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Although the infinite array techniques of Chapter 7 are excellent for system trades and preliminary design, final design requires a finite array simulation. Direct impedance (admittance) matrix methods were described in Section . These were developed by Oliner and Malech, 1966a; Galindo, 1972; Bailey, 1974; Bailey and Bostian, 1974; Cha and Hsiao, 1974; Steyskal, 1974; Bird, 1979; Luzwick and Harrington, 1982; Clarricoats et al., 1984; Pozar, 1985, 1986; Fukao et al., 1986; Deshpande and Bailey, 1989; Silvestro, 1989; Usoff and Munk, 1994; and others. When moment methods are not necessary (thin half~wave dipoles, for example), sizeable planar arrays may be. | Phased Array Antennas. Robert C. Hansen Copyright 1998 by John Wiley Sons Inc. ISBNs 0-471-53076-X Hardback 0-471-22421-9 Electronic CHAPTER EIGHT Finite Arrays METHODS OF ANALYSIS Overview Although the infinite array techniques of Chapter 7 are excellent for system trades and preliminary design final design requires a finite array simulation. Direct impedance admittance matrix methods were described in Section . These were developed by Oliner and Malech 1966a Galindo 1972 Bailey 1974 Bailey and Bostian 1974 Cha and Hsiao 1974 Steyskal 1974 Bird 1979 Luzwick and Harrington 1982 Clarricoats et al. 1984 Pozar 1985 1986 Fukao et al. 1986 Deshpande and Bailey 1989 Silvestro 1989 Usoff and Munk 1994 and others. When moment methods are not necessary thin half-wave dipoles for example sizeable planar arrays may be solved. When the element current distribution is complicated the number of moment method expansion functions needed for good convergence will restrict this method to small arrays. An elegant solution to the semi-infinite array that is an array extending to infinity on three sides is given by Wasylkiwskyj 1973 . The Weiner-Hopf factorization procedure is extended to finite Fourier transforms resulting in an expression for scan reflection coefficient of the semi-infinite array in terms of scan reflection coefficient for the corresponding infinite array and an integral of a phased sum of the infinite array scan impedances. Still another approach embeds the finite array in a matrix of identical arrays with blank space between Roederer 1971 Ishimaru et al. 1985 Skriverik and Mosig 1993 Roscoe and Perrott 1994 Cátedra et al. 1995 . For single-mode elements thin dipoles thin slots thin patches the procedure is simple. First the scan element pattern SEP is computed for the corresponding infinite array. This SEP is then Fourier transformed usually by discrete Fourier transform DFT back to the aperture. Third a periodic structure consisting of equally .

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