161_1_Lecture_16

161_1_Lecture_16 - EE161 Electromagnetic Waves Fall, 2010...

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Unformatted text preview: EE161 Electromagnetic Waves Fall, 2010 Instructor: Dr. Shenheng Xu Electrical Engineering Dept., UCLA Prof. Y. Ethan Wang Lecture 16 Arrays with Uniform Excitation Electronic Scanning of Arrays Satellite Communications Radar Systems Radio Telescopes Far Field of Linear Array Therefore, we can apply the following approximations cos cos id R Z R R i i (for phase) element spacing R R i Phase differences between different paths do not diminish (for amplitude) The final radiated far field is thus, when overall distance is large 1 cos ) , ( ) , , ( N i jikd i jkR e e A R e f R E element related field pattern array related field pattern he radiated power density as function of angle is 2 1 cos 2 2 2 ) , ( 1 ) , , ( 1 ) , , ( N jikd i e e A f R E R S The radiated power density as function of angle is, array factor 2 2 i R element pattern Element Pattern & Array Factor Thus, one can write ) , ( ) , ( ) , ( ) , , ( , 2 1 cos , a e N jikd i e F R S e A R S R S i 2 2 ) , ( 1 ) , , ( e e f R S where is the single element radiation power density 2 R 2 1 cos ) ( N jikd i a e A F is related to array only, thus defined as array factor i If defining , cos kd 2 2 1 ) ( i N ji i a A DFT e A F i i j i i e a A Recall the complex excitation for each antenna element is 2 1 cos 2 1 cos ) ( N jikd j i N jikd i a e e a e A F i The array factor is thus, i i Conclusion: The antenna array radiation pattern as a whole is equal to the product of the...
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This note was uploaded on 02/09/2011 for the course EE 161 taught by Professor Huffaker during the Spring '08 term at UCLA.

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161_1_Lecture_16 - EE161 Electromagnetic Waves Fall, 2010...

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