ANALOG CIRCUIT DESIGN IN THE FRACTIONAL ORDER DOMAIN

Abstract

This work is devoted to fractional order systems in analog circuit design. A general procedure for allocating the system poles and hence controlling the system stability for engineering applications is discussed. Two di erent transfer functions are introduced for the fractional LTI system with two di erent fractional order elements. The stability results are used to design fractional-order systems like filters and oscillators. In fractional order filters, the critical frequency points like the half power frequency, the maximum and minimum frequency and the right phase frequency points become functions of the fractional orders besides the transfer function parameters which adds extra degrees of freedom in the filter design. A general procedure to obtain Butterworth filter specifications in the fractional-order domain where an infinite number of relationships could be obtained due to the extra independent fractional-order parameters which increase the filter degrees-of-freedom. Moreover, the fractional mutual inductance is proposed as a new element and its applications like the double-tuned circuits with several examples are introduced. All the proposed circuits are verified through numerical simulations, circuit simulations using Advanced Design System (ADS) and experimentally.