Topic 3. Fundamental Parameters of Antennas. Tamer Abuelfadl

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1 Topic 3 Fundamental Parameters of Antennas Tamer Abuelfadl Electronics and Electrical Communications Department Faculty of Engineering Cairo University Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 1 / 31

2 Electromagnetic Radiation Time-changing current radiates and accelerated charge radiates. Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 2 / 31

3 Fundamental Parameters of Antennas 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Many of the denitions of these terms are taken from the IEEE Std Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 3 / 31

4 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 4 / 31

5 Radiation Patterns Antenna Radiation Pattern or Antenna Pattern The spatial distribution of a quantity that characterizes the electromagnetic eld generated by an antenna. Radiation is a spherical TEM elds with propagation in ^a r direction and elds in ^a θ and ^a φ directions. E θ and E φ 1/r E θ Eφ Phases of these elds, δ θ and δ φ.

6 Radiation Patterns Antenna Radiation Pattern or Antenna Pattern The spatial distribution of a quantity that characterizes the electromagnetic eld generated by an antenna. Radiation is a spherical TEM elds with propagation in ^a r direction and elds in ^a θ and ^a φ directions. E θ and E φ 1/r E θ Eφ Phases of these elds, δ θ and δ φ.

7 Radiation Patterns Antenna Radiation Pattern or Antenna Pattern The spatial distribution of a quantity that characterizes the electromagnetic eld generated by an antenna. Radiation is a spherical TEM elds with propagation in ^a r direction and elds in ^a θ and ^a φ directions. E θ and E φ 1/r E θ Eφ Phases of these elds, δ θ and δ φ.

8 Radiation Patterns Field Pattern: A plot of the eld magnitude ( E or H ) on a linear scale. Power Pattern: A plot of the square of the eld magnitude ( E 2 or H 2 ) on either a linear or decibel (db, 2log E ). Field Pattern Power Pattern Linear Scale Linear Scale Decibel Scale (db)

9 Radiation Patterns Radiation Pattern Lobes Major lobe Minor lobes Side lobe Back lobe

10 Radiation Patterns Isotropic, Directional, and Omnidirectional Pattern Isotropic radiator a hypothetical lossless antenna having equal radiation in all directions. Directional antenna having the property of radiating or receiving electromagnetic waves more eectively in some directions than in others, usually applied on antennas having directivity greater than that of half-wave dipole. Omnidirectional pattern having an essentially nondirectional pattern in a given plane. Directional antenna Omnidirectional in azimuth

11 Radiation Patterns Principal Patterns E-Plane The plane containing the electric-eld vector and the direction of maximum radiation. H-Plane The plane containing the magnetic-eld vector and the direction of maximum radiation. E-plane: xz plane H-plane: xy plane E-pane: any elevation plane. H-plane: azimuth plane.

12 Radiation Patterns Field Regions Reactive near eld region: reactive elds predominates radiating elds. Radiating near eld (Fresnel) region: radiation elds predominates, but the radiation pattern varies with the radius r. Far-eld (Fraunhover) region: Fields vary as e jkr, and the radiation pattern is independent on r. Electric and magnetic elds are predominantly in ^aθ and ^aφ directions, and are in phase. r

13 Radiation Patterns Solid Angle (Steradian) da = r 2 sinθdθdφ, dω = da r = sinθdθdφ 2 Ω = sinθdθdφ (sr) (θ,φ)

14 Radiation Patterns Solid Angle (Steradian) For a sphere of radius r, nd the solid angle Ω A (in square radians or steradians) of a spherical cap on the surface of the sphere over the north-pole region dened by a spherical angle of θ 3, φ 36. Solution Ω A = ˆ 2π ˆ π/6 dω = = 2π [ cosθ] π/6 = 2π ˆ 2π ˆ π/6 [ sinθdθdφ = ] ˆ 2π dφ = (sr) ˆ π/6 sinθdθ

15 Radiation Patterns Solid Angle (Steradian) For a sphere of radius r, nd the solid angle Ω A (in square radians or steradians) of a spherical cap on the surface of the sphere over the north-pole region dened by a spherical angle of θ 3, φ 36. Solution Ω A = ˆ 2π ˆ π/6 dω = = 2π [ cosθ] π/6 = 2π ˆ 2π ˆ π/6 [ sinθdθdφ = ] ˆ 2π dφ = (sr) ˆ π/6 sinθdθ

16 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 13 / 31

17 Radiation Power Density Instantaneous Poynting Vector W or S = E H W or S = instantaneous Poynting vector (W/m 2 ). E = instantaneous electric-eld intensity (V/m). H = instantaneous magnetic-eld intensity (A/m). P = instantaneous total power (W) P = W ds = W ^a n da S S Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 14 / 31

18 Radiation Power Density E (x,y,z;t) = R [ E(x,y,z)e jωt] = 1 [ Ee jωt + E e jωt] 2 H (x,y,z;t) = R [ H(x,y,z)e jωt] = 1 [ He jωt + H e jωt] 2 W or S = E H = 1 2 R[E H ] R[ E He j2ωt] Average Poynting Vector W av (x,y,z) or S av (x,y,z) = 1 2 R[E H ] P rad = = where P rad is the average radiated power. S S W rad ds = W av ^nda S 1 2 R[E H ] ds

19 Radiation Power Density Example 2.2 The radial component of the radiated power density (Poynting vector radial component) of an antenna is given by, Determine the total radiated power. W rad = ^a r W r = ^a r A sinθ r 2 (W/m 2 ),

20 Radiation Power Density Example 2.2 The radial component of the radiated power density (Poynting vector radial component) of an antenna is given by, Determine the total radiated power. Solution: W rad = ^a r W r = ^a r A sinθ r 2 (W/m 2 ), P rad = = W rad ^nda ( S ˆ 2π ˆ π ^a r A sinθ r 2 ) (^a r r 2 sinθdθdφ ) = π 2 A (W)

21 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 17 / 31

22 Radiation Intensity Radiation Intensity The power radiated from an antenna per unit solid angle, U = r 2 W rad (W/unit solid angle) U (θ,φ) = r 2 2η E(r,θ,φ) 2 = r 2 [ E θ (r,θ,φ) 2 + E φ (r,θ,φ) 2] 2η = 1 [ Eθ (θ,φ) 2 + E 2η φ (θ,φ) 2] where far-zone electric field of the antenna, E(r,θ,φ) = [ E θ (θ,φ)^a θ + E φ (θ,φ)^a φ ] e jkr r Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 18 / 31

23 Radiation Intensity Radiation Intensity The power radiated from an antenna per unit solid angle, U = r 2 W rad (W/unit solid angle) ˆ 2π ˆ π P rad = UdΩ = U sinθdθdφ Ω Radiation from an isotropic source P rad = U dω = U dω = 4πU Ω Ω U = P rad 4π Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 19 / 31

24 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 2 / 31

25 Beamwidth HPBW (Half Power Beam Width) FNBW (First-Null Beam Width) Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 21 / 31

26 Beamwidth Example 2.4 The normalized radiation intensity of an antenna is represented by, U (θ) = cos 2 (θ)cos 2 (3θ), ( θ 9, φ 36 ) 1 Find the HPBW 2 Find the FNBW 1 U (θ h ) = cos 2 (θ h )cos 2 (3θ h ) =.5 = cos(θ h )cos(3θ h ) =.77 ( ).77 θ h = cos 1, iteratively gives θ h.251rad = cos3θ h HPBW = 2θ h.52 rad = U (θ n ) = cos 2 (θ n )cos 2 (3θ n ) = θ n = π 6 rad = 3 FNBW = 2θ n = π rad = 6 3

27 Beamwidth Example 2.4 The normalized radiation intensity of an antenna is represented by, U (θ) = cos 2 (θ)cos 2 (3θ), ( θ 9, φ 36 ) 1 Find the HPBW 2 Find the FNBW 1 U (θ h ) = cos 2 (θ h )cos 2 (3θ h ) =.5 = cos(θ h )cos(3θ h ) =.77 ( ).77 θ h = cos 1, iteratively gives θ h.251rad = cos3θ h HPBW = 2θ h.52 rad = U (θ n ) = cos 2 (θ n )cos 2 (3θ n ) = θ n = π 6 rad = 3 FNBW = 2θ n = π rad = 6 3

28 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 23 / 31

29 Directivity Directivity The ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions. If the direction is not specied the direction of the maximum radiation intensity is implied. D = U U = 4πU P rad D max = D = U max U Partial Directivities D θ and D φ, = 4πU max P rad D θ = 4πU θ (P rad ) θ + (P rad ) φ, D φ = D = D θ + D φ 4πU φ (P rad ) θ + (P rad ) φ

30 Directivity Example 2.6 The radial component of the radiated power density of an innitesimal linear dipole of length l λ is given by, W av = ^a r W r = ^a r A sin 2 θ r 2. Determine the maximum directivity of the antenna and express the directivity as a function of θ and φ.

31 Directivity Example 2.6 The radial component of the radiated power density of an innitesimal linear dipole of length l λ is given by, W av = ^a r W r = ^a r A sin 2 θ r 2. Determine the maximum directivity of the antenna and express the directivity as a function of θ and φ. Solution: P rad = ˆ 2π ˆ π U = r 2 W r = A sin 2 θ A sin 2 θ sinθdθdφ = A ( 8π 3 D = 4πU = 1.5sin 2 θ P rad D max = 1.5 at θ = 9 )

32 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 26 / 31

33 Beam Solid Angle Ω A (Beam Area) Beam Solid Angle Ω A (Beam Area) The solid angle through which all the power of the antenna would ow if its radiation is constant (and equal to the maximum value of U) for all angles within Ω A. Ω A = P rad U max = Ω UdΩ = U max Ω U U max dω = 4π D max Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 27 / 31

34 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 28 / 31

Antenna Input Impedance and Radiation Eciency R r = radiation resistance of the antenna R L = loss resistance of the antenna Antenna Input Impedance Z A X A = antenna reactance Z g = R g + jx g

35 Antenna Input Impedance and Radiation Eciency R r = radiation resistance of the antenna R L = loss resistance of the antenna Antenna Input Impedance Z A X A = antenna reactance Z g = R g + jx g generator impedance Radiation Eciency η Z A = R A + jx A, R A = R r + R L The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter. η = P rad P rad = = R r = R r P Acc P rad + P losses R A R r + R L

36 Outline 1 Radiation Pattern Radiation Pattern Lobes Isotropic, Directional, and Omnidirectional Pattern Principal Patterns Field Regions Solid Angle 2 Radiation Power Density 3 Radiation Intensity 4 Beamwidth 5 Directivity 6 Beam Solid Angle Ω A (Beam Area) 7 Antenna Input Impedance and Radiation Eciency 8 Antenna Gain Tamer Abuelfadl (EEC, Cairo University) Topic 3 ELC 45A, ELC N45 3 / 31

37 Antenna Gain gain (in a given direction) The ratio of the radiation intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. Gain does not include losses arising from impedance and polarization mismatches. If the direction is not specied, the direction of maximum radiation intensity is implied. G = 4πU P Acc = ηd Partial gains in θ and φ polarization: G θ = 4πU θ P Acc, G = G θ + G φ G φ = 4πU φ P Acc

Chapter 2. Fundamental Properties of Antennas. ECE 5318/6352 Antenna Engineering Dr. Stuart Long

Chapter 2. Fundamental Properties of Antennas. ECE 5318/6352 Antenna Engineering Dr. Stuart Long Chapter Fundamental Properties of Antennas ECE 5318/635 Antenna Engineering Dr. Stuart Long 1 IEEE Standards Definition of Terms for Antennas IEEE Standard 145-1983 IEEE Transactions on Antennas and Propagation