# Computational Electromagnetics (CEM)

CEM group concentrates on theoretical research in classical electromagnetic theory. Among the currently developed topics belong radiation properties of electrically small radiators and scatterers and their optimizations. Members of the group have for many years been also involved in classical antenna theory and field propagation in artificial composite materials.

Current research activities are strongly entangled with a “source concept” paradigm, in which all involved field quantities as well as engineering metrics are described solely in terms of electromagnetic sources. The idea of the source concept is sketched in the following figure.

CEM team collaborates with other department’s teams.

### Visiting Reseachers

Vit Losenicky
Michal Masek
Martin Strambach Lamyae Akrou

## Current Projects

Source Concept of Electrically Small Antenna Synthesis  (2015-2017, GA15-10280Y)

## Active External Collaborations

University of Lund, Sweden (Mats Gustafson, Doruk Tayli; Casimir Ehrenborg)
KTH Royal Institute of Technology, Sweden (Lars Johnsson)
Catholic University of Leuven, Belgium (Guy Vandenbosch)
University of North Carolina, USA (Kurt Schab)

### Journal Papers (Last Three Years)

#### Current and Antenna Optimization

 M. Capek, M. Gustafsson, and K. Schab, "Minimization of antenna quality factor", 2017, eprint arXiv: 1612.07676. [Online]. Available: https://arxiv.org/abs/1612.07676 Abstract The optimal currents on arbitrarily shaped radiators with respect to the minimum quality factor Q are found using a simple and efficient procedure. The solution starts with a reformulation of the problem of minimizing quality factor Q as an alternative, so-called dual, problem. Taking advantage of modal decomposition and group theory, it is shown that the dual problem can easily be solved and always results in minimal quality factor Q. Moreover, the optimization procedure is generalized to minimize quality factor Q for embedded antennas, with respect to the arbitrarily weighted radiation patterns, or with prescribed magnitude of the electric and magnetic near-fields. The obtained numerical results are compatible with previous results based on composition of modal currents, convex optimization, and quasi-static approximations; however, using the methodology in this paper, the class of solvable problems is significantly extended. L. Jelinek and M. Capek, "Optimal currents on arbitrarily shaped surfaces," IEEE Trans. Antennas Propag., vol. 65, no. 1, pp. 329341, Jan. 2017. Abstract An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain G, quality factor Q, gain to quality factor ratio G/Q, and radiation efficiency $\eta$ of canonical shapes with conduction losses explicitly included. The Rao-Wilton-Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized. M. Capek and L. Jelinek, "Optimal composition of modal currents for minimal quality factor Q", IEEE Trans. Antennas Propag., vol. 64, no. 12, pp. 52305242, 2016. Abstract This work describes a powerful, yet simple, procedure how to acquire a current approaching the lower bound of quality factor Q. This optimal current can be determined for an arbitrarily shaped electrically small radiator made of a perfect conductor. Quality factor Q is evaluated by Vandenboschs relations yielding stored electromagnetic energy as a function of the source current density. All calculations are based on a matrix representation of the integro-differential operators. This approach simplifies the entire development and results in a straightforward numerical evaluation. The optimal current is represented in a basis of modal currents suitable for solving the optimization problem so that the minimum is approached by either one mode tuned to the resonance, or, by two properly combined modes. An overview of which modes should be selected and how they should be combined is provided and results concerning rectangular plate, spherical shell, capped dipole antenna and fractal shapes of varying geometrical complexity are presented. The reduction of quality factor Q and the G/Q ratio are studied and, thanks to the modal decomposition, the physical interpretation of the results is discussed in conjunction with the limitations of the proposed procedure.

#### Characteristic Modes

 M. Capek, V. Losenicky, L. Jelinek, and M. Gustafsson, "Validating the characteristic modes solvers," 2017, eprint arXiv: 1702.07037. [Online]. Available: https://arxiv.org/abs/1702.07037 Abstract Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise synthetic benchmarks which can be utilized to validate the method of moments matrix or performance of characteristic mode decomposition. Dependence on the mesh size, electrical size and other parameters can systematically be studied, including the performance of various mode tracking algorithms. A noticeable advantage is the independence on feeding models. Both theoretical and numerical aspects of characteristic mode decomposition are discussed and illustrated by examples. The performance of state-of-the-art commercial simulators and academic packages having been investigated, we can conclude that all contemporary implementations are capable of identifying the first dominant modes while having severe difficulties with higher-order modes. Surprisingly poor performance of the tracking routines is observed notwithstanding the recent ambitious development. M. Capek, P. Hazdra, M. Masek, and V. Losenicky, "Analytical representation of characteristic modes decomposition," IEEE Trans. Antennas Propag., vol. 65, pp. 713720, 2017. Abstract Aspects of the theory of characteristic modes (CMs), based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper insight into the modal behavior of radiating structures as demonstrated by a detailed analysis of three canonical structures: a dipole, an array of two dipoles and a loop, cylinder, and a sphere. It is demonstrated that knowledge of the analytical functional can be utilized to solve important problems related to the theory of CM decomposition such as the resonance of inductive modes or the benchmarking of method of moments code. M. Capek, J. Eichler, and P. Hazdra, "Evaluating radiation efficiency from characteristic currents," IET Microw. Antenna P., vol. 9, no. 1, pp. 1015, Jan. 2015. Abstract This study describes an effective technique for calculating modal radiation efficiency calculation based on decomposition into characteristic modes. The key assumption is that the current distribution on the perfect electric conductor is almost the same as in the case of a very good conductor, for example, metals such as copper, aluminium and silver. This assumption is verified against the conventional technique, the impedance boundary condition (IBC). The proposed approach does not require any modification of the formulation of method of moments for perfectly conducting surfaces, which is assumed for the modal decomposition. Modal efficiencies provide an additional insight that is useful especially for the design of small antennas. Taking the feeding into account, the modal losses can be summed up to obtain the total efficiency. The technique works perfectly for common metals, is fully comparable with the IBC, and can easily be incorporated into any present-day in-house solver. A numerical analysis of three antennas is presented to demonstrate the merits of the approach. Radiation efficiency of coupled dipoles, an electrically small meandered dipole, and PIFA were investigated by the presented method. The results are in perfect agreement with the reference commercial package. J. Eichler, P. Hazdra, and M. Capek, "Aspects of mesh generation for characteristic mode analysis," IEEE Antennas Propag. Mag., vol. 56, no. 6, pp. 172183, June 2014. Abstract This paper deals with practical aspects of mesh generation for the theory of characteristic modes. First, we describe a tool for surface-mesh generation in MATLAB. The tool is afterwards used for an analysis of relative convergence of modal results computed by an in-house modal analyzer in MATLAB. Different meshing scenarios are selected for a dipole, a rectangular patch, and a rectangular patch with a slot, and a recommendation for a mesh-refinement strategy is given. The study is supported by a simple error analysis, considering the approximation error in the evaluation of moment-matrix elements. It is shown that the results are also applicable for the commercial implementation in FEKO software.