RF CIRCUIT DESIGN CHRISTOPHER BOWICK WITH JOHN BLYLER AND CHERYL AJLUNI AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Newnes is an imprint of Elsevier CoverimagebyiStockphoto NewnesisanimprintofElsevier 30CorporateDrive,Suite400,Burlington,MA01803,USA LinacreHouse,JordanHill,OxfordOX28DP,UK Copyright©2008,ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin anyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise, withoutthepriorwrittenpermissionofthepublisher. PermissionsmaybesoughtdirectlyfromElsevier’sScience&TechnologyRights DepartmentinOxford,UK:phone:(+44)1865843830,fax:(+44)1865853333, E-mail:[email protected] viatheElsevierhomepage(http://elsevier.com),byselecting“Support&Contact” then“CopyrightandPermission”andthen“ObtainingPermissions.” Recognizingtheimportanceofpreservingwhathasbeenwritten,Elsevierprintsitsbookson acid-freepaperwheneverpossible. LibraryofCongressCataloging-in-PublicationData Bowick,Chris. RFcircuitdesign/ChristopherBowick.—2nded. p.cm. Includesbibliographicalreferencesandindex. ISBN-13:978-0-7506-8518-4 ISBN-10:0-7506-8518-2 1. RadiocircuitsDesignandconstruction.2. Radiofrequency. I.Title. TK6553.B6332008 621.384'12—dc22 2007036371 BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-0-7506-8518-4 ForinformationonallNewnespublications visitourwebsiteathttp://books.elsevier.com TypesetbyCharonTecLtd(AMacmillanCompany),Chennai,India www.charontec.com 07 08 09 10 10 9 8 7 6 5 4 3 2 1 PrintedintheUnitedStatesofAmerica PREFACE A great deal has changed since Chris Bowick’s RF Circuit Design was first published, some 25 years ago. In fact, we could just say that the RF industry has changed quite a bit since the days of Marconi andTesla—both technological visionaries woven into thefabricofhistoryasthemenwhoenabledradiocommunications.Whocouldhaveenvisionedthattheirinnovationsinthelate 1800’swouldlaythegroundworkfortheeventualcreationoftheradio—akeycomponentinallmobileandportablecommunications systems that exist today? Or, that their contributions would one day lead to such a compelling array of RF applications, ranging fromradartothecordlesstelephoneandeverythinginbetween. Today, theradiostandsasthebackboneofthewirelessindustry. Itisinvirtuallyeverywirelessdevice,whetheracellularphone,measurement/instrumentationsystemusedinmanufacturing,satellite communicationssystem,televisionortheWLAN. Of course, back in the early 1980s when this book was first written, RF was generally seen as a defense/military technology. It was utilized in the United States weapons arsenal as well as for things like radar and anti-jamming devices. In 1985, that image of RF changed when the FCC essentially made several bands of wireless spectrum, the Industrial, Scientific, and Medical (ISM) bands,availabletothepubliconalicense-freebasis.Bydoingso—andperhapswithoutevenfullycomprehendingthemomentum itsactionswouldeventuallycreate—theFCCplantedtheseedsofwhatwouldonedaybeamultibillion-dollarindustry. Todaythatindustryisbeingdrivennotbyaerospaceanddefense,butratherbytheconsumerdemandforwirelessapplicationsthat allow“anytime,anywhere”connectivity.And,itisbeingenabledbyarangeofnewandemergingradioprotocolssuchasBluetooth®, Wi-Fi(802.11WLAN),WiMAX,andZigBee®,inadditionto3Gand4GcellulartechnologieslikeCDMA,EGPRS,GSM,andLong TermEvolution(LTE).Forevidenceofthisfact, oneneedslooknofurtherthanthecellularhandset.Withinonedecade, between roughly the years 1990 and 2000, this application emerged from a very small scale semiprofessional niche, to become an almost omnipresentdevice,withthenumberofusersequalto18%oftheworldpopulation.Today,nearly2billionpeopleusemobilephones onadailybasis—notjustfortheirvoiceservices,butforagrowingnumberofsocialandmobile,data-centricInternetapplications. Thankstothemobilephoneandservicetelecommunicationsindustryrevolution,averageconsumerstodaynotonlyexpectpervasive, ubiquitousmobility,theyaredemandingit. ButwhatwillthefutureholdfortheconsumerRFapplicationspace?Theanswertothatquestionseemsfairlywell-definedasthe RFindustrynowfindsitselfrallyingbehindasinglegoal:torealizetrueconvergence.Inotherwords,thefutureoftheRFindustry liesinitsabilitytoenablenext-generationmobiledevicestocrossalloftheboundariesoftheRFspectrum. Essentiallythen, this convergedmobiledevicewouldbringtogethertraditionallydisparatefunctionality(e.g.,mobilephone,television,PCandPDA)on themobileplatform. Again, nowhere is the progress of the converged mobile device more apparent than with the cellular handset. It offers the ideal platformonwhichRFstandardsandtechnologiescanconvergetodeliverawholehostofnewfunctionalityandcapabilitiesthat,as asociety, wemaynotevenyetbeabletoimagine. Movementinthatdirectionhasalreadybegun.Accordingtoanalystswiththe IDCWorldwideMobilePhoneTrackerservice,theconvergedmobiledevicemarketgrewanestimated42percentin2006foratotal ofover80millionunits.Inthefourthquarteralone,vendorsshippedatotalof23.5milliondevices,33percentmorethanthesame quarterayearago.That’safairlyremarkableaccomplishmentconsideringthat,priortothemid-nineties,thepossibilityoftrueRF convergencewasthoughtunreachable. Themixing, samplinganddirect-conversiontechnologiesweresimplydeemedtooclunky andlimitedtoprovidethefoundationnecessaryforimplementationofsuchavision. x Preface Regardlessofhowandwhenthegoaloftrueconvergenceisfinallyrealized,onethinghasbecomeimminentlyclearinthemidstof allthegrowthandinnovationofthepasttwentyfiveyears—theRFindustryisaliveandwell.Moreimportantly,itiswellprimed forafuturefullofcontinuinginnovationandmarketgrowth. Ofcourse,whileallofthesechangescreatedawealthofbusinessopportunitiesintheRFindustry,theyalsocreatednewchallenges for RF engineers pushing the limits of design further and further. Today, new opportunities signal new design challenges which engineers—whetherexpertsinRFtechnologyornot—willlikelyhavetoface. Onekeychallengeishowtoaccommodatetheneedformulti-bandreceptionincellularhandsets.Anotherstemsfromtheneedfor higherbandwidthathigherfrequencieswhich,inturn,meansthatthecriticaldimensionsofrelevantparasiticelementsshrink.Asa result,layoutelementsthatoncecouldbeignored(e.g.,interconnect,contactareasandholes,andbondpads)becomenon-negligible andinfluencecircuitperformance. Inresponsetotheseandotherchallenges,theelectronicsindustryhasinnovated,andcontinuestoinnovate.Consider,forexample, that roughly 25 years ago or so, electronic design automation (EDA) was just an infant industry, particularly for high-frequency RF and microwave engineering. While a few tools were commercially available, rather than use these solutions, most companies opted to develop their own high-frequency design tools.As the design process became more complex and the in-house tools too costlytodevelopandmaintain,engineersturnedtodesignautomationtoaddresstheirneeds.Thankstoinnovationfromavariety ofEDAcompanies,engineersnowhaveaccesstoafullgamutofRF/microwaveEDAproductsandmethodologiestoaidthemwith everythingfromdesignandanalysistoverification. But the innovation doesn’t stop there. RF front-end architectures have and will continue to evolve in step with cellular handsets sportingmulti-bandreception.Multi-bandsubsystemsandshrinkingelementsizeshavecoupledwithongoingtrendstowardlower costanddecreasingtime-to-markettocreatetheneedfortightlyintegratedRFfront-endsandtransceivercircuits.Thesehighlevels of system integration have in turn given rise to single-chip modules that incorporate front-end filters, amplifiers and mixes. But implementing single-chip RF front-end designs requires a balance of performance trade-offs between the interfacing subsystems, namely, theantennaanddigitalbasebandsystems.AchievingtherequiredsystemperformancewhenimplementingintegratedRF front-endsmeansthatanalogdesignersmustnowworkmorecloselywiththeirdigitalbasebandcounterpart,thusleadingtogreater integrationofthetraditionalanalog–digitaldesignteams. OtherareasofinnovationintheRFindustrywillcomefromimprovedRFpowertransistorsthatpromisetogivewirelessinfrastructure poweramplifiersnewlevelsofperformancewithbetterreliabilityandruggedness.RFICshopetoextendtheroleofCMOStoenable emergingmobilehandsetstodelivermultimediafunctionsfromacompactpackageatlowercost.Incumbentslikegalliumarsenide (GaAs) have moved to higher voltages to keep the pace going.Additionally, power amplifier-duplexer-filter modules will rapidly displaceseparatecomponentsinmulti-bandW-CDMAradios.Single-chipmultimodetransceiverswilldisplaceseparateEDGEand W-CDMA/HSDPA transceivers inW-EDGE handsets.And, to better handle parasitic and high-speed effects on circuits, accurate modelingandback-annotationofever-smallerlayoutelementswillbecomecritical,aswillaccurateelectromagnetic(EM)modeling ofRFon-chipstructureslikecoilsandinterconnect. StillfurtherinnovationwillcomefromemergingtechnologiesinRFsuchasgalliumnitrideandmicro-electro-mechanicalsystems (MEMS).Inthelattercase,theseadvancedmicromachineddevicesarebeingintegratedwithCMOSsignalprocessingandcondi- tioning circuits for high-volume markets such as mobile phones and portable electronics.According to market research firmABI Research,by2008useofMEMsinmobilephoneswilltakeoff.Thisisduetothetechnology’ssmallsize,flexibilityandperformance advantages,allofwhicharecriticaltoenablingtheadaptive,multifunctionhandsetsofthefuture. It is this type of innovation, coupled with the continuously changing landscape of existing application and market opportunities, which has prompted a renewed look at the content in RF Circuit Design. It quickly became clear that, in order for this book to continue to serve its purpose as your hands-on guide to RF circuit design, changes were required. As a result, this new 25th anniversaryeditioncomestoyouwithupdatedinformationonexistingtopicslikeresonantcircuits, impedancematchingandRF amplifierdesign, aswellasnewcontentpertainingtoRFfront-enddesignandRFdesigntools. Thisinformationisapplicableto anyengineerworkingintoday’sdynamicallychangingRFindustry,aswellasforthosetruevisionariesworkingonthecuspofthe information/communication/entertainmentmarketconvergencewhichtheRFindustrynowinspires. CherylAjluniandJohnBlyler CONTENTS Preface ix Acknowledgments xi CHAPTER1 1 Components and Systems Wire–Resistors–Capacitors–Inductors–Toroids–ToroidalInductorDesign–PracticalWindingHints CHAPTER2 23 Resonant Circuits SomeDefinitions–Resonance(LosslessComponents)–LoadedQ–InsertionLoss–ImpedanceTransformation– CouplingofResonantCircuits–Summary CHAPTER3 37 Filter Design Background–ModernFilterDesign–NormalizationandtheLow-PassPrototype–FilterTypes–Frequencyand ImpedanceScaling–High-PassFilterDesign–TheDualNetwork–BandpassFilterDesign–Summaryofthe BandpassFilterDesignProcedure–Band-RejectionFilterDesign–TheEffectsofFiniteQ CHAPTER4 63 Impedance Matching Background–TheLNetwork–DealingWithComplexLoads–Three-ElementMatching–Low-QorWideband MatchingNetworks–TheSmithChart–ImpedanceMatchingontheSmithChart–SoftwareDesignTools–Summary CHAPTER5 103 The Transistor at Radio Frequencies RFTransistorMaterials–TheTransistorEquivalentCircuit–YParameters–SParameters–UnderstandingRF TransistorDataSheets–Summary CHAPTER6 125 Small-Signal RF Amplifier Design SomeDefinitions–TransistorBiasing–DesignUsingYParameters–DesignUsingSParameters viii Contents CHAPTER7 169 RF (Large Signal) Power Amplifiers RFPowerTransistorCharacteristics–TransistorBiasing–RFSemiconductorDevices–PowerAmplifierDesign– MatchingtoCoaxialFeedlines–AutomaticShutdownCircuitry–BroadbandTransformers–PracticalWindingHints– Summary CHAPTER8 185 RF Front-End Design HigherLevelsofIntegration–BasicReceiverArchitectures–ADC’SEffectonFront-EndDesign– SoftwareDefinedRadios–CaseStudy—ModernCommunicationReceiver CHAPTER9 203 RF Design Tools DesignToolBasics–DesignLanguages–RFICDesignFlow–RFICDesignFlowExample–SimulationExample1– SimulationExample2–Modeling–PCBDesign–Packaging–CaseStudy–Summary APPENDIXA 227 APPENDIXB 229 BIBLIOGRAPHY 233 INDEX 237 C H A COMPONENTS P T E and Systems R 1 Components, those bits and pieces which make up a radio frequency (RF) circuit, seem at times to EXAMPLE1-1 be taken for granted. A capacitor is, after all, a GiventhatthediameterofAWG50wireis1.0mil(0.001 capacitor—isn’tit?A1-megohmresistorpresents inch),whatisthediameterofAWG14wire? an impedance of at least 1 megohm—doesn’t it? The reactance of an inductor always increases with frequency, Solution right?Well,asweshallseelaterinthisdiscussion,thingsaren’t AWG50=1mil alwaysastheyseem.Capacitorsatcertainfrequenciesmaynot AWG44=2×1mil=2mils becapacitorsatall,butmaylookinductive,whileinductorsmay looklikecapacitors,andresistorsmaytendtobealittleofboth. AWG38=2×2mils=4mils AWG32=2×4mils=8mils Inthischapter,wewilldiscussthepropertiesofresistors,capac- itors,andinductorsatradiofrequenciesastheyrelatetocircuit AWG26=2×8mils=16mils design.But,first,let’stakealookatthemostsimplecomponent AWG20=2×16mils=32mils ofanysystemandexamineitsproblemsatradiofrequencies. AWG14=2×32mils=64mils(0.064inch) WIRE WireinanRFcircuitcantakemanyforms.Wirewoundresistors, inductors,andaxial-andradial-leadedcapacitorsalluseawire Thedepthintotheconductoratwhichthecharge-carriercurrent ofsomesizeandlengtheitherintheirleads,orintheactualbody density falls to 1/e, or 37% of its value along the surface, is ofthecomponent,orboth.Wireisalsousedinmanyinterconnect knownastheskindepthandisafunctionofthefrequencyand applicationsinthelowerRFspectrum.Thebehaviorofawirein thepermeabilityandconductivityofthemedium.Thus,differ- theRFspectrumdependstoalargeextentonthewire’sdiameter ent conductors, such as silver, aluminum, and copper, all have andlength.Table1-1lists,intheAmericanWireGauge(AWG) differentskindepths. system, each gauge of wire, its corresponding diameter, and Thenetresultofskineffectisaneffectivedecreaseinthecross- other characteristics of interest to the RF circuit designer. In sectionalareaoftheconductorand,therefore,anetincreasein the AWG system, the diameter of a wire will roughly double the ac resistance of the wire as shown in Fig. 1-1. For copper, every six wire gauges. Thus, if the last six gauges and their theskindepthisapproximately0.85cmat60Hzand0.007cm correspondingdiametersarememorizedfromthechart,allother at 1MHz. Or, to state it another way: 63% of the RF current wire diameters can be determined without the aid of a chart flowinginacopperwirewillflowwithinadistanceof0.007cm (Example1-1). oftheouteredgeofthewire. SkinEffect Straight-WireInductors Aconductor,atlowfrequencies,utilizesitsentirecross-sectional Inthemediumsurroundinganycurrent-carryingconductor,there areaasatransportmediumforchargecarriers.Asthefrequency exists a magnetic field. If the current in the conductor is an is increased, an increased magnetic field at the center of the alternatingcurrent, thismagneticfieldisalternatelyexpanding conductor presents an impedance to the charge carriers, thus andcontractingand,thus,producingavoltageonthewirewhich decreasing the current density at the center of the conductor opposesanychangeincurrentflow. Thisoppositiontochange and increasing the current density around its perimeter. This iscalledself-inductanceandwecallanythingthatpossessesthis increasedcurrentdensityneartheedgeoftheconductorisknown qualityaninductor.Straight-wireinductancemightseemtrivial, asskineffect.Itoccursinallconductorsincludingresistorleads, but as will be seen later in the chapter, the higher we go in capacitorleads,andinductorleads. frequency,themoreimportantitbecomes. 2 RF CIRCUIT DESIGN A (cid:1)pr2 electriccurrent.Bydefinition: 1 1 A (cid:1)pr2 1voltacross1ohm=1coulombpersecond 2 2 Skin Depth Area (cid:1)A2(cid:2)A1 =1ampere (cid:1)p(r2(cid:2)r2) 2 1 Thethermaldissipationinthiscircumstanceis1watt. P=EI r 2 =1volt×1ampere r1 =1watt Resistorsareusedeverywhereincircuits,astransistorbiasnet- RF current flow works,pads,andsignalcombiners.However,veryrarelyisthere in shaded region any thought given to how a resistor actually behaves once we departfromtheworldofdirectcurrent(DC).Insomeinstances, suchasintransistorbiasingnetworks,theresistorwillstillper- formitsDCcircuitfunction,butitmayalsodisruptthecircuit’s FIG.1-1. Skindepthareaofaconductor. RFoperatingpoint. Theinductanceofastraightwiredependsonbothitslengthand ResistorEquivalentCircuit itsdiameter,andisfoundby: The equivalent circuit of a resistor at radio frequencies is (cid:1) (cid:2) (cid:3) (cid:4) 4l shown in Fig. 1-2. R is the resistor value itself, L is the lead L=0.002l 2.3log −0.75 µH (Eq.1-1) d inductance, and C is a combination of parasitic capacitances whichvariesfromresistortoresistordependingontheresistor’s where, structure. Carbon-composition resistors are notoriously poor L=theinductanceinµH, high-frequencyperformers.Acarbon-compositionresistorcon- l=thelengthofthewireincm, sistsofdenselypackeddielectricparticulatesorcarbongranules. Between each pair of carbon granules is a very small parasitic d=thediameterofthewireincm. capacitor. These parasitics, in aggregate, are not insignificant, however,andarethemajorcomponentofthedevice’sequivalent ThisisshownincalculationsofExample1-2. circuit. L L R EXAMPLE1-2 Findtheinductanceof5centimetersofNo.22copper C wire. Solution FromTable1-1,thediameterofNo.22copperwireis FIG.1-2. Resistorequivalentcircuit. 25.3mils.Since1milequals2.54×10−3cm,thisequals Wirewoundresistorshaveproblemsatradiofrequenciestoo.As 0.0643cm.SubstitutingintoEquation1-1gives maybeexpected,theseresistorstendtoexhibitwidelyvarying (cid:1) (cid:2) (cid:3) (cid:4) 4(5) impedances over various frequencies. This is particularly true L=(0.002)(5) 2.3log 0.0643 −0.75 of the low resistance values in the frequency range of 10MHz to 200MHz. The inductor L, shown in the equivalent circuit =50nanohenries of Fig. 1-2, is much larger for a wirewound resistor than for acarbon-compositionresistor.Itsvaluecanbecalculatedusing thesingle-layerair-coreinductanceapproximationformula.This Theconceptofinductanceisimportantbecauseanyandallcon- formula is discussed later in this chapter. Because wirewound ductors at radio frequencies (including hookup wire, capacitor resistorslooklikeinductors,theirimpedanceswillfirstincrease leads,etc.)tendtoexhibitthepropertyofinductance.Inductors as the frequency increases. At some frequency (Fr), however, willbediscussedingreaterdetaillaterinthischapter. theinductance(L)willresonatewiththeshuntcapacitance(C), producinganimpedancepeak.Anyfurtherincreaseinfrequency will cause the resistor’s impedance to decrease as shown in RESISTORS Fig.1-3. Resistanceisthepropertyofamaterialthatdeterminestherateat A metal-film resistor seems to exhibit the best characteris- whichelectricalenergyisconvertedintoheatenergyforagiven tics over frequency. Its equivalent circuit is the same as the Resistors 3 F r EXAMPLE1-3 InFig.1-2,theleadlengthsonthemetal-filmresistorare ) 1.27cm(0.5inch),andaremadeupofNo.14wire.The Z e ( totalstrayshuntcapacitance(C)is0.3pF.Iftheresistor c n a valueis10,000ohms,whatisitsequivalentRFimpedance d e p at200MHz? m I Solution FromTable1-1,thediameterofNo.14AWGwireis64.1 mils(0.1628cm).Therefore,usingEquation1-1: (cid:1) (cid:2) (cid:3)(cid:4) 4(1.27) L=(0.002)(1.27) 2.3log −0.75 Frequency (F) 0.1628 =8.7nanohenries FIG.1-3. Impedancecharacteristicofawirewoundresistor. Thispresentsanequivalentreactanceat200MHzof: X =ωL L carbon-compositionandwirewoundresistor,butthevaluesofthe =2π(200×106)(8.7×10−9) individualparasiticelementsintheequivalentcircuitdecrease. =10.93ohms The impedance of a metal-film resistor tends to decrease with frequency above about 10MHz, as shown in Fig. 1-4. This is Thecapacitor(C)presentsanequivalentreactanceof: due to the shunt capacitance in the equivalent circuit. At very 1 highfrequencies,andwithlow-valueresistors(under50(cid:1)),lead Xc= ωC inductance and skin effect may become noticeable. The lead 1 inductance produces a resonance peak, as shown for the 5(cid:1) = 2π(200×106)(0.3×10−12) resistanceinFig.1-4,andskineffectdecreasestheslopeofthe curveasitfallsoffwithfrequency. =2653 120 Thecombinedequivalentcircuitforthisresistor,at200 5Ω MHz,isshowninFig.1-5. ce) 100 100Ω j10.93Ω j10.93Ω n esista 80 1KΩ 10K dc r 10KΩ % 60 e ( Carbon Composition (cid:2) j2653Ω nc 40 a d pe 100 KΩ FIG.1-5. EquivalentcircuitvaluesforExample1-3. m 20 I 1 MΩ Fromthissketch,wecanseethat,inthiscase,thelead 0 inductanceisinsignificantwhencomparedwiththe10K 1.0 10 100 1000 seriesresistanceanditmaybeneglected.Theparasitic Frequency (MHz) capacitance,ontheotherhand,cannotbeneglected. Whatwenowhave,ineffect,isa2653(cid:1)reactancein parallelwitha10,000(cid:1)resistance.Themagnitudeofthe FIG.1-4. Frequencycharacteristicsofmetal-filmvs.carbon-composition combinedimpedanceis: resistors.(AdaptedfromHandbookofComponentsforElectronics, McGraw-Hill) Z= (cid:5) RXe Many manufacturers will supply data on resistor behavior at R2+X2 e radiofrequenciesbutitcanoftenbemisleading.Onceyouunder- (10K)(2653) standthemechanismsinvolvedinresistorbehavior,however,it = (cid:5) willnotmatterinwhatformthedataissupplied. Example1-3 (10K)2+(2653)2 illustratesthatfact. =2564.3ohms Therecenttrendinresistortechnologyhasbeentoeliminateor Thus,our10K resistorlookslike2564ohmsat200MHz. greatlyreducethestrayreactancesassociatedwithresistors.This has led to the development of thin-film chip resistors, such as 4 RF CIRCUIT DESIGN thoseshowninFig.1-6.Theyaretypicallyproducedonalumina However, the farad is much too impractical to work with, so orberylliasubstratesandofferverylittleparasiticreactanceat smallerunitsweredevised. frequenciesfromDCto2GHz. 1microfarad=1µF=1×10−6farad 1picofarad=1pF=1×10−12 farad Asstatedpreviously,acapacitorinitsfundamentalformconsists of two metal plates separated by a dielectric material of some sort. If we know the area (A) of each metal plate, the distance (d)betweentheplate(ininches),andthepermittivity(ε)ofthe dielectric material in farads/meter (f/m), the capacitance of a parallel-platecapacitorcanbefoundby: 0.2249εA C = picofarads (Eq.1-2) dε 0 where ε =free-spacepermittivity=8.854×10−12 f/m. 0 In Equation 1-2, the area (A) must be large with respect to the distance(d).Theratioofεtoε isknownasthedielectriccon- 0 stant(k)ofthematerial.Thedielectricconstantisanumberthat providesacomparisonofthegivendielectricwithair(seeFig. FIG.1-6. Thin-filmresistors.(CourtesyofVishayIntertechnology) 1-7). The ratio of ε/ε0 for air is, of course, 1. If the dielectric constantofamaterialisgreaterthan1,itsuseinacapacitoras CAPACITORS adielectricwillpermitagreateramountofcapacitanceforthe Capacitors are used extensively in RF applications, such as same dielectric thickness as air. Thus, if a material’s dielectric bypassing,interstagecoupling,andinresonantcircuitsandfil- constantis3,itwillproduceacapacitorhavingthreetimesthe ters.Itisimportanttoremember,however,thatnotallcapacitors capacitanceofonethathasairasitsdielectric.Foragivenvalue lend themselves equally well to each of the above-mentioned of capacitance, then, higher dielectric-constant materials will applications. TheprimarytaskoftheRFcircuitdesigner, with producephysicallysmallercapacitors.But,becausethedielec- regardtocapacitors,istochoosethebestcapacitorforhispar- tric plays such a major role in determining the capacitance of ticularapplication. Costeffectivenessisusuallyamajorfactor a capacitor, it follows that the influence of a dielectric on intheselectionprocessand,thus,manytrade-offsoccur.Inthis capacitor operation, over frequency and temperature, is often section, we’ll take a look at the capacitor’s equivalent circuit important. and we will examine a few of the various types of capacitors usedatradiofrequenciestoseewhicharebestsuitedforcertain Dielectric K Air 1 applications.Butfirst,alittlereview. Polystrene 2.5 Paper 4 Parallel-PlateCapacitor Mica 5 Ceramic (low K) 10 A capacitor is any device which consists of two conducting Ceramic (high K) 100(cid:2)10,000 surfaces separated by an insulating material or dielectric. The dielectricisusuallyceramic,air,paper,mica,plastic,film,glass, oroil.Thecapacitanceofacapacitoristhatpropertywhichper- FIG.1-7. Dielectricconstantsofsomecommonmaterials. mits the storage of a charge when a potential difference exists between the conductors. Capacitance is measured in units of farads.A1-faradcapacitor’spotentialisraisedby1voltwhenit Real-WorldCapacitors receivesachargeof1coulomb. Theusageofacapacitorisprimarilydependentuponthechar- Q acteristics of its dielectric. The dielectric’s characteristics also C = V determine the voltage levels and the temperature extremes at whichthedevicemaybeused.Thus,anylossesorimperfections where, inthedielectrichaveanenormouseffectoncircuitoperation. C=capacitanceinfarads, TheequivalentcircuitofacapacitorisshowninFig.1-8,whereC Q=chargeincoulombs, equalsthecapacitance,R istheheat-dissipationlossexpressed s V=voltageinvolts. eitherasapowerfactor(PF)orasadissipationfactor(DF),R p