lecture33 - 1 ECE 303 Fall 2007 Farhan Rana Cornell...

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Unformatted text preview: 1 ECE 303 Fall 2007 Farhan Rana Cornell University Lecture 33 Antenna Arrays and Phase Arrays In this lecture you will learn: Antenna arrays Gain and radiation pattern for antenna arrays Antenna beam steering with phase array antennas ECE 303 Fall 2007 Farhan Rana Cornell University Two Hertzian Dipoles A Two Element Array y z ( ) ( ) 3 h r d I z r J r r r r = x h r 1 h r J r 1 J r ( ) ( ) 1 3 1 1 h r d I z r J r r r r = ( ) ( ) [ ] ( ) ( ) ( ) , , , sin 4 sin 4 1 1 . 1 . . 1 . F r e I I e I I e r d I k j e I e I e r kd 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 = + = + = r r r r r r r 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: Consider first an array of just two Hertzian dipoles: Element Factor Array Factor Each antenna in the array is an element of the array 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 2 ECE 303 Fall 2007 Farhan Rana Cornell University An N-Element Antenna Array - I 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- but with possibly different current phasors Let the current phasor of the m-th antenna be I m Let the position vector of the m-th antenna be m h r y x m h r z m I I 1 I 1 N I z 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: ( ) ( ) ( ) ( ) , , , , , 1 ....
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lecture33 - 1 ECE 303 Fall 2007 Farhan Rana Cornell...

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