{"id":"https://openalex.org/W2460688588","doi":"https://doi.org/10.1109/jssc.2016.2543729","title":"Energy-Efficient Hybrid Analog/Digital Approximate Computation in Continuous Time","display_name":"Energy-Efficient Hybrid Analog/Digital Approximate Computation in Continuous Time","publication_year":2016,"publication_date":"2016-05-05","ids":{"openalex":"https://openalex.org/W2460688588","doi":"https://doi.org/10.1109/jssc.2016.2543729","mag":"2460688588"},"language":"en","primary_location":{"id":"doi:10.1109/jssc.2016.2543729","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jssc.2016.2543729","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/A5039052970","display_name":"Ning Guo","orcid":"https://orcid.org/0000-0002-0829-7262"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ning Guo","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060545672","display_name":"Yipeng Huang","orcid":"https://orcid.org/0000-0003-3171-6901"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yipeng Huang","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066910380","display_name":"Tao Mai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153776","display_name":"Apple (United States)","ror":"https://ror.org/059hsda18","country_code":"US","type":"company","lineage":["https://openalex.org/I4210153776"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tao Mai","raw_affiliation_strings":["Apple, Cupertino, CA, USA"],"affiliations":[{"raw_affiliation_string":"Apple, Cupertino, CA, USA","institution_ids":["https://openalex.org/I4210153776"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052754300","display_name":"Sharvil Patil","orcid":"https://orcid.org/0000-0001-5952-3162"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sharvil Patil","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037112611","display_name":"Chi Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127325","display_name":"Broadcom (United States)","ror":"https://ror.org/035gt5s03","country_code":"US","type":"company","lineage":["https://openalex.org/I4210127325"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chi Cao","raw_affiliation_strings":["Broadcom Corporation, Irvine, CA, USA"],"affiliations":[{"raw_affiliation_string":"Broadcom Corporation, Irvine, CA, USA","institution_ids":["https://openalex.org/I4210127325"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011887658","display_name":"Mingoo Seok","orcid":"https://orcid.org/0000-0002-9722-0979"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingoo Seok","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030436580","display_name":"Simha Sethumadhavan","orcid":"https://orcid.org/0000-0002-6180-7153"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Simha Sethumadhavan","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056549524","display_name":"Y. Tsividis","orcid":"https://orcid.org/0000-0002-7775-7218"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yannis Tsividis","raw_affiliation_strings":["Department of Electrical Engineering, Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5039052970"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":5.2992,"has_fulltext":false,"cited_by_count":92,"citation_normalized_percentile":{"value":0.95983616,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"51","issue":"7","first_page":"1514","last_page":"1524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9998999834060669,"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/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9998999834060669,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9998999834060669,"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/T11417","display_name":"Advancements in PLL and VCO Technologies","score":0.9997000098228455,"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/analog-computer","display_name":"Analog computer","score":0.6277985572814941},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6155413389205933},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6032735109329224},{"id":"https://openalex.org/keywords/cmos","display_name":"CMOS","score":0.5595758557319641},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5301500558853149},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5244786143302917},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.47900599241256714},{"id":"https://openalex.org/keywords/static-random-access-memory","display_name":"Static random-access memory","score":0.4760729670524597},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4637286067008972},{"id":"https://openalex.org/keywords/chip","display_name":"Chip","score":0.45734262466430664},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.41503429412841797},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.41026172041893005},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3292464017868042},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.326736181974411},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.27049019932746887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24159055948257446},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.15344098210334778},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1029839813709259},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08505386114120483}],"concepts":[{"id":"https://openalex.org/C90915687","wikidata":"https://www.wikidata.org/wiki/Q63759","display_name":"Analog computer","level":2,"score":0.6277985572814941},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6155413389205933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6032735109329224},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.5595758557319641},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5301500558853149},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5244786143302917},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.47900599241256714},{"id":"https://openalex.org/C68043766","wikidata":"https://www.wikidata.org/wiki/Q267416","display_name":"Static random-access memory","level":2,"score":0.4760729670524597},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4637286067008972},{"id":"https://openalex.org/C165005293","wikidata":"https://www.wikidata.org/wiki/Q1074500","display_name":"Chip","level":2,"score":0.45734262466430664},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.41503429412841797},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.41026172041893005},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3292464017868042},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.326736181974411},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.27049019932746887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24159055948257446},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.15344098210334778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1029839813709259},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08505386114120483},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jssc.2016.2543729","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jssc.2016.2543729","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":[{"score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G371929084","display_name":null,"funder_award_id":"CNS 1239134","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W106246445","https://openalex.org/W1503043354","https://openalex.org/W1610163302","https://openalex.org/W1620991513","https://openalex.org/W1992784342","https://openalex.org/W1997643519","https://openalex.org/W2020217519","https://openalex.org/W2022780439","https://openalex.org/W2026733181","https://openalex.org/W2063852130","https://openalex.org/W2119599456","https://openalex.org/W2149005611","https://openalex.org/W2149429476","https://openalex.org/W2149992244","https://openalex.org/W2158831443","https://openalex.org/W2166250385","https://openalex.org/W2295623142","https://openalex.org/W4244552319","https://openalex.org/W4251054771","https://openalex.org/W6681772123","https://openalex.org/W6683502422"],"related_works":["https://openalex.org/W4392590355","https://openalex.org/W2347486132","https://openalex.org/W3151633427","https://openalex.org/W2212894501","https://openalex.org/W2793465010","https://openalex.org/W3024050170","https://openalex.org/W1976168335","https://openalex.org/W2109451123","https://openalex.org/W2071118425","https://openalex.org/W2119025037"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,50,103,115,129,169],"unit":[3,101],"that":[4],"performs":[5],"continuous-time":[6],"hybrid":[7,55],"approximate":[8],"computation,":[9],"in":[10,67,147],"which":[11],"both":[12],"analog":[13,97],"and":[14,39,82,92,124,150,157],"digital":[15],"signals":[16],"are":[17,47,145],"functions":[18,46],"of":[19,30,95,106,117,131,136,155,161],"continuous":[20],"time.":[21],"Our":[22],"65":[23],"nm":[24],"CMOS":[25],"prototype":[26],"system":[27],"is":[28,40,65],"capable":[29],"solving":[31],"nonlinear":[32],"differential":[33],"equations":[34],"up":[35],"to":[36,42,72,89,109,120,134,165],"4th":[37],"order,":[38],"scalable":[41],"higher":[43],"orders.":[44],"Nonlinear":[45],"generated":[48],"by":[49],"programmable,":[51],"clockless,":[52],"continuoustime":[53],"8-bit":[54],"architecture":[56],"(ADC":[57],"+":[58,60],"SRAM":[59],"DAC).":[61],"Digitally":[62],"assisted":[63],"calibration":[64],"used":[66],"all":[68],"analog/mixed-signal":[69],"blocks.":[70,98],"Compared":[71],"the":[73,100,173],"prior":[74],"art,":[75],"our":[76],"chip":[77],"makes":[78],"possible":[79],"arbitrary":[80],"nonlinearities":[81],"achieves":[83,102],"16\u00d7":[84],"lower":[85],"power":[86],"dissipation,":[87],"thanks":[88],"technology":[90],"scaling":[91],"extensive":[93],"use":[94],"class-AB":[96],"Typically,":[99],"computational":[104,126,148],"accuracy":[105],"about":[107],"0.5%":[108],"5%":[110],"RMS,":[111],"solution":[112],"times":[113],"from":[114,128],"fraction":[116,130],"1":[118,132],"\u03bcs":[119],"several":[121],"hundred":[122],"\u03bcs,":[123],"total":[125],"energy":[127,151],"nJ":[133],"hundreds":[135],"nJ,":[137],"depending":[138],"on":[139],"equation":[140],"details.":[141],"Very":[142],"significant":[143],"advantages":[144],"observed":[146],"speed":[149],"(over":[152],"two":[153],"orders":[154],"magnitude":[156],"over":[158],"one":[159],"order":[160],"magnitude,":[162],"respectively)":[163],"compared":[164],"those":[166],"obtained":[167],"with":[168],"modern":[170],"microcontroller":[171],"for":[172],"same":[174],"RMS":[175],"error.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}