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IETMATERIALS,CIRCUITS AND DEVICES SERIES 48 Gyrators, Simulated Inductors and Related Immittances Othervolumesinthisseries: Volume2 AnalogueICDesign:Thecurrent-modeapproachC.Toumazou,F.J.Lidgey andD.G.Haigh(Editors) Volume3 Analogue-DigitalASICs:Circuittechniques,designtoolsandapplications R.S.Soin,F.MalobertiandJ.France(Editors) Volume4 AlgorithmicandKnowledge-BasedCADforVLSIG.E.TaylorandG.Russell (Editors) Volume5 SwitchedCurrents:Ananaloguetechniquefordigitaltechnology C.Toumazou,J.B.C.HughesandN.C.Battersby(Editors) Volume6 High-FrequencyCircuitEngineeringF.Nibleretal. Volume8 Low-PowerHigh-FrequencyMicroelectronics:Aunifiedapproach G.Machado(Editor) Volume9 VLSITesting:Digitalandmixedanalogue/digitaltechniquesS.L.Hurst Volume10 DistributedFeedbackSemiconductorLasersJ.E.Carroll,J.E.A.Whiteaway andR.G.S.Plumb Volume11 SelectedTopicsinAdvancedSolidStateandFibreOpticSensorsS.M. 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Kruzelecky,W.R.Jamroz Volume71 RadioFrequencyandMicrowavePowerAmplifiers:Vol1andVol2 A.Grebennikov(Editor) Volume73 VLSIandPost-CMOSElectronicsVolume1:VLSIandpost-CMOS electronicsandVolume2:Materials,devicesandinterconnectsR.Dhiman andR.Chandel(Editors) This page intentionally left blank Gyrators, Simulated Inductors and Related Immittances Realizations and applications Raj Senani, Data Ram Bhaskar, Vinod Kumar Singh and Abdhesh Kumar Singh The Institution of Engineering andTechnology PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom TheInstitutionofEngineeringandTechnologyisregisteredasaCharityinEngland& Wales(no.211014)andScotland(no.SC038698). †TheInstitutionofEngineeringandTechnology2020 Firstpublished2020 ThispublicationiscopyrightundertheBerneConventionandtheUniversalCopyright Convention.Allrightsreserved.Apartfromanyfairdealingforthepurposesofresearch orprivatestudy,orcriticismorreview,aspermittedundertheCopyright,Designsand PatentsAct1988,thispublicationmaybereproduced,storedortransmitted,inany formorbyanymeans,onlywiththepriorpermissioninwritingofthepublishers,orin thecaseofreprographicreproductioninaccordancewiththetermsoflicencesissued bytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethose termsshouldbesenttothepublisherattheundermentionedaddress: TheInstitutionofEngineeringandTechnology MichaelFaradayHouse SixHillsWay,Stevenage Herts,SG12AY,UnitedKingdom www.theiet.org Whiletheauthorsandpublisherbelievethattheinformationandguidancegiveninthis workarecorrect,allpartiesmustrelyupontheirownskillandjudgementwhenmaking useofthem.Neithertheauthorsnorpublisherassumesanyliabilitytoanyoneforany lossordamagecausedbyanyerrororomissioninthework,whethersuchanerroror omissionistheresultofnegligenceoranyothercause.Anyandallsuchliabilityis disclaimed. Themoralrightsoftheauthorstobeidentifiedasauthorsofthisworkhavebeen assertedbytheminaccordancewiththeCopyright,DesignsandPatentsAct1988. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisproductisavailablefromtheBritishLibrary ISBN978-1-78561-670-9(Hardback) ISBN978-1-78561-671-6(PDF) TypesetinIndiabyMPSLimited PrintedintheUKbyCPIGroup(UK)Ltd,Croydon Dedication This monograph is dedicated to: The Legendary Indian Music Composer-Duo The Melody Twins: Shankar–Jaikishan whose highly creative, melodious and ageless musical compositions provided immense inspiration in the research work of the authors over the past four decades in general and during the writing of this monograph in particular. This page intentionally left blank Contents Abouttheauthors xvii Preface xxi Acknowledgement xxiii 1 Gyrators, integrated inductors andsimulated inductors 1 Abstract 1 1.1 Prologue 1 1.2 Basic one-port circuit elements 2 1.3 Basic two-port circuit elements 3 1.3.1 The transformer 3 1.3.2 The gyrator 4 1.3.3 The two-port impedance converters and inverters 6 1.4 The pathological elements 8 1.5 Multi-terminal gyrator 10 1.6 Multiport inverters/converters 12 1.7 Commercially available inductors and Coilcraft 12 1.8 Basic difficulties in micro-miniaturization of inductors 13 1.9 Integrated inductors and transformerson the chip 15 1.10 Powergyrators 16 1.11 Useof ANSYSand COMSOLfor the analysis of inductor designs 17 1.12 The need forsimulated inductors 17 1.13 Concluding remarks 18 References 19 2 Gyrators andsimulated inductorsusingop-amps 27 Abstract 27 2.1 Introduction 27 2.2 The gyrator 28 2.3 Op-amp gyratorsand related circuits 31 2.3.1 NIC-based gyrator 31 2.3.2 VCCS-based gyrator 32 2.3.3 Generalized impedance converters (GIC)/gyrators 33 2.3.4 Two-op-amp resistively variable capacitance simulators 36 2.3.5 Two-op-amp lossless inductance simulator 40 2.3.6 Tripathi–Patranabis losslessgrounded inductor 41

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