Circuit model of a resonator array for a WPT system by means of a continued fraction

Alberto, Jose

doi:10.1109/rtsi.2016.7740586

Cited by 11 publications

(20 citation statements)

References 9 publications

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“…It can be noticed that when the array is perfectly terminated (R T = R eq,∞ ), the current magnitude decreases smoothly from the first to the last resonator. The perfectly matching impedance is the termination impedance that makes the equivalent impedance of the array constant and equal to R T regardless of the number of resonators; its value is [11] and for the array considered in the example R eq,∞ = 1.38 Ω. If the array is terminated with a different impedance, the current magnitude oscillates from the first to the last resonator and the peaks occur on even or odd resonators, depending When the array is perfectly terminated we havê…”

Section: Currents In the Resonatorsmentioning

confidence: 99%

“…Further, by means of Eqs. (10) and (11), the following considerations can be made. The dependency of R T,ηmax and R T,P R T max on N is clearly shown in Figs.…”

Section: Efficiency and Power Delivered To A Load Or A Receiver Over mentioning

confidence: 99%

“…In order to overcome the loss of efficiency in cases where the emitter and receiver coils are distant, arrays of resonators can be used to transfer power over longer distances [6][7][8][9][10]. In these arrays the first resonator is usually connected to a power source and transmits power through magnetic coupling to the other resonators of the array, which are arranged in a plane with parallel axes [9,[11][12][13][14][15], or alternatively, in domino configurations [7,8,10].…”

Section: Introductionmentioning

confidence: 99%

“…These arrays have been studied in literature using magnetoinductive wave theory [9,15], with a representation of the array as a cascade of identical two-ports [10], or using circuit analysis [7,8,11]. Regarding the circuit model of a resonator array, it is also known in literature that the array can be represented by an impedance matrix which contains the impedance of each resonator and the mutual inductances between pairs of resonators as in [7-9, 12, 16, 17].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accurate Calculation of the Power Transfer and Efficiency in Resonator Arrays for Inductive Power Transfer

Alberto¹,

Reggiani²,

Sandrolini³

et al. 2019

PIER B

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This paper studies the power transfer characteristics of a resonator array for inductive power transfer by means of the accurate analytical solution of its circuit model. Through the mathematical inversion of a tridiagonal matrix, it is possible to obtain closed-form expressions for the current in each resonator and consequently expressions for the power transfer and efficiency of the system. The method can be applied to a resonator array powering a load at the end of the array or a receiver facing the array at any position. With the expressions obtained, it is possible not only to achieve a better understanding of the power transfer characteristics in resonator arrays but also to obtain the conditions for maximum power transfer or maximum efficiency, for several conditions and parameters of the system. A prototype of a stranded-wire resonator array powered by a resonant inverter, capable of delivering power to a load from 65 W to 90 W with efficiency values between 63% and 88%, was built in order not only to validate the expressions obtained but also to show their practical applicability and demonstrate that these arrays can be used for higher power transfer applications.

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Section: Currents In the Resonatorsmentioning

confidence: 99%

“…Further, by means of Eqs. (10) and (11), the following considerations can be made. The dependency of R T,ηmax and R T,P R T max on N is clearly shown in Figs.…”

Section: Efficiency and Power Delivered To A Load Or A Receiver Over mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accurate Calculation of the Power Transfer and Efficiency in Resonator Arrays for Inductive Power Transfer

Alberto¹,

Reggiani²,

Sandrolini³

et al. 2019

PIER B

Self Cite

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“…(2) and (3) can be written withẐ = R, [18] an example is shown by applying Eq. (2) repeatedly in order to determine the equivalent impedance of a resonator array loaded with two receivers.…”

Section: Equivalent Impedance With a Receiver Over The Resonator Linementioning

confidence: 99%

Fast Calculation and Analysis of the Equivalent Impedance of a Wireless Power Transfer System Using an Array of Magnetically Coupled Resonators

Alberto¹,

Reggiani²,

Sandrolini³

et al. 2018

PIER B

Self Cite

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Abstract-In this paper the equivalent impedance of resonator arrays for wireless power transfer systems is obtained in closed-form from a continued fraction expression. Using the theory of difference equations, the continued fraction is described as the general term of a complex sequence defined by recurrence, and its convergence is analyzed. It is shown that the equivalent impedance can be easily found in closed-form in terms of the system parameters. In this way, the obtained closed-form expressions may help electrical engineers to quickly predict the behaviour of a system with the changes of its parameters. Some numerical examples of the theoretical results are given and discussed. Finally, the analytical formulae obtained in this work are validated with measurements and a good agreement is observed.

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Two‐port network compact representation of resonator arrays for wireless power transfer with variable receiver position

Sandrolini

Simonazzi

Barmada

et al. 2022

Circuit Theory & Apps

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This paper presents an equivalent circuit characterization of an array of resonators for wireless power transfer (WPT) applications. These apparatuses are composed of magnetically coupled resonant coils acting as a transmitter which feeds a receiver coil that can be placed over them at any position, allowing the tolerance of the system to the receiver misalignment to be dramatically enhanced. This advantage makes resonator arrays a suitable solution for both low-and high-power applications. The latter usually involve battery charging, with the resonator array acting as a transformer stage, ensuring galvanic isolation. An equivalent two-port network can be defined for any receiver position, allowing the array to be treated as a traditional transformer. Thereby, the simulation of the system can be simplified, as it is required in the design steps of a converter and control strategy. Analytical expressions of the two-port network parameters are proposed for arrays of any size and length. The formulas have been numerically and experimentally validated.battery charging, circuit modeling, inductive power transfer, resonator array, transformer, wireless power transfer | INTRODUCTIONIn the last decade, wireless power transfer (WPT) systems have become a convenient and reliable solution in many applications, ranging from powering portable electronic devices to automatic machines and electric vehicle (EV) charging. [1][2][3] These apparatuses offer many advantages, as the ability of operating in difficult environments or the possibility to transfer power to moving loads. The size and weight of high-power batteries can be reduced by more frequent charging, which can be dramatically eased by wireless chargers. Several different technologies have been proposed in literature for both stationary and dynamic charging. [4][5][6] For high-power transfer, among near-field WPT technologies, inductive power transfer (IPT) is largely employed. One of its major limits is the misalignment between the transmitter and receiver apparatuses, which dramatically affects the efficiency and the transferred power. In order to improve the tolerance to the misalignment, arrays of magnetically coupled resonating L-C circuits (also referred as relay coils) can be used, which represent a very cheap solution since only few passive electronic components are required. [7][8][9][10][11] In these systems, the power travels from the source to the load through the relay coils at the expense of an increased sensitivity to the mismatch between the input and output side impedances, 12,13 which reflects also on the magnetic near-field distribution. 14 Solutions to this problem have been proposed in Sandoval et al, 15,16 making arrays of

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Circuit model of a resonator array for a WPT system by means of a continued fraction

Cited by 11 publications

References 9 publications

Accurate Calculation of the Power Transfer and Efficiency in Resonator Arrays for Inductive Power Transfer

Accurate Calculation of the Power Transfer and Efficiency in Resonator Arrays for Inductive Power Transfer

Fast Calculation and Analysis of the Equivalent Impedance of a Wireless Power Transfer System Using an Array of Magnetically Coupled Resonators

Two‐port network compact representation of resonator arrays for wireless power transfer with variable receiver position

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