LongPwrPtsCh6-0221a71

LongPwrPtsCh6-0221a71 - 1 Chapter 6 Chapter 6 Part 1 Part 1...

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Unformatted text preview: 1 Chapter 6 Chapter 6 Part 1 Part 1 Array Basics Array Basics ECE 5318/6352 ECE 5318/6352 Antenna Engineering Antenna Engineering Spring 2006 Spring 2006 Dr. Stuart Long Dr. Stuart Long 2 ¡ ¡ Array Rationale Array Rationale ¡ Single elements Single elements Usually broad beamwidth Relatively low directivity ¡ Often system requirements demand higher directivities Often system requirements demand higher directivities Can increase electrical size or form an “assembly” of elements in an electrical and geometrical configuration called an ARRAY ARRAY 3 ¡ Assumptions for our coverage Assumptions for our coverage 1. All elements are identical 2. No coupling between elements 3. Total field is vector sum of individual radiation patterns ¡ Use array to control overall pattern shape by: Use array to control overall pattern shape by: 1. Geometrical configuration of overall array (linear, circular, rectangular, spherical, …) 2. Relative displacement between radiators 3. Amplitude of excitement of each element 4. Excitation phase of each element 5. Individual element pattern 4 ¡ ¡ Two element array Two element array simplest case simplest case ψ 5 ¡ Two identical horizontal sources along the z axis, a distance “ d ” apart, constant amplitudes; upper element leads lower one in phase by amount “ β “ look at [ y - z ] plane ( φ = 90°) only there sin ψ = cos θ ¡ Similar case of horizontal dipole above a ground plane, except 2 nd . source not necessarily 180° out of phase – but similar analysis ¡ Two element array Two element array (cont) (cont) 6 ¡ Total Field Total Field ¡ Two element array Two element array (cont) (cont) 2 2 ) 2 ( 2 cos 4 2 θ π η β r e I k j E r k j o − − ≅ A 2 cos 2 d r r θ ≅ + 2 1 E E E G G G + ≅ t 1 1 ) 2 ( 1 cos 4 1 θ π η β r e I k j E r k j o − − ≅ A θ cos 2 1 d r r − ≅ [6-2] 7 ¡ Total Field Total Field [6-3] ¡ Two element array Two element array (cont) (cont) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + ≅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − 2 cos 2 cos cos 4 ˆ β θ β θ θ θ π η kd j kd j jkr o t e e r e I k j A G a E 1 2 2 2 1 2 1 2 ˆ cos cos 4 j k r j k r o t k I e e j r r β β θ η θ θ π ⎛ ⎞ ⎛ ⎞ − − − − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎡ ⎤ ⎢ ⎥ ≅ + ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ E a G A 8 [6-3] Element Factor Array Factor [AF] [E e ] ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ≅ − 2 cos cos 2 cos 4 ˆ β θ θ π η θ kd r e I k j E r k j o t A a ¡ Two element array Two element array (cont) (cont) 9 θ π η cos 4 ] [E e r e I k j r k j o − ≅ A ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ≅ 2 cos cos 2 [AF] β θ kd as function of kd and β ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ≅ 2 cos cos (AF) β θ kd n [6-4] ¡ Two element array Two element array (cont) (cont) 10 ¡ Example Example 4 λ = d 2 4 2 π λ λ π = = d k ( ) AF cos cos 4 n π θ ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ( a ) = β ( ) θ cos E e = n ¡ Two element array Two element array (cont) (cont) 11...
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LongPwrPtsCh6-0221a71 - 1 Chapter 6 Chapter 6 Part 1 Part 1...

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