350lect13 - 13 Arrays and feed networks Performance of...

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13 Arrays and feed networks Performance of antenna arrays depends on our ability to feed the array ele- ments with input currents having accurate phase relationships. This can be accomplished by using appropriately designed “feed networks” consisting of transmission line (TL) segments. We continue our study of antenna arrays with examples illustrating feed network design issues. x y z r ˜ E = ˆ θ ˜ E θ ˜ E × ˜ H * d cos θ x r - ˆ xd I o e - I o e - j 2 α I o e - j 3 α I o θ φ θ x Example 1: Consider a 4-element phased array with ˆ z -polarized short dipole elements, progressive phasing with increments α ,ande lemen t - to -e tspac ing s d = λ 2 along the x -axis. It is desired that the array has a gain maximum on θ =90 plane along φ =45 directions. Determine α such that I 1 = I 0 e - and suggest aTLfeednetworkthatcanbeusedtod istr ibutetherequ iredinputcurrentso f the array elements. Solution: Let ˜ E 0 ( r ) denote the far-Feld phasor due to the array element at the origin. The phasor due to the element at ( d, 0 , 0) can then be expressed (in the far-Feld) as ˜ E 1 ( r )= ˜ E 0 ( r ) e - e jkd cos θ x = ˜ E 0 ( r ) e - e sin θ cos φ . Since we are interested in θ case, we can simplify this as ˜ E 1 ( r ˜ E 0 ( r ) e j ( kd cos φ - α ) . Since we want constructive interference in φ direction, we will demand that e j ( cos φ - α ) =1 α = cos φ for φ , i.e, α = 2 π λ λ 2 cos 45 = π 2 rad .
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350lect13 - 13 Arrays and feed networks Performance of...

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