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Power Transfer Analysis of an Asymmetric Wireless Transmission System Using the Scattering Parameters

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Power Transfer Analysis of an Asymmetric Wireless Transmission System Using the Scattering Parameters electronics Article Power Transfer Analysis of an Asymmetric Wireless Transmission System Using the Scattering Parameters Živadin Despotovi´c , Dejan Relji´c* , Veran Vasi´c and Djura Oros Department of Power, Electronic and Telecommunication Engineering, Faculty of Technical Sciences, University of Novi Sad, Novi Sad 21000, Serbia; [email protected] (Ž.D.); [email protected] (V.V.); [email protected] (D.O.) * Correspondence: [email protected]; Tel.: +381-21-485-4545 Abstract: The most widely adopted category of the mid-range wireless power transmission (WPT) systems is based on the magnetic resonance coupling (MRC), which is appropriate for a very wide range of applications. The primary concerns of the WPT/MRC system design are the power transfer capabilities. Using the scattering parameters based on power waves, the power transfer of an asymmetric WPT/MRC system with the series-series compensation structure is studied in this paper. This approach is very convenient since the scattering parameters can provide all the relevant characteristics of the WPT/MRC system related to power propagation. To maintain the power transfer capability of the WPT/MRC system at a high level, the scattering parameter S21 is used to determine the operating frequency of the power source. Nevertheless, this condition does not coincide with the maximum possible power transfer efficiency of the system. In this regard, the WPT/MRC system is thereafter configured with a matching circuit, whereas the scattering parameter 0 S21 S21’is used to calculate and then adjust the matching frequency of the system. This results in the maximum available power transfer efficiency and thereby increases the overall performance Citation: Despotovi´c,Ž.; Relji´c,D.; of the system. Theoretical investigations are followed by numerical simulation and experimental Vasi´c,V.; Oros, D. Power Transfer validation. Analysis of an Asymmetric Wireless Transmission System Using the Keywords: wireless power transfer; asymmetric system; magnetic resonance; two-port networks; Scattering Parameters. Electronics S-parameters 2021, 10, 906. https://doi.org/ 10.3390/electronics10080906 Academic Editor: Massimo Donelli 1. Introduction Wireless power transmission (WPT) is an emerging technology that has been studied Received: 17 March 2021 since the work of Tesla and his ideas for wireless transmission [1]. Up to now, WPT has Accepted: 5 April 2021 Published: 10 April 2021 drawn a lot of attention, while much research has been devoted to improving power transfer capability (PTC) and power transfer efficiency (PTE), including transmission range. Publisher’s Note: MDPI stays neutral It is expected that the WPT will be used on a bigger scale in the times to come. with regard to jurisdictional claims in The most popular WPT method is based on the concept of inductive coupling. Since published maps and institutional affil- the WPT via magnetic resonance coupling (MRC) was reported in [2], it has attracted iations. researches more than ever before. WPT/MRC is a system that operates at resonance to make the circuit behave as the purely resistive. In many publications, one can find WPT/MRC as a category of inductive power transfer (IPT) [3] called resonant inductive power transfer [4]. The main advantage of the WPT/MRC system over the well-known IPT is a higher PTE. This advantage has provided the implementation of the WPT/MRC systems not only Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. in low-power devices [5–7], but also in high-power applications, such as electric vehicle This article is an open access article charging solutions [8,9]. In order to increase the PTE at the medium distance, resonant distributed under the terms and coils (resonant relays) were introduced. Therefore, WPT/MRC system may consist of one conditions of the Creative Commons or more resonant coils. With regard to the compensation topology, two-coil WPT/MRC Attribution (CC BY) license (https:// systems are categorized as series-series (SS), series-parallel (SP), parallel-series (PS), or creativecommons.org/licenses/by/ parallel-parallel (PP) compensated systems as shown in Figure1. In addition, few hybrid 4.0/). compensation topologies have been introduced [3]. Based on the transmitter and receiver Electronics 2021, 10, 906. https://doi.org/10.3390/electronics10080906 https://www.mdpi.com/journal/electronics Electronics 2021, 10, 906 2 of 16 Electronics 2021, 10, x FOR PEER REVIEW 2 of 17 parameters,parameters, the the WPT/MRC systems systems are are catego categorizedrized as as symmetric, symmetric, quasi-symmetric, quasi-symmetric, and asymmetricasymmetric (Figure (Figure 11).). The symmetric system isis composedcomposed ofof identicalidentical coilscoils (inductances(inductances L and L ) and compensation capacitors (capacitances C and C ), which results in the same 1 and 2) and compensation capacitors (capacitances1 and2 ), which results in the resonant frequencies ( f and f02) on transmitter and receiver sides. In a quasi-symmetric same resonant frequencies01 ( and ) on transmitter and receiver sides. In a quasi-sym- metricsystem, system, the transmitter the transmitter and receiver and receiver have alsohave thealso same the same resonant resonant frequency, frequency, but theybut theyconsist consist of non-identical of non-identical coils coils and and capacitors. capacitors. The The difference difference between between quasi-symmetric quasi-symmetric and andasymmetric asymmetric systems systems is that is that the transmitterthe transmitte andr and receiver receiver of the of asymmetricthe asymmetric system system do notdo nothave have the the same same resonant resonant frequencies. frequencies. WPT/MRC SS SP PS PP Symmetric Quasi-symmetric Asymmetric L1=L2 L1≠L2 L1≠L2 C1=C2 C1≠C2 C1≠C2 f01=f02 f01=f02 f01≠f02 FigureFigure 1. 1. TheThe magnetically magnetically coupled coupled resonant resonant wireless wireless power power transmission transmission (WPT/MRC) (WPT/MRC) system system classification.classification. Series-series Series-series (SS), (SS), series-parallel series-parallel (SP), (SP), parallel-series parallel-series (PS), (PS), and and parallel-parallel parallel-parallel (PP) (PP) compensated structures. compensated structures. NumerousNumerous studies studies of of symmetric symmetric and and quasi-sy quasi-symmetricmmetric systems systems have have been been reported reported in thein theliterature literature over over the theyears. years. The Theoperating operating frequency frequency of such of such systems systems is equal is equal to the to res- the onantresonant frequency frequency in inthe the under-coupled under-coupled and and critical-coupled critical-coupled regime. regime. In In the the over-coupled over-coupled regime,regime, however, thethe transmitting transmitting power power at at the the resonant resonant frequency frequency is significantly is significantly reduced; re- duced;thus, the thus, operating the operating frequency frequency needs needs to be adoptedto be adopted to provide to provide the maximum the maximum PTC PTC [10]. [10].The frequencyThe frequency splitting splitting phenomena, phenomena, caused caus byed the by over-coupled the over-coupled regime, regime, has a significanthas a sig- nificantinfluence influence on the PTC on the and PTC has and been has widely been studiedwidely studied [11–13]. [11–13]. ManyMany techniques techniques for for tracking tracking and and eliminatin eliminatingg issues issues of of the the freq frequencyuency splitting have beenbeen proposed. proposed. In In [14,15], [14,15], the the analysis analysis of of frequency frequency splitting splitting and and the the PTE PTE of of two-coil two-coil and and four-coilfour-coil systems systems have have been been reported. reported. In In [14] [14],, a a symmetric symmetric system system has has been been analysed in in termsterms of of voltage voltage gains gains and and output output power. power. With With regard regard to to the the PTE, PTE, defined defined as as the the ratio of loadload power power and and available available source source power, power, an an optimal optimal ratio ratio of of load and source resistances hashas been investigated, keepingkeeping thethe originaloriginal resonant resonant frequency. frequency. However, However, matching matching circuit cir- cuitbetween between the sourcethe source and the and system, the system, which provideswhich provides the flow the of availableflow of available source power source to powerthe system, to the has system, not been has considered. not been considered. The similar The analysis similar has analysis been reported has been in reported [15], but forin [15],a four-coil but for system. a four-coil system. ToTo overcome overcome issues issues of of the the over-coupled over-coupled regime, regime, a anew new WPT/MRC WPT/MRC method method based based on splittingon splitting frequencies frequencies is proposed is proposed in [16]. in [16 Th].e The power power transfer transfer performances performances have have been been in- vestigatedinvestigated theoretically theoretically and and experimentally. experimentally. Yet, Yet, only only the thesymmetric symmetric system system has been has been dis- cussed.discussed. In the In case the caseof different of different quality quality factors factors of the of transmitter the transmitter and the and receiver, the receiver, the exact the calculationexact calculation of splitting of splitting frequencies frequencies is rather is rathercomplex complex [16].
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