A class of fractal-chain fractance approximation circuit

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 $\alpha$ and the progression ratio of capacitance $\beta$, can be expressed as $\mu =-lg\alpha /lg(\alpha \beta )$. 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).

KEYWORDS:

• Constant phase element
• fractor
• fractance
• fractional calculus

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Key Research and Development Program Foundation of China [2018YFC0830300]; National Natural Science Foundation of China [61571312].