0018-926X (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2019.2934902, IEEE Transactions on Antennas and Propagation > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract—In this paper, an approach combining the electric field integral equation (EFIE) and impedance boundary condition (IBC) is presented for the characteristic mode analysis (CMA) of composite metallic-dielectric structures. Different from published works, only the electric currents are used in this approach and the computed eigencurrents are in a similar form as those of purely metallic structures. To ensure completeness and orthogonality of the eigencurrents, symmetry of the IBC-EFIE operator has been carefully examined. For lossy structures, a new formulation is deduced for CMA. The presented IBC-EFIE formulation is able to handle a variety of problems, e.g., lossy metals, thin dielectrics, thin dielectric coated conductors, and metasurfaces. Several numerical examples are provided for those problems, and full-wave CMA solutions are used to verify the IBC-EFIE formulation. It is shown that this method is fairly accurate while computationally efficient, which makes CMA a promising tool for large scale or complex composite structures. Index Terms—Characteristic mode, composite structures, impedance boundary condition, lossy metal, metasurface. I. INTRODUCTION HARACTERISTIC mode analysis (CMA) has found a series of useful applications in recent years. Thanks to the physical insights provided by the eigencurrents and eigenvalues of the CMA, many interesting and promising works have been reported during the last decade for purely metallic structures [1]. Nowadays, more and more antenna structures are designed and fabricated on printed circuit boards, e.g., the terminal and base station antennas for the fifth generation (5G) mobile systems. In addition, metamaterials and metasurfaces play an important role in the enhancement of antenna performance or antenna miniaturization [2] [3]. Therefore, more attentions are now paid to the CMA of composite metallic and dielectric structures. To date, only a few works deal with the CMA of composite metallic-dielectric structures. Among those excellent works, the first attempt seems to be the CMA of a microstrip patch antenna using the surface equivalence principle (SEP) [4], in Paper received August 15, 2018, revised January 6, 2019 and May 10, 2019. This work was supported by in part by National Natural Science Foundation of China under grant 61521091 and in part by the National Key Research and Development Program of China under grant 2017YFF0204903. Q. Wu is with the School of Electronics and Information Engineering, Beihang University, Beijing 100191, China (e-mail: qwu@buaa.edu.cn). which the surface triangular meshes are utilized to model both the metallic and dielectric structures. However, spurious modes may appear from the dielectric substrate, which is difficult to be discriminated from normal (radiation) modes. As an alternative, the CMA of similar microstrip patch antennas can be performed using the multilayer Green’s function, in which the ground plane and dielectric substrate are assumed to be infinite in the transverse directions [5]. This method is highly efficient but limited to planar patch structures printed on dielectric substrate with an infinite size. On the other hand, the volume equivalence principle (VEP) can avoid spurious modes when modeling dielectric bodies [6]. Based on this principle, the eigencurrents on the metallic part and the eigenvalues of the whole structure are calculated using the sub-structure treatment [7]. In addition to microstrip patch antennas, a printed dipole antenna and a smartphone chassis have been analyzed recently using the volume-surface integral equation (VSIE) [8]. Furthermore, it is found that the number of unknowns grows in a similar rate as that of purely metallic structures if the dielectric substrate is electrically thin [8]. However, even with all these attempts, the computational burden is still heavy for the CMA if the antenna structure is comparable to the wavelength or becomes electrically large. The impedance boundary condition (IBC) has been used to model different metallic-dielectric interfaces for a long time, which defines a linear relation between the tangent components of the electric and magnetic fields on the interfaces [9]. In such way, the structure is significantly simplified with a reasonable accuracy [10]. Recently, the IBC is introduced to the CMA of closed surfaces and yields a rather good accuracy for spherical ones [11]. A weak form of the electric field integral equation (EFIE) operator, with both the electric and magnetic currents, is used to present the eigenvalue equation [11]. As an alternative, an IBC-EFIE form with only the electric current is proposed for the CMA of metallic-dielectric objects [12]. One advantage of the IBC-EFIE form is that the computed eigencurrents are in a similar form as those of purely metallic objects. One may find a great convenience for such similarity. In this paper, the IBC-EFIE formulation is presented for the CMA of composite metallic-dielectric structures. Deduction of the CMA formulation is elaborated in Section II. Symmetry of the IBC-EFIE operator is also carefully examined and a new formulation is deduced for the lossy IBCs in Section II. Section III discusses the IBC for different structures. As the presented Characteristic Mode Analysis of Composite Metallic-Dielectric Structures using Impedance Boundary Condition Qi Wu, Member, IEEE C