Miloslav Capek

A Method for the Evaluation of Radiation Q Based on Modal Approach

A new formula for the evaluation of the modal radiation Q factor is derived. The total Q of selected structures is to be calculated from the set of eigenmodes with associated eigen-energies and eigen-powers. Thanks to the analytical expression of these quantities, the procedure is highly accurate, respecting arbitrary current densities flowing along the radiating device. The electric field integral equation, Delaunay triangulation, method of moments, Rao-Wilton-Glisson basis function and the theory of characteristic modes constitute the underlying theoretical background. In terms of the modal radiation Q, all necessary relations are presented and the essential points of implementation are discussed. Calculation of the modal energies and Q factors enable us to study the effect of the radiating shape separately to the feeding. This approach can be very helpful in antenna design. A few examples are given, including a thin-strip dipole, two coupled dipoles a bowtie antenna and an electrically small meander folded dipole. Results are compared with prior estimates and some observations are discussed. Good agreement is observed for different methods.

The Measurable Q Factor and Observable Energies of Radiating Structures

New expressions are derived to calculate the Q factor of a radiating device. The resulting relations link Q based on the frequency change of the input impedance at the input port (QX, QZ) with expressions based solely on the current distribution on an radiating device. The question of which energies of a radiating system are observable is reviewed, and then the proposed Q factor as defined in this paper is physical. The derivation is based on potential theory rather than fields. This approach hence automatically eliminates all divergent integrals associated with electromagnetic energies in infinite space. The new formulas allow us to study the radiation Q factor for antennas without feeding (through e.g., characteristic modes) as well as fed by an arbitrary number of ports. The new technique can easily be implemented in any numerical software dealing with current densities. To present the merits of proposed technique, three canonical antennas are studied. Numerical examples show excellent agreement between the measurable QZ derived from input impedance and the new expressions.

Radiation

In this letter, we present an investigation of the radiation Q-factors of two coupled thin dipole antennas with sinusoidal current distribution. The approach is based on novel rigorous equations for radiated power and stored energies recently derived by Vandenbosch. First, we study the validity of the used thin-wire approximation with a reduced kernel. Good agreement between the assumed sinusoidal current distribution and the real cylindrical antenna modeled with the full-wave method of moments (MoM) is observed. Then, radiation Q-factors are evaluated for half-wave side-by-side coupled dipole antennas with different feeding configurations. It is found that every such combination of studied coupled dipoles presents minimum Q for specific feeding arrangement and separation distance.

{Q}

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 η 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.

-Factors of Thin-Wire Dipole Arrangements

The functional relation between the fractional bandwidth and the quality factor of a radiating system is investigated in this communication. Several widely used definitions of the quality factor are compared with 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 the 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.

Optimal Currents on Arbitrarily Shaped Surfaces

Modal methods are used to effectively design a dual-band orthogonally polarized fractal patch antenna. This letter summarizes the workflow from generating a fractal motif through modal analysis to feeding design and full-wave analysis. As the antennas feeding and matching structure, a dual L-probe was proposed to widen its bandwidth. The full-wave simulation is in very good agreement with the measurement. The motif size is 50 × 50 mm2, and the antenna operates at 1.25 and 2.1 GHz. The relative bandwidths are 4.18% and 11.4%, respectively.

On the Functional Relation Between Quality Factor and Fractional Bandwidth

This paper describes the implementation of a complex MATLAB tool to calculate the characteristic modes and associated antenna parameters. The first code, written in FORTRAN, was presented in the early seventieths by Harrington and Mautz. Here, we utilize MATLAB, which is widely known and used in the antenna community these days. Because eigen-decomposition is time consuming, parallel and distributed computing is used. Thanks to the hundreds of built-in functions in MATLAB, computation of the surface currents from the eigenvectors obtained, as well as other important characteristics, are very easy and effective. The practical features are discussed with two examples.

Design of a Dual-Band Orthogonally Polarized L-Probe-Fed Fractal Patch Antenna Using Modal Methods

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 an up-to-date frequency domain method that is extensively used in practice. Both concepts are discussed and compared on the basis of examples of varying complexity.

Implementation of the Theory of Characteristic Modes in MATLAB

This paper 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 Vandenboschs 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.

Stored electromagnetic energy and quality factor of radiating structures

The chosen rectangular and fractal microstrip patch antennas above an infinite ground plane are analyzed by the theory of characteristic modes. The resonant frequencies and radiation are evaluated. A novel method by Vandenbosch for rigorous evaluation of the radiation is employed for modal currents on a Rao-Wilton-Glisson (RWG) mesh. It is found that the resonant frequency of a rectangular patch antenna with a dominant mode presents quite complicated behaviour including having a minimum at a specific height. Similarly, as predicted from the simple wire model, the radiation exhibits a minimum too. It is observed that the presence of out-of-phase currents flowing along the patch antenna leads to a significant increase of the factor.