Arbitrary-order fractance approximation circuits with high order-stability characteristic and wider approximation frequency bandwidth

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.