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Volume 7 Issue 5
Sep.  2020

IEEE/CAA Journal of Automatica Sinica

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Qiu-Yan He, Yi-Fei Pu, Bo Yu and Xiao Yuan, "Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1425-1436, Sept. 2020. doi: 10.1109/JAS.2020.1003009
Citation: Qiu-Yan He, Yi-Fei Pu, Bo Yu and Xiao Yuan, "Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1425-1436, Sept. 2020. doi: 10.1109/JAS.2020.1003009

Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

doi: 10.1109/JAS.2020.1003009
Funds:  This work was supported by the National Key Research and Development Program Foundation of China (2018YFC0830300) and National Natural Science Foundation of China (61571312)
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  • This paper discusses a novel rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth. The fractor has been exploited extensively in various scientific domains. The well-known shortcoming of the existing fractance approximation circuits, such as the oscillation phenomena, is still in great need of special research attention. Motivated by this need, a novel algorithm with high order-stability characteristic and wider approximation frequency bandwidth is introduced. In order to better understand the iterating process, the approximation principle of this algorithm is investigated at first. Next, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched, respectively. Furthermore, approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Finally, a fractance approximation circuit with the impedance function of negative 2/3-order is designed. The high order-stability characteristic and wider approximation frequency bandwidth are fundamental important advantages, which make our proposed algorithm competitive in practical applications.

     

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    Highlights

    • Fractor is a burgeoning new circuit element with fractance (abbreviation of fractional-order impedance). The ideal fractor does not currently exist and its approximate physical realization is called a fractance approximation circuit. There are oscillation phenomena in the existing fractance approximation circuits. This paper discusses an improved rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth.
    • Compared with the related algorithms, the predistortion exponent of this algorithm is not limited to be zero and has a value between -1 and 1. In order to better understand that why the algorithm is with high order-stability characteristic and wider approximation frequency bandwidth, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched in detail.
    • Approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Moreover, a fractance approximation circuit with the impedance function of -2/3-order is designed to verify the practicality of the algorithm.

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