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.

In this paper was analysed a wireless power transfer system (WPT) with multiple resonators supplying, for example, sensors or LED lighting. Energy is transferred simultaneously using a group of identical planar spiral circular coils acting as transmitters and receivers. These coils were arranged to form transmitting and receiving planes. The receivers were connected to independent power supply circuits of each, e.g., sensor or LED lighting. Higher power reliability and flexibility can be achieved by isolating these circuits. The proposed system was described and discussed. Taking into account the skin effect and mutual couplings, a theoretical analysis was made. A detailed analysis was made at the resonant frequency of the system. The system was modeled using a matrix equation and appropriate formulas. The calculations were verified experimentally for different loads and two distances between transmitters and receivers. The efficiency and receiver power were compared and discussed. The maximum efficiency was about 45% at the small distance between the planes. The maximum efficiency of the WPT system decreased more than two times to less than 20% when the distance between the coils was doubled. The results and discussion of the conducted analysis may provide valuable knowledge when designing this type of system.

The article shows an analysis of the influence of the skin effect on the maximum efficiency and maximum power of a receiver in a wireless power transfer system (WPT). For this purpose, the original solution of the WPT system was used, which contained periodically arranged planar coils. The results concern the multi-variant analysis of the WPT system. The geometry of the coils was taken into account, i.e., the size of coils, the number of turns, as well as the distance between the transmitting and receiving coils. The calculations were carried out over the frequency range of 0.1–1 MHz. In order to analyse the influence of the skin effect on the proposed WPT system, two approaches were used: analytical and numerical. The article analyses the appropriate selection of load impedance in order to obtain maximum efficiency or maximum power of the receiver. In this analysis, the influence of the skin effect on each of the two operating procedures was examined. The obtained analytical and numerical results differed by no more than 0.45%, which confirmed the correctness of the proposed WPT model. Based on the results, it was determined that the greatest influence of the skin effect occurred at 1 MHz. Then, the efficiency decreased by no more than 9%, while in the case of the receiver power decreased by an average of 25%. Detailed analysis shows the influence of the skin effect on the system parameters, and can also be an important element in the design of WPT systems.

We are currently seeing an increasing number of devices that support wireless power transfer (WPT) technology. In order to avoid early prototyping and carry out a series of experimental analyses, it was possible to use numerical methods at the design stage to estimate the potential power transfer and efficiency of the system. The purpose of this study is to present a method of analysis for a periodic wireless power transfer system, using periodically arranged planar coils with field and circuit models. A three-dimensional numerical model of a multi-segment charging system with periodic boundary conditions was solved with the finite element method (FEM). An equivalent circuit model of the periodic WPT system was proposed, and the required lumped parameters were obtained using analytical formulas. Mathematical formulas were supplemented with the analysis of several geometric variants, taking into account different sizes of transmitting and receiving coils, as well as different numbers of turns. Both proposed methods of analysis allowed for the determination of load resistance values at which the variants of WPT systems considered in the research had maximum efficiency. The ranges of load resistance values in which the efficiency of the system exceeded 50% were indicated. The results obtained are very helpful in the proper selection of the load resistance, without the need for multiple tests and their resulting multiple measurements. The results also showed that the proposed circuit model was able to achieve similar accuracy as the numerical model, and the complexity of the model and analysis was significantly reduced. The obtained results will allow the design of WPT systems with appropriate selections of load resistance to achieve maximum efficiency.