Projects (Miloslav Čapek)

In case you will be interested in any particular project below or you will get your own idea of potential topic, please do not hesitate and contact me at (Back to profile)
Notice that all required literature is available as well as all softare and hardware.

Individual projects, bachelor and diploma projects

  1. Poynting streamlines and effective area for receiving antennas

    Study definition and ways how to calculate Poynting streamlines. Then can be used for visual inspection of absorption properties of receiving antennas and for estimation of effective area of antenna aperture. Focus on automatization and acceleration of the computation (it will contain evaluation of near field everywhere around the antenna), i.e., calculation for arbitrary cut or plane. With code implemented in MATLAB, investigate behavior of canonical structures like a sphere, a dipole, or a patch antenna, and compare the aperture size with geometrical cross-section. The outcomes of the project can be implemented into AToM project and used then in practice.


    [1] Bohren, C. F.: How Can a Particle Absorb More Than the Light Incident on It?, Am. J. Phys., Vol. 51, No. 4, pp. 323-327, April 1983.
    [2] Shamonina, A., Kalinin, V. A., Ringhofer, K. H., and Solymar, L: Short Dipole as a Receiver: Effective Aperture Shapes and Streamlines of the Poynting Vector, IEEE Proc.-Microw. Antennas Propag., Vol. 149, No. 3, pp. 153-159, June 2002.
    [3] Diao, J. and Warnick, K. F.: Poynting Streamlines, Effective Area Shape, and the Design of Superdirective Antennas, IEEE Trans. Antennas and Propagation, Vol. 65, No. 2, pp. 861-866, Feb. 2017.
  2. Direct visibility of point sets for RWG basis functions (triangularized surface)

    Study and implement method for determination of what points are visible from given point of view and given set (cloud) of points forming triangularized surface. To do that , use "Hidden Point Removal" (HPR) operator [1]. Complete Matlab code and verify it for several examples. Additionaly, propose a interface between Matlab and TikZ, which will be capable to export triangularization from Matlab, processed by HPR into TikZ.


    [1] Katz, S., Tal, A., Basri, R.: Direct Visibility of Points Sets, AMC Transactions on Graphics, Vol. 26, No. 3., July 2007.
  3. Gaussian quadrature for EM operators in AToM

    Study Gaussian quadrature over triangular domains and implement it for evaluation of far-field from current flowing on triangularized surface. Summarize what operators are, in general, available (e.g., impedance matrix, stored energy matrix, lossy matrix, ...), what are their properties [1] and how can they be utilized for efficient decomposition and optimization.


    [1] Capek, M.: MoM-Based Matrix Operators in AToM, (see document AToM operators)
  4. Pareto-type current optimization using EM operators

    Enumerate relevant multi-objective optimization scenarios (focus on those being important in electrically small region) and review available techniques for their evaluation. In the second part of the project, implement selected known techniques and, where possible, test several different approaches. Finally, verify the results and evaluate the computational complexity of various approaches.

    [1] Gustafsson, M., Capek, M., Schab, K.: Trade-off Between Antenna Efficiency and Q-Factor, pp. 1-11, arxiv [On-line:].

    [2] Capek, M., Jelinek, L., Schab, K., Gustafsson, M., Jonsson, B.L.G., Ferrero, F., Ehrenborg, C.: Optimal Planar Electric Dipole Antenna, pp. 1-10, arxiv, [On-line:]

  5. Antenna shape synthesis without a priory knowledge of the feeding

    Study the possibilities of antenna synthesis by utilizing characteristic modes (CM). To design efficient and electrically small antenna, the initial shape and the operational frequency is given and then the optimal geometry is found using heuristic binary optimization algorithm which will be able to cooperate with characteristic mode decomposition. The CM decomposition is already implemented in Matlab.

    [1] Ethier, J. L. T., McNamara, D. A.: Antenna Shape Synthesis without Prior Specification of the Feedpoint Locations, IEEE Trans. AP, 2014.


  6. Circuits for determination of the fractal measure

    Project will be focused on study of fractal geometry and its electromagnetic properties, particularly on generation and utilization of Sierpinski triangle. Calculate its fractal measure and find its resonant frequencies depending on an iteration (modal method which is able to determine the eigen-frequency is available). Finally, propose an electrical circuit which mimics the fractal's behaviour via input impedance of the circuit.

    [1] Kigami, J.: Analysis on Fractals, Cambridge University Press, 2001,
    [2] Boyle, B., Cekala, K., Ferrone, D., Rifkin, N., Teplyaev, A.: Electrical resistance of N-gasket fractal networks, Pacific Journal of Mathematics, Vol. 233, No. 1, pp. 15--40, Nov. 2007,
    [3] Wing, O.: Classical Circuit Theory, Springer, 2008,
    [4] Falconer, K. J.: Fractal Geometry - Mathematical Foundations and Applications, John Wiley, 2003.
  7. Design of superbackscattering arrays

    The aim of the project is to find an optimal number and arrangement of perfectly conducting scatterers which yield maximal directivity to the direction of incoming incident plane-wave. Such an antenna system is called backstattering arrays. The design procedure is limited by available space in which the scatterers can be placed and by their limited number. The full-wave numerical methods like method of moment are available as well as optimization routines and code for evaluation of antenna directivity. Optionally, the project can be extended towards evaluation of ohmic losses. Thus, the antenna gain can be optimized instead of antenna directivity.

    [1] Liberal, I., Ederra, I., Gonzalo, R., Ziolkowski, R. W.: Superbackscattering Antenna Arrays, IEEE Trans. AP, Vol. 63, No. 5, pp. 2011--2021, May 2015,
    [2] Uzkov, A. I.: An approach to the problem of optimum directive antennae design, Compt. Rend. Dokl. Acad. Sci. URSS, Vol. 53, pp. 35–38, 1946,
    [3] Balanis, C. A.: Advanced Engineering Electromagnetics, John Wiley, 1989.
  8. Optimization of radiation body by adding slots and feeders

    Try to modify a rectangular perfectly conducting plate so that it can be fed by a finite number of feeders and the resulting current density yields quality factor Q similar to the value of optimal current (which have been obtained without any feeding connected). All required tools in Matlab are available. To solve the problem, use any optimization technique you prefer (linear, quadratic programming, heuristic approach, cut and try technique) and focus on adding slots and feeders. Study the influence of shape's corrugation on the quality factor Q.

    [1] Harrington, R. F., Mautz, J. R.: Theory of characteristic modes for conducting bodies, IEEE Trans. AP, Vol. 19, No. 5, pp. 622–628, Sept. 1971,
    [2] Gustafsson, M., Nordebo, S.: Optimal antenna currents for Q, superdirectivity, and radiation patterns using convex optimization, IEEE Trans. AP, Vol. 61, No. 3, pp. 1109–1118, March 2013,
    [3] Vandenbosch, G. A. E.: Reactive energies, impedance, and Q factor of radiating structures, IEEE Trans. AP, Vol. 58, No. 4, pp. 1112–1127, Apr. 2010,
    [4] Capek, M. and Hazdra, P. and Eichler, J.: A Method for the Evaluation of Radiation Q Based On Modal Approach, IEEE Trans. AP, Vol. 60, No. 10, pp. 4556-4567, Oct. 2012.
  9. Study of fractal dimension

    Recapitulate all available definitions of fractal measure and propose an algorithm to evaluate it (one of available techniques is so-called box-counting). Focus on implementation aspects like algorithm’s robustness and speed. The resulting algorithm should be able to evaluate complex fractal shapes (great number of holes etc.). The project will be concluded by verification of the algorithm’s precision on examples with analytically known values. The project can be extended towards theoretical and practical investigation of non-integer topological dimension and its utilization to improve radiation properties of small antennas.

    [1] Falconer, K. J.: Fractal Geometry - Mathematical Foundations and Applications, John Wiley, 2003,
    [2] Kolmogorov, A. N., Fomin, S. V.: Elements of the Theory of Functions and Functional Analysis, Dover, 1999,
    [3] Kigami, J.: Analysis on Fractals, Cambridge University Press, 2001.
  10. Quality factor minimization of PEC plate using pixelling

    Implement so-called pixelling technique in Matlab. Pixelling utilizes heuristic (often genetic) algorithm and, together with method of moments, allows optimization of the radiator's geometry. The pixelling technique removes selected rows and columns of the impedance matrix (precalculated by the method of moments) which is equivalent to modification of geometry. All required algorithms except the genetic algorithm are available. Within the project, all tools and codes need to be merged together and the optimization loop needs to be set up. The project will be concluded by optimization of rectangular plate.

    [1] Rao, S. M., Wilton, D. R., Glisson, A. W.: Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. AP, Vol. 30, No. 3, pp. 409–418, May 1982,
    [2] Harrington, R. F.: Field Computation by Moment Methods, John Wiley, 1993,
    [3] Rahmat-Samii, Y., Michielssen, E.: Electromagnetic Optimization by Genetic Algorithm, John Wiley, 1999,
    [4] Gustafsson, M., Nordebo, S.: Optimal antenna currents for Q, superdirectivity, and radiation patterns using convex optimization, IEEE Trans. AP, Vol. 61, No. 3, pp. 1109–1118, March 2013.
  11. Stored electromagnetic energy for scatterers

    Project will be focused on utilization of novel method to evaluate stored electromagnetic energy which is currently developed at Department of Electromagnetic Field. The method is based on EM simulation in FEKO software (where the source currents are acquired), data export in Matlab and extensive postprocessing (ifft, integration of the time-harmonic far-field). One of the big advantage is that the novel method can be used for evaluation of the energy stored by a scatterer. Try to adapt the method so that these calculations will be possible (mainly algorithmic updates), calculate several basic scaterrers and study the results.

    [1] Capek, M., Jelinek, L., Vandenbosch, G. A. E.: Stored Electromagnetic Energy and Quality Factor of Radiating Structures, 2015, eprint arxiv:,
    [2] Vandenbosch, G. A. E.: Reactive Energies, Impedance, and Q Factor of Radiating Structures, IEEE Trans. AP, Vol. 58, No. 4, pp. 1112-1127, Apr. 2010,
    [3] Capek, M., Jelinek, L., Hazdra, P., Eichler, J.: The Measurable Q Factor and Observable Energies of Radiating Structures, IEEE Trans. AP, Vol. 62, No. 1, pp. 311-318, Jan. 2014.
  12. Your own topic...

    Have you your own project's topic?

    Do you want to modify any of offered projects? No problem! Just let me know...



Ph.D. studies - Open topics

1. Analysis of Optimal Electrically Small Radiators Using Source Concept

Topic deals with a utilization of optimization techniques, both convex and heuristic, in conjunction with modal and structural decomposition to design optimal electrically small antennas and scatterers. The framework aspiring to utilize the mixture of all these techniques is called Source Concept. Source Concept is capable of representing all antenna parameters and quantities solely in terms of electric and/or magnetic currents and important part of this work is focused on its generalization New perspectives of the Source Concept will also be studied together with practical application, code implementation and verification.

2. Electrically Small Multiport Antennas

Most of the existing electrically small antennas are single port antennas. Such designs almost exclusively employs the dominant TM (electric dipole-like) mode which performance is however far from the fundamental bounds. On the other hand, the combination of the TM and TE (magnetic dipole-like) modes, promises valuable improvements in terms of most relevant antenna parameters (i.e., directivity, efficiency, bandwidth). Unfortunately, it turns out that such a combination cannot be fed by a single port, consequently multiport antennas should be utilized. Usage of multi-port antennas introduces new problems of interpreting parameters like quality factor Q, but also calls for robust optimization routines determining optimal combination of radiator’s shape, feeding position and feeding complex amplitudes.

3. Topology Optimization and Shape Synthesis

The fundamental bounds on electrically small antenna performance are already well-known, however, they are described in terms of optimal free-space current densities. Such currents cannot be supported with any conducting platform when only realistic number of feeding positions (typically only one) is demanded. The major task is thus a synthesis of conducting supports performing close to the principal bounds. At the current level of understanding such task is an NP hard problem accessible solely to heuristic algorithms. That means that new problem parametrizations and advanced algorithms are needed together with deeper understanding of the optimization problem. The effective solution can reside in the realm of machine or deep learning. Notice that the problem of topology and shape optimization is still considered as open problem in practically all areas of engineering.

4. Advanced Theory of Characteristic Modes and Its Utilization in Antenna Design

Theory of characteristic modes presents one of the leading approaches to efficient analysis, synthesis and design of electrically small antennas for variety of potential applications as for example broad-band antennas, multi-band antennas, or MIMO antennas. A lot of fresh new findings related to characteristic modes have been published in recent years and deserve further investigation and deeper understanding. Many others are still awaiting their discovery. This broad research topic deals with both analytical and numerical advancement of characteristic modes theory, and will also demand investigation into topics of model order reduction and operator theory.


Projects and theses - Formal aspects

  • It is highly recommended to prepare draft in MS Word and then type it in LaTeX (tutorials / manuals available),

  • it is recommended to prepare all figures as vector graphics (TikZ recommended),

  • it is possible to write the bachelor and diploma thesis in Czech, however it is recommended to write it in English,

  • all Ph.D. theses should be written (and defended) in English.


Back to profile

/Edited 22. 09. 2018, MC/