On Systematic Design of Fractional-Order Element Series.

In this paper a concept for the efficient design of a series of floating fractional-order elements (FOEs) is proposed. Using even single or a very limited number of so-called "seed" FOEs it is possible to obtain a wide set of new FOEs featuring fractional order α being in the range [-n,n], where n is an arbitrary integer number, and hence enables to overcome the lack of commercial unavailability of FOEs. The systematic design stems from the utilization of a general immittance converter (GIC), whereas the concept is further developed by proposing a general circuit structure of the GIC that employs operational transconductance amplifiers (OTAs) as active elements. To show the efficiency of the presented approach, the use of only up to two "seed" FOEs with a properly selected fractional order αseed as passive elements results in the design of a series of 51 FOEs with different α being in the range [-2,2] that may find their utilization in sensor applications and the design of analog signal processing blocks. Comprehensive analysis of the proposed GIC is given, whereas the effect of parasitic properties of the assumed active elements is determined and the optimization process described to improve the overall performance of the GIC. Using OTAs designed in 0.18 µµm TSMC CMOS technology, Cadence Virtuoso post-layout simulation results of the GIC are presented that prove its operability, performance optimization, and robustness of the proposed design concept.

Synthesis of elements with fractional-order impedance based on homogenous distributed resistive-capacitive structures and genetic algorithm.

The work proposes a synthesis method of capacitive fractional-order impedance element which is composed of homogenous distributed resistive-capacitive (RC) structures (lines). The method employs genetic algorithm and searches for optimal connection schemes and parameters of the partial RC structures. The synthesis algorithm is described in detail including the coding of the properties of the structures for the purpose of the genetic algorithm. The user interface of the design tool is introduced and the input and output parameters of the synthesis are explained. The algorithm was verified by computer simulations and particularly by measurements of element samples fabricated in thick-film technology. The results correspond to the required impedance characteristics, which confirm the validity of the synthesis method.