Lect33Arrays_1

# Lect33Arrays_1 - ECE 3030 Electromagnetic Fields and Waves...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 33 2009/11/13 Antenna Arrays Gain and Radiation Patterns Antenna Beam Steering with Phased Arrays 1 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 33: Instructor: Dr. Wesley E. Swartz A Two Hertzian Dipole Element Array Consider first an array of just two Hertzian dipoles: Each antenna in the array is an “element” of the array. y z   0 3 0 0 ˆ h r d I z r J x 0 h 1 h 0 J 1 J   1 3 1 1 ˆ h r d I z r J kd One can write the E-field in the far-field as a superposition of the E- fields produced by all the elements in the array: 3 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 33:      , , , sin 4 ˆ sin 4 ˆ 1 0 1 0 . ˆ 0 1 . ˆ 0 0 0 . ˆ 1 . ˆ 0 F r e I I e I I e r d I k j e I e I e r j r E h r k j h r k j r k j o h r k j h r k j r k j o ff Element Factor Array Factor The “element factor” is just the E-field produced by the first element if it were sitting at the origin The “array factor” captures all the interference effects N-Element Antenna Arrays (1) Consider an N-element antenna array where the elements are: all identical (all loops, or all Hertzian dipoles, or all Half-wave dipoles, etc) all oriented in the same way Let the position vector of the m -th antenna be but with possibly different current phasors Let the current phasor of the m -th antenna be I m Then one can write the E-field in the far-field as a superposition of the E-fields produced by all the elements in the array: m h 4 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 33: E fields produced by all the elements in the array: y x m h z m I 0 I 1 I 1 N I z , , , , , 1 0 . ˆ 0 F r e I I r r E N m h r k j m ff m N-Element Antenna Arrays (2) Far-field has two parts Element factor Array factor Gain: , , , 1 0 . ˆ 0 F r Ε e I I r r E N m h r k j m ff m Ε 2 2 2 , , of part angular 4 ˆ , , F r, r P r t r S G 5 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 33: Pattern: max , , , G G p y x m h z m I 0 I 1 I 1 N I z

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Lect33Arrays_1 - ECE 3030 Electromagnetic Fields and Waves...

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