DESIGN OF -1/2~n ORDER ANALOG FRACTANCE APPROXIMATION CIRCUIT USING CONTINUED FRACTIONS DECOMPOSITION

摘要

In order to solve the most important problem of the fractional calculus (FC) application, the realization of analog circuit of fractance, continued fraction theory is applied to design the -1/2™ order analog fractance approximation circuit. The author presents a network function of ideal fractance and decomposes it in continued fractions (CFs) form to obtain the corresponding analog fractance approximation circuit. The new circuit consists of ordinary passive RC component through network synthesis method. Simulations are performed for the verification of the new circuit. Experimental evidence has proved that the performance of novel -1/2" order analog fractance approximation circuit is good in both amplitude-frequency response and phase-frequency response.