{"id":"https://openalex.org/W7127325735","doi":"https://doi.org/10.1109/jssc.2026.3654912","title":"A Low Phase Noise and High-Efficiency Biharmonic Class-F <sup>\u22121</sup> VCO With Improved Waveform Shaping","display_name":"A Low Phase Noise and High-Efficiency Biharmonic Class-F <sup>\u22121</sup> VCO With Improved Waveform Shaping","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127325735","doi":"https://doi.org/10.1109/jssc.2026.3654912"},"language":null,"primary_location":{"id":"doi:10.1109/jssc.2026.3654912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jssc.2026.3654912","pdf_url":null,"source":{"id":"https://openalex.org/S83637746","display_name":"IEEE Journal of Solid-State Circuits","issn_l":"0018-9200","issn":["0018-9200","1558-173X"],"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 Journal of Solid-State Circuits","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/A5111559300","display_name":"Yue Wu","orcid":"https://orcid.org/0009-0007-6626-2838"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":true,"raw_author_name":"Yue Wu","raw_affiliation_strings":["State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0009-0007-6626-2838","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023268503","display_name":"Yatao Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Yatao Peng","raw_affiliation_strings":["State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0002-6978-0282","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jun Yin","orcid":"https://orcid.org/0000-0002-4195-4551"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Jun Yin","raw_affiliation_strings":["State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0002-4195-4551","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040604428","display_name":"R. P. Martins","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Rui P. Martins","raw_affiliation_strings":["State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0003-2821-648X","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028828492","display_name":"Guohe","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Pui-In Mak","raw_affiliation_strings":["State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0002-3579-8740","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Analog and Mixed-Signal VLSI, the Institute of Microelectronics, and FST ECE, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5111559300"],"corresponding_institution_ids":["https://openalex.org/I204512498"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21954194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"5","first_page":"1860","last_page":"1875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.5357000231742859,"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/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.5357000231742859,"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/T11248","display_name":"Advanced Power Amplifier Design","score":0.38420000672340393,"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/T11160","display_name":"Acoustic Wave Resonator Technologies","score":0.022099999710917473,"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/voltage-controlled-oscillator","display_name":"Voltage-controlled oscillator","score":0.7757999897003174},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.6751000285148621},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.6018000245094299},{"id":"https://openalex.org/keywords/phase-noise","display_name":"Phase noise","score":0.5929999947547913},{"id":"https://openalex.org/keywords/sawtooth-wave","display_name":"Sawtooth wave","score":0.5604000091552734},{"id":"https://openalex.org/keywords/figure-of-merit","display_name":"Figure of merit","score":0.5501000285148621},{"id":"https://openalex.org/keywords/resonator","display_name":"Resonator","score":0.5281000137329102},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.5042999982833862}],"concepts":[{"id":"https://openalex.org/C5291336","wikidata":"https://www.wikidata.org/wiki/Q852341","display_name":"Voltage-controlled oscillator","level":3,"score":0.7757999897003174},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.6751000285148621},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.6018000245094299},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"score":0.5929999947547913},{"id":"https://openalex.org/C148837635","wikidata":"https://www.wikidata.org/wiki/Q1742397","display_name":"Sawtooth wave","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C130277099","wikidata":"https://www.wikidata.org/wiki/Q3676605","display_name":"Figure of merit","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C97126364","wikidata":"https://www.wikidata.org/wiki/Q349669","display_name":"Resonator","level":2,"score":0.5281000137329102},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.517300009727478},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.4255000054836273},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.387800008058548},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3797000050544739},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3718000054359436},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3506999909877777},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3492000102996826},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.29280000925064087},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C26571440","wikidata":"https://www.wikidata.org/wiki/Q7106415","display_name":"Oscillator phase noise","level":5,"score":0.26499998569488525}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jssc.2026.3654912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jssc.2026.3654912","pdf_url":null,"source":{"id":"https://openalex.org/S83637746","display_name":"IEEE Journal of Solid-State Circuits","issn_l":"0018-9200","issn":["0018-9200","1558-173X"],"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 Journal of Solid-State Circuits","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8088296055793762}],"awards":[{"id":"https://openalex.org/G1751195390","display_name":null,"funder_award_id":"0151/2022/A3","funder_id":"https://openalex.org/F4320315893","funder_display_name":"VNU Science and Technology Development Fund"},{"id":"https://openalex.org/G3983981533","display_name":null,"funder_award_id":"0001/2025/NRP","funder_id":"https://openalex.org/F4320315893","funder_display_name":"VNU Science and Technology Development Fund"},{"id":"https://openalex.org/G7191969512","display_name":null,"funder_award_id":"62304004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7989035043","display_name":null,"funder_award_id":"2024A1515012295","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"}],"funders":[{"id":"https://openalex.org/F4320315893","display_name":"VNU Science and Technology Development Fund","ror":"https://ror.org/044vr6g03"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"an":[3,128,234],"inverse":[4],"class-F":[5],"(class-F<sup":[6],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,72,115,158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22121</sup>)":[8],"voltage-controlled":[9],"oscillator":[10],"(VCO)":[11],"architecture":[12],"that":[13],"achieves":[14,201],"a":[15,48,202,219,224],"higher":[16],"figure":[17],"of":[18,132,181,215,227,237],"merit":[19],"(FoM)":[20],"compared":[21],"with":[22,80],"the":[23,45,69,91,98,105,122,125,133,136,155,165,170,176,195],"reported":[24],"RF":[25],"harmonic":[26,63,93,102,112],"VCOs.":[27],"The":[28,84,198,230],"design":[29],"conditions":[30,46],"for":[31],"FoM":[32,226,236],"improvement":[33],"in":[34,104,169],"biharmonic":[35],"VCOs":[36],"(with":[37],"sole":[38],"2nd":[39,62,92,111],"harmonic)":[40],"are":[41,189],"analyzed.":[42],"To":[43],"meet":[44],"revealed,":[47],"distributed":[49],"dual-mode":[50],"resonator":[51],"(DMR)":[52],"without":[53,149],"magnetic":[54],"flux":[55],"cancellation,":[56],"featuring":[57],"simultaneously":[58],"high":[59],"1st":[60],"and":[61,186,191,222],"impedances,":[64],"is":[65,87],"introduced":[66,156],"to":[67,89,144,193,209],"realize":[68],"proposed":[70,85,196],"class-F<sup":[71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22121</sup>":[73],"VCO,":[74],"enabling":[75],"improved":[76],"phase":[77],"noise":[78],"(PN)":[79],"reduced":[81,145],"power":[82,177],"consumption.":[83],"structure":[86],"able":[88],"boost":[90],"voltage":[94,103,113,152],"components":[95],"while":[96],"suppressing":[97],"detrimental":[99],"misaligned":[100],"3rd":[101],"output":[106,171],"waveforms":[107],"by":[108],"introducing":[109],"significant":[110],"(<inline-formula":[114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[116,159],"<tex-math":[117,160],"notation=\"LaTeX\">$V_{\\mathrm":[118,161],"{G2}}$</tex-math>":[119,162],"</inline-formula>)":[120],"at":[121,218,243],"gates.":[123],"Consequently,":[124],"waveform":[126,134],"exhibits":[127],"extended":[129],"flat":[130],"region":[131],"where":[135],"impulse":[137],"sensitivity":[138],"function":[139],"(ISF)":[140],"approaches":[141],"zero,":[142],"leading":[143],"noise-to-PN":[146],"conversion,":[147],"even":[148],"excessive":[150],"D-to-G":[151],"gain.":[153],"Meantime,":[154],"<inline-formula":[157],"</inline-formula>":[163],"enlarges":[164],"zero-current":[166],"(ZC)":[167],"zone":[168],"current":[172],"waveform,":[173],"thus":[174],"improving":[175],"efficiency.":[178],"Two":[179],"prototypes":[180],"VCO":[182,200,232],"targeting":[183],"room-temperature":[184],"(RT)":[185],"cryogenic":[187,231],"applications":[188],"designed":[190],"measured":[192,233],"verify":[194],"architecture.":[197],"RT":[199],"frequency":[203],"tuning":[204],"range":[205],"(FTR)":[206],"from":[207],"9.37":[208],"10.86":[210],"GHz,":[211],"delivering":[212],"state-of-the-art":[213],"PN":[214],"\u2212143":[216],"dBc/Hz":[217,239],"10-MHz":[220],"offset,":[221],"attaining":[223],"peak":[225],"198.9":[228],"dBc/Hz.":[229],"average":[235],"210.2":[238],"under":[240],"sub-1":[241],"mW":[242],"4.2":[244],"K.":[245]},"counts_by_year":[],"updated_date":"2026-04-25T06:01:18.069262","created_date":"2026-02-04T00:00:00"}
