# Ece5318 ch2

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- 1. 1Chapter 2Fundamental Propertiesof AntennasECE 5318/6352Antenna EngineeringDr. Stuart Long

2. 2IEEE StandardsDefinition of Terms for AntennasIEEE Standard 145-1983IEEE Transactions on Antennas andPropagation Vol. AP-31, No. 6, Part II, Nov. 1983 3. 3Radiation Pattern(or Antenna Pattern)The spatial distribution of a quantity whichcharacterizes the electromagnetic fieldgenerated by an antenna. 4. 4Distribution can be aMathematical functionGraphical representationCollection of experimental data points 5. 5Quantity plotted can be aPower flux density W[W/m]Radiation intensity U [W/sr]Field strength E [V/m]Directivity D 6. 6 Graph can bePolar or rectangular 7. 7 Graph can beAmplitude field |E| or power |E| patterns(in linear scale) (in dB) 8. 8Graph can be2-dimensional or 3-Dmost usually several 2-D cuts in principleplanes 9. 9Radiation pattern can beIsotropicEqual radiation in all directions (not physically realizable, but valuable for comparison purposes)DirectionalRadiates (or receives)more effectivelyin some directions than in othersOmni-directionalnondirectional in azimuth, directional in elevation 10. 10Principle patternsE-planePlane defined by E-field and direction of maximum radiationH-planePlane defined by H-field and direction of maximum radiation(usually coincide with principle planes of the coordinate system) 11. 11Coordinate SystemFig. 2.1 Coordinate system for antenna analysis. 12. 12Radiation pattern lobesMajor lobe (main beam) in direction of maximum radiation (may be more than one)Minor lobe - any lobe but a major oneSide lobe - lobe adjacent to major oneBack lobe minor lobe in direction exactly opposite to major one 13. 13Side lobe level or ratio (SLR)(side lobe magnitude / major lobe magnitude)- 20 dB typical< -50 dB very difficultPlot routine included on CD for rectangular and polar graphs 14. 14Polar PatternFig. 2.3(a) Radiation lobes andbeamwidths of an antenna pattern 15. 15Linear PatternFig. 2.3(b) Linear plot of power pattern andits associated lobes and beamwidths 16. 16Field RegionsReactive near fieldenergy stored not radiated= wavelengthD= largest dimension of the antenna 362.0DR 17. 17Field RegionsRadiating near field (Fresnel)radiating fields predominatepattern still depend on Rradial component may still be appreciable= wavelengthD= largest dimension of the antenna 23262.0DRD 18. 18Field RegionsFar field (Fraunhofer Fraunhofer)field distribution independent of Rfield components are essentially transverse 22DR 19. 19RadianFig. 2.10(a) Geometrical arrangements for defining a radianr2 radians in full circlearc length of circle 20. 20Steradianone steradian subtends an area of4 steradians in entire sphereddrdAsin2Fig. 2.10(b) Geometrical arrangementsfor defining a steradian.ddrdAdsin2 2rA 21. 21 Radiation power densityHEW Instantaneous Poynting vectorTime average Poynting vector[ W/m ]Total instantaneousPowerAverage radiatedPower[ W/m ] ssWP d[ W ]HEW Re21avg savgraddPsW[ W ][2-8][2-9][2-4][2-3] 22. 22 Radiation intensityPower radiated per unit solid angleavgWrU2far zone fields without 1/r factor22),,( 2),( rrUE 222),,(),,( 2 rErEr[W/unit solid angle][2-12a]22oo1(,)(,) 2EE Note: This final equation does not have an r in it. The zero superscript means that the 1/r term is removed. 23. 23Directive GainRatio of radiation intensity in a given direction to the radiation intensity averaged over all directionsradogPUUUD4Directivity Gain(Dg) -- directivity in a given direction[2-16]04radPU (This is the radiation intensity if the antenna radiated its power equally in all directions.)201,sin4SUUdd Note: 24. 24DirectivityradmaxomaxoPUUUD4Do (isotropic) = 1.0ogDD0Directivity-- Dovalue of directive gain in direction of maximum radiation intensity 25. 25BeamwidthHalf power beamwidthAngle between adjacent points where field strength is 0.707 times the maximum, or the power is 0.5 times the maximum(-3dB below maximum)First null beamwidthAngle between nulls in patternFig. 2.11(b) 2-D power patterns (in linear scale)of U()=cos()cos() 26. 26Approximate directivity foromnidirectional patternsMcDonald2HPBW0027.0HPBW 101 oD Pozar(HPBW in degrees)Results shown with exact values in Fig. 2.18HPBW1818.01914.172oD nUsinBetter if no minor lobes [2-33b][2-32][2-33a]For example 27. 27Approximate directivity for directional patternsKraus1212441,253orrddD /2 Tai & PereiraAntennas with only one narrow main lobe and very negligible minor lobes22212221815,7218.22ddrroD nUcos[2-30b][2-31][2-27]For example( ) HPBW in two perpendicular planes in radians or in degrees)12,rr12,ddNote: According to Elliott, a better number to use in the Kraus formula is 32,400 (Eq. 2-271 in Balanis). In fact, the 41,253 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one). 28. 28Approximate directivity fordirectional patternsCan calculate directivity directly (sect.2.5),can evaluate directivity numerically (sect. 2.6)(when integral for Prad cannot be done analytically,analytical formulas cannot be used ) 29. 29GainLike directivity but also takes into account efficiency of antenna(includes reflection, conductor, and dielectric losses) oinoinZZZZ ;12eo : overall eff.er : reflection eff.ec : conduction eff.ed : dielectric eff.Efficiency source) isotropic(lossless,PUPUeDeGinmaxradmaxooooabs 44 dcroeeee dccdeee[2-49c]radcdinPeP radoincPeP 30. 30GainBy IEEE definition gain does not include losses arising from impedancemismatches (reflection losses) and polarization mismatches (losses) source) isotropic(lossless,PUDeGinmaxocdo 4[2-49a] 31. 31Bandwidthfrequency range over which some characteristic conforms to a standardPattern bandwidthBeamwidth, side lobe level, gain, polarization, beam directionpolarization bandwidth example: circular polarization with axial ratio < 3 dBImpedance bandwidthusually based on reflection coefficientunder 2 to 1 VSWR typical 32. 32BandwidthBroadband antennasusually use ratio (e.g. 10:1)Narrow band antennasusually use percentage (e.g. 5%) 33. 33PolarizationLinearCircularEllipticalRight or left handedrotation in time 34. 34PolarizationPolarization loss factorp is angle between wave and antenna polarization22 coswapPLF[2-71] 35. 35Input impedanceRatio of voltage to current at terminals of antennaZA = RA + jXARA = Rr + RLRr = radiation resistanceRL = loss resistanceZA = antenna impedance at terminals a-b 36. 36Input impedanceAntenna radiation efficiency 2221211() 22grrcdrLgrgLIRPowerRadiatedbyAntennaPePowerDeliveredtoAntennaPPIRIR [2-90]LrrcdRRRe Note: this works well for those antennas that are modeled as a series RLC circuit like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values. 37. 37Friis Transmission EquationFig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis transmission equation 38. 38Friis Transmission Equationet = efficiency of transmitting antennaer = efficiency of receiving antennaDt= directive gain of transmitting antennaDr = directive gain of receiving antenna= wavelengthR = distance between antennasassuming impedance andpolarization matches224),(),( RDDeePPrrrtttrttr [2-117] 39. 39Radar Range EquationFig. 2.32 Geometrical arrangement oftransmitter, target, and receiver forradar range equation22144),(),( RRDDeePPrrrttttrcdrcdt [2-123] 40. 40Radar Cross SectionRCSUsually given symbol Far field characteristicUnits in [m]4rincUW incident power density on body from transmit directionincW scattered power intensity in receive directionrUPhysical interpretation: The radar cross section is the area of an equivalent ideal black body absorber that absorbs all incident power that then radiates it equally in all directions. 41. 41Radar Cross Section (RCS)Function ofPolarization of the waveAngle of incidenceAngle of observationGeometry of targetElectrical properties of targetFrequency 42. 42Radar Cross Section (RCS)