A class of fractal-chain fractance approximation circuit. Issue 10 (2nd October 2020) - He, Qiu-Yan; Pu, Yi-Fei; Yu, Bo; Yuan, Xiao
ABSTRACT: A class of fractal-chain fractance approximation circuit (FCFAC) has been discussed in this paper. The FCFAC type 1 (FCFAC-1) can achieve the rational approximation of negative-half-order fractances. Changing the series and parallel connections or the positions of resistors and capacitors in FCFAC-1 produces another three FCFACs of negative-half-order. Making scaling extensions to the four original FCFACs, the scaling FCFACs can be obtained and achieve the rational approximation of fractances of arbitrary-order. The operational order, which is determined by the progression ratio of resistance α and the progression ratio of capacitance β, can be expressed as μ = − lg α / lg ( α β ) . The approximation performance of the scaling FCFACs has been improved and the optimised circuits are really simple. The oscillation phenomena of the frequency-domain characteristics of the scaling FCFACs have been described quantitatively. In addition, a comparison of approximation performance shows the scaling FCFACs provide a good choice in available fractance approximation circuits (FACs).