The details of a more general form of the sub-structure characteristic mode concept are presented than previously done. The orthogonality properties of these modes are stated, proven, and discussed. Sub-structure characteristic modes are interpreted in terms of loading. V C 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58: [481][482][483][484][485][486] 2016; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.29590Key words: electromagnetic; characteristic modes; Green's functions
INTRODUCTIONThe sub-structure characteristic mode concept was introduced earlier in Ref. 1 for the case of conducting objects. It was intended to deal with the restricted type of problem discussed in Ref. 1, and so was presented in a less general form than is in fact possible. The concept is reviewed, and the more general form discussed here, in Section 2. In addition, the details of the orthogonality properties of the substructure modes, not available elsewhere, are properly dealt in Section 3. These are listed as a set of simple proofs, along with some discussion of their significance. Section 4 provides an interesting interpretation of sub-structure modes in terms of loading. Section 5 concludes the paper. We note that the sub-structure characteristic mode concept was extended to the case of a conducting object in the presence of a dielectric (and vice versa) in Ref. 2, and that a related formulation has been used by the authors of Ref. 3 in the design of slot-fed dielectric resonator antennas. In Ref. 2, the sub-structure concept was also related to the use of modified Green's functions. However, space limitations prevented a full discussion of the details of the sub-structure mode formulation, and statements/proofs of the various orthogonality relations are satisfied by such modes. This material is provided in full in the present paper.
THE GENERAL SUB-STRUCTURE CHARACTERISITIC MODE CONCEPTWe suppose we have a perfectly conducting (PEC) structure, composed of two objects or parts, as shown in Figure 1, with S 0 5S A [ S B . The electromagnetic scattering problem related to this structure can be modeled using an electric field integral equationfor the surface electric current density J s everywhere on the structure, with E scat tan 5Z J s f g, and integral operator Z ::: f g incorporating a free space Green's function as the kernel of the IE. The EFIE can be solved using the method of moments [4,5]. Expansion and weighting functions are distributed over the PEC surface S 0 (on both constituent objects), and the matrix equationformed as the discretized version of the EFIE, where the symbols have their usual meanings. The superscript "fs" explicitly recognizes use of the "free-space" Green's function. It is assumed that a Galerkin approach is used, so that ½Z fs is symmetrical. In practice, even if this is not the case, the matrix operator will usually be sufficiently close to being symmetric for the purposes of characteristic mode computation if sufficiently fine meshing is used.It is possible-and...
