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- 1. 1 Chapter 2 Fundamental Properties of Antennas ECE 5318/6352 Antenna Engineering Dr. Stuart Long
- 2. 2 IEEE Standards Definition of Terms for Antennas IEEE Standard 145-1983 IEEE Transactions on Antennas and Propagation Vol. AP-31, No. 6, Part II, Nov. 1983
- 3. 3 Radiation Pattern (or Antenna Pattern) “The spatial distribution of a quantity which characterizes the electromagnetic field generated by an antenna.”
- 4. 4 Distribution can be a Mathematical function Graphical representation Collection of experimental data points
- 5. 5 Quantity plotted can be a Power flux density W[W/m²] Radiation intensity U [W/sr] Field strength E [V/m] Directivity D
- 6. 6 Graph can be Polar or rectangular
- 7. 7 Graph can be Amplitude field |E| or power |E|² patterns (in linear scale) (in dB)
- 8. 8 Graph can be 2-dimensional or 3-D most usually several 2-D “cuts” in principle planes
- 9. 9 Radiation pattern can be Isotropic Equal radiation in all directions (not physically realizable, but valuable for comparison purposes) Directional Radiates (or receives) more effectively in some directions than in others Omni-directional nondirectional in azimuth, directional in elevation
- 10. 10 Principle patterns E-plane Plane defined by E-field and direction of maximum radiation H-plane Plane defined by H-field and direction of maximum radiation (usually coincide with principle planes of the coordinate system)
- 11. 11 Coordinate System Fig. 2.1 Coordinate system for antenna analysis.
- 12. 12 Radiation pattern lobes Major lobe (main beam) in direction of maximum radiation (may be more than one) Minor lobe - any lobe but a major one Side lobe - lobe adjacent to major one Back lobe – minor lobe in direction exactly opposite to major one
- 13. 13 Side lobe level or ratio (SLR) (side lobe magnitude / major lobe magnitude) - 20 dB typical < -50 dB very difficult Plot routine included on CD for rectangular and polar graphs
- 14. 14 Polar Pattern Fig. 2.3(a) Radiation lobes and beamwidths of an antenna pattern
- 15. 15 Linear Pattern Fig. 2.3(b) Linear plot of power pattern and its associated lobes and beamwidths
- 16. 16 Field Regions Reactive near field energy stored not radiated λ= wavelength D= largest dimension of the antenna 362.0DR
- 17. 17 Field Regions Radiating near field (Fresnel) radiating fields predominate pattern still depend on R radial component may still be appreciable λ= wavelength D= largest dimension of the antenna 23262.0DRD
- 18. 18 Field Regions Far field ( Fraunhofer Fraunhofer) field distribution independent of R field components are essentially transverse 22DR
- 19. 19 Radian Fig. 2.10(a) Geometrical arrangements for defining a radian r 2 radians in full circle arc length of circle
- 20. 20 Steradian one steradian subtends an area of 4π steradians in entire sphere ddrdAsin2 Fig. 2.10(b) Geometrical arrangements for defining a steradian. ddrdAdsin2 2rA
- 21. 21 Radiation power density HEW Instantaneous Poynting vector Time average Poynting vector [ W/m ² ] Total instantaneous Power Average radiated Power [ W/m ² ] ssWP d [ W ] HEW Re21avg savgraddPsW [ W ] [2-8] [2-9] [2-4] [2-3]
- 22. 22 Radiation intensity “Power radiated per unit solid angle” avgWrU2 far zone fields without 1/r factor 22),,( 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. 23 Directive Gain Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions radogPUUUD4 Directivity 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. 24 Directivity radmaxomaxoPUUUD4 Do (isotropic) = 1.0 ogDD0 Directivity -- Do value of directive gain in direction of maximum radiation intensity
- 25. 25 Beamwidth Half power beamwidth Angle 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 beamwidth Angle between nulls in pattern Fig. 2.11(b) 2-D power patterns (in linear scale) of U()=cos²()cos³()
- 26. 26 Approximate directivity for omnidirectional patterns McDonald 2HPBW0027.0HPBW 101 oD π π Pozar (HPBW in degrees) Results shown with exact values in Fig. 2.18 HPBW1818.01914.172oD nUsin Better if no minor lobes [2-33b] [2-32] [2-33a] For example
- 27. 27 Approximate directivity for directional patterns Kraus 1212441,253orrddD π/2 π Tai & Pereira Antennas with only one narrow main lobe and very negligible minor lobes 22212221815,7218.22ddrroD nUcos [2-30b] [2-31] [2-27] For example ( ) HPBW in two perpendicular planes in radians or in degrees) 12,rr12,dd Note: 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. 28 Approximate directivity for directional patterns Can 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. 29 Gain Like directivity but also takes into account efficiency of antenna (includes reflection, conductor, and dielectric losses) oinoinZZZZ ;12 eo : overall eff. er : reflection eff. ec : conduction eff. ed : dielectric eff. Efficiency source) isotropic(lossless,PUPUeDeGinmaxradmaxooooabs 44 dcroeeee dccdeee [2-49c] radcdinPeP radoincPeP
- 30. 30 Gain By IEEE definition “gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses)” source) isotropic(lossless,PUDeGinmaxocdo 4 [2-49a]
- 31. 31 Bandwidth “frequency range over which some characteristic conforms to a standard” Pattern bandwidth Beamwidth, side lobe level, gain, polarization, beam direction polarization bandwidth example: circular polarization with axial ratio < 3 dB Impedance bandwidth usually based on reflection coefficient under 2 to 1 VSWR typical
- 32. 32 Bandwidth Broadband antennas usually use ratio (e.g. 10:1) Narrow band antennas usually use percentage (e.g. 5%)
- 33. 33 Polarization Linear Circular Elliptical Right or left handed rotation in time
- 34. 34 Polarization Polarization loss factor p is angle between wave and antenna polarization 22 ˆˆcoswapPLF [2-71]
- 35. 35 Input impedance “Ratio of voltage to current at terminals of antenna” ZA = RA + jXA RA = Rr + RL Rr = radiation resistance RL = loss resistance ZA = antenna impedance at terminals a-b
- 36. 36 Input impedance Antenna 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. 37 Friis Transmission Equation Fig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis transmission equation
- 38. 38 Friis Transmission Equation et = efficiency of transmitting antenna er = efficiency of receiving antenna Dt= directive gain of transmitting antenna Dr = directive gain of receiving antenna = wavelength R = distance between antennas assuming impedance and polarization matches 224),(),( RDDeePPrrrtttrttr [2-117]
- 39. 39 Radar Range Equation Fig. 2.32 Geometrical arrangement of transmitter, target, and receiver for radar range equation22144),(),( RRDDeePPrrrttttrcdrcdt [2-123]
- 40. 40 Radar Cross Section RCS Usually given symbol Far field characteristic Units in [m²] 4rincUW incident power density on body from transmit directionincW scattered power intensity in receive directionrU Physical 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. 41 Radar Cross Section ( RCS) Function of Polarization of the wave Angle of incidence Angle of observation Geometry of target Electrical properties of target Frequency
- 42. 42 Radar Cross Section ( RCS)

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