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350lect12 - 12 Interference antenna arrays contd E H We...

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12 Interference, antenna arrays — cont’d. We continue with our study of interference e ff ects and antenna arrays. x y z θ φ r ˜ E = ˆ θ ˜ E θ ˜ E × ˜ H * θ d r - ˆ zd d cos θ 2 d 3 d Beam patterns of N -element antenna arrays examined last lecture were isotropic in φ direction — the main e ff ect of increasing the array size Nd appeared to be narrowing the mainlobe of the pattern in θ direction. New vocabulary: Broadside arrays Array axis Broadside direction These so-called broadside arrays — meaning that they mainly ra- diate in the “broadside direction” of the “array axis” — are good for broadcasting purposes at relatively high frequencies ω 2 π in the FM band ( 100 MHz), where array sizes Nd , in excess of many λ ’s, become practicable (as opposed to in AM band where ω 2 π 1 MHz and λ 300 m). They may also be used as “elements” of arrays built along x - or y -axis directions which we will consider next. In that case it will be possible to produce antenna beam patterns anisotropic in the azimuth plane (in φ direction). We will also consider phasing the element input currents so that the mainlobe of the beam can be steered into desired directions in the azimuth plane. 1
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x y z θ φ r ˜ E = ˆ θ ˜ E θ ˜ E × ˜ H * d d cos θ x 2 d 3 d r - ˆ xd θ x Consider an array of elements polarized in ˆ z -direction positioned along the x -axis as shown above. Our initial analysis of this array will assume equal input currents I o for all the elements. Let ˜ E 0 ( r ) e - jk | r | | r | denote the field at the observation point r due to the element at the origin. Then, using the paraxial approximation, the field phasor at a dis- tant observation point due to the next element at ( d, 0 , 0) can be expressed in terms of ˜ E 0 ( r ) as ˜ E 1 ( r ) ˜ E 0 ( r ) e jkd cos θ x where θ x is the angle between vectors r and ˆ x , i.e., cos θ x = ˆ r · ˆ x = (sin θ cos φ ˆ x +sin θ sin φ ˆ y +cos θ ˆ z ) ·
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