Phase Array AntennaMicrowave EngineeringEE 172Dr. Ray KwokAtmospheric Radar ArrayShigaraki, JapanPhase Array Antenna - Dr. Ray KwokFeatures• High directivity by adding up lower efficient antennas constructively• Lower cost (usually - including more complex feeding network)• Beam steering without moving mechanical parts (faster, reliable)• Ability to change beam shape remotely.• Simultaneously tracking multiple targets (at a cost).Phase Array Antenna - Dr. Ray KwokArray Factor (AF)dIoI1dI2I3dθ⋅⋅⋅+++≡θβθβcos22cos1djdjoeIeIIAFfor constructive interference at far field.For equal phasing: αjnoneII =multiple both sides by ejψ[]( )( )( ) ( )( )( )( )=−−=−−=−=−==⋅⋅⋅++++=−−−=−=∑∑2sin2sin111112/12/2/2/2/2/2/11032ψψψψψψψψψψψψψψψψψψψNeIAFeeeeeeIeeIAFeIeAFeIeAFeIeeeIAFNjojjjjNjNjNojjNojNojNnjnojNnjnojjjo(1)(2)(1) – (2)phaseθβαψcosd+=(wave interference theory)AF gives relative field strength at a given distance, i.e. angular dependence only!Phase Array Antenna - Dr. Ray KwokPattern FactorDefine a Pattern Factor As ψ → 0, eqn(1) says AF = NIoSo as eqn(2) if we ignore the phase (signal delay).=2sin2sin)(ψψψNNf(1)(2)[ ]( )==⋅⋅⋅++++=−−=∑2sin2sin12/11032ψψψψψψψNeIAFeIeeeIAFNjoNnjnojjjonormalized to 1 when ψ = 0Phase Array Antenna - Dr. Ray KwokPattern Plot=2sin2sin)(ψψψNNfN = 602πψperiodic1)(ψfHPBWBWFNside lobesfirst null1. N ↑, main lobe narrows2. N ↑, # of side lobes↑3. Width of side lobe = 2ππππ/N( in ψ ψ ψ ψ )Width of main lobe = 4ππππ/N4. N↑, side lobe level (SLL) ↓5. |f(ψψψψ)| is symmetric about ψ ψ ψ ψ = ππππ# of main lobe = 1# of side lobes = N – 2Total full lobes = N - 1Phase Array Antenna - Dr. Ray Kwok00.20.40.60.8100. 050. 10. 150. 20. 250. 30. 350. 40. 450.50. 550. 60. 650. 70. 750.80. 850.90. 9511. 051. 11. 151. 21. 251. 31. 351. 41. 451. 51. 551. 61. 651. 71. 751. 81. 851. 91. 9522. 052. 12. 152. 22. 252. 32. 352. 42. 452. 52. 552. 62. 652. 72. 752. 82. 852. 92. 9533. 053. 13. 153. 23. 253. 33. 353. 43. 453. 53. 553. 63. 653. 73. 753. 83. 853. 93. 9544. 054. 14. 154. 24. 254. 34. 354. 44. 454. 54. 554. 64. 654. 74. 754. 84. 854. 94. 9555. 055. 15. 155. 25. 255. 35.355. 45. 455. 55. 555. 65. 655. 75. 755. 85. 855. 95. 9566.056. 16. 156.26. 256. 283Polar Plot1. N ↑, main lobe narrows2. N ↑, # of side lobes↑3. Width of side lobe = 2ππππ/N( in ψ ψ ψ ψ )Width of main lobe = 4ππππ/N4. N↑, side lobe level (SLL) ↓5. |f(ψψψψ)| is symmetric about ψ ψ ψ ψ = ππππ# of main lobe = 1# of side lobes = N – 2Total full lobes = N - 1( in ψψψψ )Phase Array Antenna - Dr. Ray KwokArray Pattern( in θθθθ )θαβdsymmetrical patternelementsorientation(not in scale)Phase Array Antenna - Dr. Ray KwokExample – 5 x 1 arrayAntenna Theory& DesignStutzman & ThielePhase Array Antenna - Dr. Ray KwokRadiation Pattern(Array Pattern)x(Element Pattern)Match up with orientation and origin shift.Example: truck with 2 dipolesFor m x n array, treat 1 x n linear array firstGet the radiation pattern for the 1 x n array together with element pattern.Now treat the 1 x n array as the element of the m x 1 array. Follow the same steps.Phase Array Antenna - Dr. Ray KwokExample – Truck: 2 dipolesPhase Array Antenna - Dr. Ray KwokOverall pattern (2 x 1)Phase Array Antenna - Dr. Ray KwokExample – 4 dipole arrays4 x 12 x 22 x 2Phase Array Antenna - Dr. Ray KwokSingle λλλλ/2 dipole elementPhase Array Antenna - Dr. Ray Kwok1 x 2 array (λλλλ/4 along z)λ/4Phase Array Antenna - Dr. Ray Kwok1 x 2 total radiation (along z)λ/4= element * arrayPhase Array Antenna - Dr. Ray Kwok1 x 2 array (λλλλ/2 along z)λ/2Phase Array Antenna - Dr. Ray Kwok1 x 4 total pattern (along z)λ/4 each= (2-elements_z pattern)(1 x 2 array)Phase Array Antenna - Dr. Ray Kwok2 x 1 array (λλλλ/4 along x)λ/4Phase Array Antenna - Dr. Ray Kwok2 x 2 total pattern - zx (all λλλλ/4)λ/4λ/4= (2-elements_z pattern)(2 x 1 array)pole-topPhase Array Antenna - Dr. Ray Kwok2 x 1 array (λλλλ/4 along y)λ/4Phase Array Antenna - Dr. Ray Kwok2 x 2 total pattern - zy (all λλλλ/4)λ/4λ/4car-top= (2-elements_z pattern)(2 x 1 array)Phase Array Antenna - Dr. Ray Kwoksqueezed, elongated donutcompressed donutλ/2 dipolesλ/4