Antenna Theory

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AntennaTheory ANTENNA Consistsofawireorotherconductor,oracollectionofwiresorconductors,that converts electrical energy into electromagnetic waves for transmission, and electromagneticwavesintoelectricalenergyforreception Anantennapassivereciprocaldevice. Acts as a transducer to convert electrical oscillations in a transmission line or waveguidetoapropagatingwaveinfreespaceandviceversa. Functions as an impedance matcher between a transmission line or waveguide andfreespace. All antennas have a radiation pattern which is a plot of the field strength or powerdensityatvariousangularpositionsrelativetotheantenna. BasicAntennaOperation

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Thecouplingdevice(couplingcoil)connectsthetransmittertothefeeder. The feeder is a transmission line that carries energy to the antenna. The antenna radiatesthisenergyintospace. AntennaTerminologyandParameters Radiation Pattern a polar diagram or graph representing field strengths or power densitiesatvariousangularpositionsrelativetoanantenna. Absoluteradiationpatternradiationpatternplottedinvariabledistance,fixedpower Relativeradiationpatternradiationpatternplottedinvariablepower,fixeddistance Frontlobemajorlobe;lobethatreceivesthemostenergy Sidelobeslobesadjacenttothefrontlobe Backlobeslobesindirectionexactlyoppositethefrontlobe

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Fronttobackratioratioofthefrontlobepowertothebacklobepower Fronttosideratioratioofthefrontlobepowertothesidelobepower Line of shoot or point of shoot line bisecting the major lobe from the center of the antennainthedirectionofmaximumradiation Nearfieldfieldpatternthatisclosetotheantenna(inductionfield) Farfieldfieldpatternthatisatagreatdistance(radiationfield) Duringonehalfofacycle,powerisradiatedfromanantennawheresomeofthe powerisstoredtemporaryinthenearfield.Duringthesecondhalfofthecycle,power inthenearfieldisreturnedtotheantenna.

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Radiation resistance the resistance that, if it replaced the antenna, would dissipate exactlythesameamountofpowerthattheantennaradiates P Rr = 2 i Antennaefficiencyratioofthepowerradiatedbyanantennatothesumofthepower radiatedandthepowerdissipated P Prad Rr = rad = = Pin Prad + Pd R r + R e Where: =antennaefficiency Prad=powerradiatedbyanantenna(W) Pd=powerdissipatedinantenna(W) Rr=radiationresistance(ohms) Re=effectiveantennaresistance(groundresistance,ohms) i=antennacurrentattheinput AntennaGain Directive gain ratio of the power density radiated in a particular direction to the powerdensityradiatedtothesamepointbyareferenceantenna(isotropicantenna) Directivitymaximumdirectivegain PD D= PD(ref ) Power gain same as directive gain, except that antenna efficiency is taken into account indB: A P = 10 log D A P = D ; Foranisotropicantenna,powergainisapproximately1.64(2.15dB) EffectiveIsotropicRadiatedPower(EIRP) EIRP = Prad D t = Pin A t Where: Prad=powerradiatedbyanantenna(W) Dt=transmitantennadirectivegain(unitless) Pin=totalantennainputpower(W) At=transmitantennapowergain(unitless) Engr. Divino Fiel A. de Bien AntennaTheory


TodeterminethepowerdensityatagivendistanceRfromatransmitantenna: P D P A PD = in 2t = rad 2 t 4R 4R AntennaCaptureArea AC 4 Ar 2 ; Ar = AC = 4 2 Capturedpower: P A Pcap = in 2t AC 4R Where: AC=effectivecapturearea =wavelengthofreceivesignal Arreceiveantennapowergain(unitless) R=distancebetweentransmitandreceiveantennas AntennaPolarizationorientationofelectricfieldradiatedfromtheantenna Antenna Beamwidthangularseparationbetweentwohalfpower(3dB)pointson themajorlobeofanantennasradiationpattern Antennagainisinverselyproportionaltobeamwidth Antennabandwidthfrequencyrangeoverwhichantennaoperationissatisfactory Antennainputimpedanceorfeedpointpointontheantennawherethetransmission lineisconnected;generallycomplex Ra=antennaresistance Za=Ra+jXa where: Ra=Re+Rr Xa=antennareactance Engr. Divino Fiel A. de Bien



Problems: 1. For an antenna with input power of 100 W, rms current of 2 A and effective resistanceof2ohms,determinethe(a)antennaradiationresistance;(b)antenna efficiency;(c)powerradiatedfromtheantenna. Solution: P 100 (a) Rr = 2 = 2 = 25 i 2 Rr 25 = = 92.59% (b) = Rr + Re 25 + 2 P (c) = rad ; Prad = Pin = 0.9259 (100 ) = 92.59W Pin 2. DeterminethepowergainindBforanantennawithadirectivegainof50dBand efficiencyof75% AP = 10 log D ; 50 = 10 log D; D = 100,000 AP = 10 log [(100,000)(0.75)] = 48.75 dB 3. DeterminetheEIRPindBmforanantennawithdirectivityof33dB,efficiencyof 82%andinputpowerof100W. EIRP = Prad D t = Pin A t 33 = 10 log Dt ; Dt = 1995 .262 Prad = ; Prad = Pin = 0.82(100 ) = 82W Pin EIRP = Prad Dt = 82(1995.262 ) = 163 ,611.5098W 163 ,611 .5098W in dBm : 10 log = 82.13 dBm 1x10 3 4. Find the power density at a point 20 km from an antenna with input power of 1kWandpowergainof23dB. 23 = 10 log At ; At = 199 .526 P A 1k (199.526) PD = in 2t = = 39.694 W / m 2 2 4R 4 ( 20000)

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5. Ahalfwavedipoleisdrivenwitha10Wsignalat200MHz.Areceivingdipole 100 km away is aligned such that the gain is cut in half. Determine the receive powerandvoltageintothe73ohmreceiver. Forahalfwavedipole:D=1.64 Forthewavelength:=c/f=1.5m Receivedpower: Pin At (10)(1.64) (0.5)(1.64)(1.5) 2 AC = = 19.16 x 10 12 W Pcap = 2 2 4 4R 4 (100 k ) Where: Ar 2 (0.5)(1.64)(1.5) 2 AC = = 4 4 Forthevoltagereceived:P=V2/R;V=37.4V a. BasicAntenna ElementaryDoubletanelectricallyshortdipole ThroughMaxwellsEquation: 60 Il sin E= R Where: E=electricfieldintensity(V/m) I=dipolecurrent(A,rms) l=endtoendlengthofthedipole R=distancefromthedipole =wavelength = angle between the axis of the antenna and the direction of radiation Since:PD=E2/120: 30 I 2 l 2 sin 2 PD = 2 R 2

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Pro oblem:An nelementarydoubl letis8cm mlong.If the20M MHzcurren ntflowing gthrough h it is 3A, what is the field stre s ength 25k away from the doublet in a direction of km y e t, f max ximumra adiation? Forthe ewavelength:=c/ /f=15m 60 Il sin 60 ( 3)(0.08) sin 90 s E= = = 120.64 V / m R k) (15)( 25k Hal lfWaveD Dipole G Generally yreferredasHertza antenna W Widelyus sedatfreq quenciesa above2M MHz A Aresonan ntantenna a(amulti ipleofqu uarterwav velengtha andopen circuitedatthefar r end) e

Qua arterwav veGround dedAnten nna Monop pole(singl le)antenn naonequarterwav velengthlo ongmoun ntedverticallywith h thelow werendeitherdirec ctlyconne ectedtogr roundort througha acoupling gnetwork k Alsoca alledMarc conniante enna Charac ctersiticsa aresimila artotheH Hertzante ennabeca auseofth heground dreflected d waves Curren ntmaxima aoccursat tthegrou undedend ds Toredu ucepowe erlosses,g groundsh houldbea agoodcon nductor.A Analtern nativeway y ofimpr rovingcon nductivity yisthrou ughacoun nterpoise Size is only half as long compared to the H f d Hertz ant tenna but should b located t be d closeto oground Engr. Divino Fiel A. de Bien

Ant tennaTheory y


AntennaLoading Physicaldimensionsforlowfrequencyantennasarenotpractical.Toincreaseelectrical length,loadingtechniquesareapplied.

AntennaArrays Formed when two or more antenna elements are combined to form a single antenna Increasethedirectivityoftheantennaandconcentratesradiatedpowerwithina smallgeographicarea Antenna elements can be driven or parasitic. Driven elements are directly connectedtothetransmissionlineandreceivepowerfromthesource.Parasitic elements receive energy through mutual induction with a driven or another parasiticelement.

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BroadsideArray Madebyplacingseveralresonantdipolesofequalsizeinparallelwitheachother andinastraightline.Allelementsarefedinphasefromthesource Radiatesatrightanglestotheplaneofthearrayandverylittletothedirectionof theplane

EndfireArray Sameelementconfigurationasthebroadsidearrayexceptthatthetransmission lineisnotcrisscrossedbetweenelements Engr. Divino Fiel A. de Bien



RhombicAntenna AnonresonantantennasuitedforHFtransmission Madeupoffournonresonantelementsterminatedinaresistor

SpecialPurposeAntennas FoldedDipole Asingleantennamadeupoftwoelements Inputimpedanceisequaltohalfwaveimpedance(72)timesthesquareofthe numberoffoldedwires.(22*72=288)

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YagiUdaAntenna A linear array consisting of a dipole and two or more parasitic elements: one reflectorandoneormoredirectors CommonlyusedforVHFTVtransmission

TurnstileAntenna Formed by placing two dipoles at right angles to each other (90 degrees out of phase) Radiationpatternproducesnearlyanomnidirectionalpattern

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LogPeriodicAntenna Consists of several dipoles of different length and spacing that are fed from a singlesourceatthesmallend.Thetransmissionlineiscrisscrossedbetweenthe feedpointsofadjacentpairsofdipoles Advantage: independent of radiation resistance and radiation pattern to frequency Notatypeofantennabutaclassofantenna Physicalstructureisrepetitive,makingelectricalcharacteristicsrepetitiveaswell

Formulafordipolelengthandspacing: R2 R3 R4 1 L2 L3 L4 = = = = = = R1 R2 R3 L1 L2 L3 L 1 Rn = = n Rn1 Ln1 Where: R=dipolespacing L=dipolelength =designratio(lessthan1) Engr. Divino Fiel A. de Bien



Foratypicaldesign:=0.7;=30 HelicalAntenna A broadband VHF or UHF antenna suited for applications for which radiating circularlypolarizedelectromagneticwavesarerequire