[139],"signal,":[141],"AD-modulated":[144],"designs.":[145]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
