tailieunhanh - Electromagnetic Waves and Antennas combined - Chapter 20

Như chúng ta đã đề cập ở Sec. 19,4, vấn đề thiết kế mảng cơ bản là tương đương với vấn đề thiết kế bộ lọc FIR kỹ thuật số DSP. Sau này tương đương, chúng ta thảo luận về phương pháp thiết kế một số mảng, chẳng hạn như: 1. 2. 3. 4. 5. Phương pháp sắp xếp không Schelkunoff của Chuỗi Fourier phương pháp với Woodward-Lawson cửa sổ tần số lấy mẫu thiết kế chùm tia hẹp thấp sidelobe phương pháp thiết kế Multi-chùm mảng thiết kế. | 20 Array Design Methods Array Design Methods As we mentioned in Sec. the array design problem is essentially equivalent to the problem of designing FIR digital filters in DSP. Following this equivalence we discuss several array design methods such as 1. Schelkunoff s zero placement method 2. Fourier series method with windowing 3. Woodward-Lawson frequency-sampling design 4. Narrow-beam low-sidelobe design methods 5. Multi-beam array design Next we establish some common notation. One-dimensional equally-spaced arrays are usually considered symmetrically with respect to the origin of the array axis. This requires a slight redefinition of the array factor in the case of even number of array elements. Consider an array of N elements at locations xm along the x-axis with element spacing d. The array factor will be A 4 amejkxXm amejkXn ms l m m where kx k cos cf for polar angle Ỡ tt 2. If N is odd say N 2M 1 we can define the element locations xm symmetrically as xm md m 0 1 2. M This was the definition we used in Sec. . The array factor can be written then as a discrete-space Fourier transform or as a spatial z-transform M M A p a I I a m -M m l M M Alz amzm a0 amzm amzm m -M m l . Array Design Methods 803 where kxd kd cos cf and z . On the other hand if N is even say N 2M in order to have symmetry with respect to the origin we must place the elements at the half-integer locations x m tnd - m - d m l The array factor will be now M AW s a-me-j m-1 2 m l M A z 12 I a I J m l In particular if the array weights am are symmetric with respect to the origin am a_m as they are in most design methods then the array factor can be simplified into the cosine forms M A 0 2 am cos mựt N 2M 1 m l M A lp 2 amcos m - 1 2 ự N 2M m l In both the odd and even cases Eqs. and can be expressed as the left-shifted version of a right-sided z-transform A z z N 1 2Ã z z N 1 2 dnzn n 0 where a ão is the vector of array .