In the article, a wireless charging system with the use of periodically arranged planar coils is presented. The efficiency of two wireless power transfer (WPT) systems with different types of inductors, i.e., circular and square planar coils is compared, and two models are proposed: analytical and numerical. With the appropriate selection of a load resistance, it is possible to obtain either the maximum efficiency or the maximum power of a receiver. Therefore, the system is analyzed at two optimum modes of operation: with the maximum possible efficiency and with the highest power transmitted to the load. The analysis of many variants of the proposed wireless power transfer solution was performed. The aim was to check the influence of the geometry of the coils and their type (circular or square) on the efficiency of the system. Changes in the number of turns, the distance between the coils (transmit and receive) as well as frequency are also taken into account. The results obtained from analytical and numerical analysis were consistent; thus, the correctness of the adopted circuit and numerical model (with periodic boundary conditions) was confirmed. The proposed circuit model and the presented numerical approach allow for a quick estimate of the electrical parameters of the wireless power transmission system. The proposed system can be used to charge many receivers, e.g., electrical cars on a parking or several electronic devices. Based on the results, it was found that the square coils provide lower load power and efficiency than compared to circular coils in the entire frequency range and regardless of the analyzed geometry variants. The results and discussion of the multivariate analysis allow for a better understanding of the influence of the coil geometry on the charging effectiveness. They can also be valuable knowledge when designing this type of system.

This article presents the results of the proposed numerical and analytical analysis of the Wireless Power Transfer System (WPT). The system consists of a transmitting surface and a receiving surface, where each of them is composed of planar spiral coils. Two WPT systems were analysed (periodic and aperiodic) considering two types of coils (circular and square). In the aperiodic system, the adjacent coils were wound in the opposite direction. The influence of the type of coils, the winding direction, the number of turns, and the distance between the coils on the efficiency of the WPT system was compared. In periodic models, higher efficiency was obtained with circular rather than square coils. The results obtained with both proposed methods were consistent, which confirmed the correctness of the adopted assumptions. In aperiodic models, for a smaller radius of the coil, the efficiency of the system was higher in the square coil models than in the circular coil models. On the other hand, with a larger radius of the coil, the efficiency of the system was comparable regardless of the coil type. When comparing both systems (periodic and aperiodic), for both circular and square coils, aperiodic models show higher efficiency values (the difference is even 57%). The proposed system can be used for simultaneous charging of many sensors (located in, e.g., walls, floors).

In this article, novel 3D printed sensors for temperature measurement are presented. A planar structure of the resistive element is made, utilizing paths of a conductive filament embedded in an elastic base. Both electrically conductive and flexible filaments are used simultaneously during the 3D printing procedure, to form a ready–to–use measuring device. Due to the achieved flexibility, the detectors may be used on curved and irregular surfaces, with no concern for their possible damage. The geometry and properties of the proposed resistance detectors are discussed, along with a printing procedure. Numerical models of considered sensors are characterized, and the calculated current distributions as well as equivalent resistances of the different structures are compared. Then, a nonlinear influence of temperature on the resistance is experimentally determined for the exemplary planar sensors. Based on these results, using first–order and hybrid linear–exponential approximations, the analytical formulae are derived. Additionally, the device to measure an average temperature from several measuring surfaces is considered. Since geometry of the sensor can be designed utilizing presented approach and printed by applying fused deposition modeling, the functional device can be customized to individual needs.

The article presents an analysis of the maximum efficiency and maximum load power, which are available to obtain in periodic wireless power transfer (WPT) systems. The numerical computations of the proposed WPT structures are performed using the finite element method and branch current method. Two theoretical models are discussed, i.e., a numerical model with simplified structure and boundary conditions as well as an equivalent circuit model is proposed to solve WPT systems with many magnetically coupled planar coils. A multivariate analysis is performed, which takes into account the variability of the number of turns, distance between a transmitting and receiving coil, and the frequency of an energy source. The outputs, such as overall efficiency, power of the source and power transferred to a load are discussed. The formulas for the load impedance required to maximize the efficiency or load power, which are taking into account the electrical parameters of the system resulting from its geometry, are presented. The results obtained from proposed models are consistent, which confirm the correctness of the adopted circuit model, which is less complex and faster to compute than numerical one. It is also possible to perform a quick assessment of electrical parameters of the analyzed WPT structure, using presented analytical formulas and numerical model or experimental data. The results allow for a detailed discussion of the dependence of the efficiency and power of the WPT system with respect to geometry of spiral coils.

This article presents a method for analysis of the low-power periodic Wireless Power Transfer (WPT) system, using field and circuit models. A three-dimensional numerical model of multi-segment charging system, with periodic boundary conditions and current sheet approximation was solved by using the finite element method (FEM) and discussed. An equivalent circuit model of periodic WPT system was proposed, and required lumped parameters were obtained, utilizing analytical formulae. Mathematical formulations were complemented by analysis of some geometrical variants, where transmitting and receiving coils with different sizes and numbers of turns were considered. The results indicated that the proposed circuit model was able to achieve similar accuracy as the numerical model. However, the complexity of model and analysis were significantly reduced.

In this paper, we present the method for determination of effective electromagnetic parameters of complex building materials. By application of the proposed algorithm, it is possible to analyze electromagnetic field distribution for large-scale problems with heterogeneous materials. The two-dimensional numerical model of building components (hollow brick) with periodic boundary conditions was solved using the finite-difference time-domain method (FDTD) and discussed. On this basis, the resultant transmission coefficient was found and then the equivalent relative permeability and electric conductivity of heterogeneous dielectric structures, in the developed homogenization algorithm, were identified. The homogenization of material properties was achieved by performing a multi-variant optimization scheme and finally, selecting optimal electric parameters. Despite the analysis of heterogeneous building materials, the presented algorithm is shown as a tool for the homogenization of complex structures when scattering of a high-frequency electromagnetic field is considered.