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It will be shown below that mutual coupling is responsible for all the unique characteristics of phased arrays. The task, then, is to understand it, and to make advantageous use of it. This chapter is concerned with infinite arrays for two reasons. First, the essential characteristics of all scanning arrays exist in infinite arrays, and are most easily calculated there. Second, most array design starts with an infinite array, with finite array (edge) effects included near the end of the design edge effects are the subject of Chapter 8. Mutual coupling fundamentals are discussedfirst. . | 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 SEVEN Mutual Coupling INTRODUCTION It will be shown below that mutual coupling is responsible for all the unique characteristics of phased arrays. The task then is to understand it and to make advantageous use of it. This chapter is concerned with infinite arrays for two reasons. First the essential characteristics of all scanning arrays exist in infinite arrays and are most easily calculated there. Second most array design starts with an infinite array with finite array edge effects included near the end of the design process. These edge effects are the subject of Chapter 8. Mutual coupling fundamentals are discussed first. There follow discussions of the basic analysis methods spatial domain element-by-element spectral domain periodic cell scatting matrix all may include moment method techniques. Finally methods for compensation of scan impedance are covered. FUNDAMENTALS OF SCANNING ARRAYS Current Sheet Model The simplest concept of a phased array is an infinite flat current sheet carrying a uniform current flow parallel to one of the coordinate axes and is due to Wheeler 1948 1965 . This current is phased to radiate at an angle away from broadside. Such a current sheet can be used as a gedanken to derive key scanning properties of phased arrays. The sheet may be either receiving or transmitting with the two situations giving related behavior. First consider an incident plane wave receiving case. Figure shows the current sheet in side view both for a wave incident in the E-plane and in the -plane. If the current sheet is matched for normal incidence 0 0 to rj ohms per square then at other scan angles there is a mismatch. For -plane incidence the incoming wave sees a section of current sheet which is wider than the section 215 216 MUTUAL COUPLING Figure Electric current sheet a - -plane b E-plane. of .

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