arXiv subjects

Miloslav Capek

Publications and source records attributed to Miloslav Capek.

52 records · Page 3Linked to original sources

arXiv2019

Modal Tracking Based on Group Theory

Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode behavior over arbitrary frequency ranges. The implementation and capabilities of the proposed procedure are demonstrated using characteristic mode decomposition as a motivating example. The procedure is, nevertheless, general and can be applied to an arbitrarily parametrized eigenvalue problems. A treatment of modal degeneracies is included and several examples are presented to illustrate modal tracking improvements and the immediate consequences of improper modal tracking. An approach leveraging a symmetry-adapted basis to accelerate computation is also discussed. A relationship between geometrical and physical symmetries is demonstrated on a practical example.

physics.comp-ph↗

arXiv2019

Optimal Planar Electric Dipole Antenna

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.

physics.class-ph↗

arXiv2019

Inversion-Free Evaluation of Nearest Neighbors in Method of Moments

A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for parallelization and scales favorably with the number of unknowns. The reconstruction completes the nearest neighbors procedure for an evaluation of the smallest shape perturbation. The performance of the method is studied with a greedy search over a Hamming graph representing the structure in which initial positions are chosen from a random set. The method is shown to be effective data mining tool for machine learning-related applications.

physics.comp-ph↗

arXiv2019

Shape Synthesis Based on Topology Sensitivity

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique, provide important advantages, one of them being impedance matrix inversion free evaluation of the sensitivity. The devised procedure utilizes port modes and their superposition which, together with only a single evaluation of all matrix operators, leads to a computationally effective procedure. The proposed method is approximately one hundred times faster than contemporary approaches, which allows the investigation of the sensitivity and the modification of shapes in real-time. The method is compared with known approaches and its validity and effectiveness is verified using a series of examples. The procedure can be implemented in up-to-date EM simulators in a straightforward manner. It is shown that the iterative repetition of the topology sensitivity evaluation can be used for gradient-based topology synthesis. This technique can also be employed as a local step in global optimizers.

physics.comp-ph↗

arXiv2018

Maximum Gain, Effective Area, and Directivity

Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived formulas are valid for arbitrarily shaped radiators of a given conductivity. All the optimization tasks are reduced to eigenvalue problems, which are solved efficiently. The second part of the paper deals with superdirectivity and its associated minimal costs in efficiency and Q-factor. The paper is accompanied with a series of examples practically demonstrating the relevance of the theoretical framework and entirely spanning wide range of material parameters and electrical sizes used in antenna technology. Presented results are analyzed from a perspective of effectively radiating modes. In contrast to a common approach utilizing spherical modes, the radiating modes of a given body are directly evaluated and analyzed here. All crucial mathematical steps are reviewed in the appendices, including a series of important subroutines to be considered making it possible to reduce the computational burden associated with the evaluation of electrically large structures and structures of high conductivity.

physics.class-ph↗

arXiv2018

Accurate and Efficient Evaluation of Characteristic Modes

A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method of moments (MoM) solution of the electric field integral equation to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated illustrating the improved accuracy and performance of the new method.

physics.comp-ph↗

arXiv2018

Trade-off Between Antenna Efficiency and Q-Factor

The trade-off between radiation efficiency and antenna bandwidth, expressed in terms of Q-factor, for small antennas is formulated as a multi-objective optimization problem in current distributions of predefined support. Variants on the problem are constructed to demonstrate the consequences of requiring a self-resonant current as opposed to one tuned by an external reactance. The resulting Pareto-optimal sets reveal the relative cost of valuing low radiation Q-factor over high efficiency, the cost in efficiency to require a self-resonant current, the effects of lossy parasitic loading, and other insights.

physics.app-ph↗

arXiv2018

Dissipation Factors of Spherical Current Modes on Multiple Spherical Layers

Radiation efficiencies of modal current densities distributed on a spherical shell are evaluated in terms of dissipation factor. The presented approach is rigorous, yet simple and straightforward, leading to closed-form expressions. The same approach is utilized for a two-layered shell and the results are compared with other models existing in the literature. Discrepancies in this comparison are reported and reasons are analyzed. Finally, it is demonstrated that radiation efficiency potentially benefits from the use of internal volume which contrasts with the case of the radiation Q-factor.

physics.class-ph↗

arXiv2017

Validating the Characteristic Modes Solvers

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.

physics.comp-ph↗

arXiv2016

Minimization of Antenna Quality Factor

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.

physics.class-ph↗

arXiv2016

Analytical Representation of Characteristic Modes Decomposition

Aspects of the theory of characteristic modes, 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 characteristic modes decomposition such as the resonance of inductive modes or the benchmarking of method of moments code.

physics.class-ph↗

arXiv2016

Optimal Composition of Modal Currents For Minimal Quality Factor Q

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 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.

physics.optics↗

arXiv2015

Various Interpretations of the Stored and the Radiated Energy Density

Three contradictory but state-of-the-art concepts for defining and evaluating stored electromagnetic energy are treated in this communication, and are collated with the widely accepted definition of stored energy, which is the total energy minus the radiated energy. All three concepts are compared, and the results are discussed on an example of a dominant spherical mode, which is known to yield dissimilar results for the concepts dealt with here. It is shown that various definitions of stored energy density immanently imply diverse meanings of the term "radiation".

physics.class-ph↗

arXiv2015

Stored Electromagnetic Energy and Quality Factor of Radiating Structures

This paper deals with the old yet unsolved problem of defining and evaluating the stored electromagnetic energy - a quantity essential for calculating the quality factor, which reflects the intrinsic bandwidth of the considered electromagnetic system. A novel paradigm is proposed to determine the stored energy in the time domain leading to the method, which exhibits positive semi-definiteness and coordinate independence, i.e. two key properties actually not met by the contemporary approaches. The proposed technique is compared with two up-to-date frequency domain methods that are extensively used in practice. All three concepts are discussed and compared on the basis of examples of varying complexity, starting with lumped RLC circuits and finishing with realistic radiators.

physics.class-ph↗

arXiv2015

Comments on "On Stored Energies and Radiation Q"

The commented paper claims to provide a new expression for an energy stored around a general radiator. The major purpose of this comment is to show that the claim is unjustified. Alongside with this issue, it is pointed out that some of the core formulas of the commented paper are not completely correct, and that their correct form has in fact been derived elsewhere, though for the purpose of evaluating the quality factor QZ and not the stored energies.

physics.class-ph↗

arXiv2014

On the Functional Relation Between Quality Factor and Fractional Bandwidth

The functional relation between the fractional band-width and the quality factor of a radiating system is investigated in this note. Several widely used definitions of the quality factor are compared on two examples of RLC circuits that serve as a simplified model of a single resonant antenna tuned to its resonance. It is demonstrated that for a first-order system, only the quality factor based on differentiation of input impedance has unique proportionality to the fractional bandwidth, whereas e.g. the classical definition of the quality factor, i. e. the ratio of the stored energy to the lost energy per one cycle, is not uniquely proportional to the fractional bandwidth. In addition, it is shown that for higher-order systems the quality factor based on differentiation of the input impedance ceases to be uniquely related to the fractional bandwidth.

physics.class-ph↗