The Double Infinite Arrays with Arbitrary Element Orientation

Here denotes the mutual array impedances between the reference element in array k and all the elements in array m while Z i, Z/,2, and Z/,3 denote the load impedances in the respective array elements. 

Note that the element orientation can vary from stick to stick while the interstick spacing can be arbitrary. Only the element spacing in the z direction must be the same from stick to stick. Otherwise, Floquet s Theorem will be violated. 

7 THE DOUBLE INFINITE ARRAYS WITH ARBITRARY ELEMENT ORIENTATION 

In my first book we found the vector potential as well as the magnetic and electric fields for double infinife arrays of arbifrarily orienfed Hertzian elemenfs of length dl [63]. However, our investigation of elements of arbitrary length was basically limited to elements contained in the plane of the array (but of arbitrary shape and orientation in that plane). 

It was also pointed out that several of the author s former students and others have tackled that problem [66-71]. The reason for not considering it further in my first book was that it leads to a very messy nested integration that could lead to certain convergence problems. The following derivation by Peter Munk avoids this problem, and we therefore find if appropriate to present it here.  

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