On Systematic Design of Fractional-Order Element Series

Area of Science:

• Electrical Engineering
• Analog Electronics
• Circuit Design

Background:

• Fractional-order elements (FOEs) are crucial for advanced analog signal processing and sensor applications.
• The commercial unavailability of a wide range of FOEs limits their practical implementation.
• Existing design methods for FOEs can be complex and require specialized components.

Purpose of the Study:

• To propose an efficient and systematic concept for designing a diverse series of floating fractional-order elements (FOEs).
• To overcome the limitations posed by the lack of commercially available FOEs.
• To demonstrate the versatility and effectiveness of the proposed design approach.

Main Methods:

• Utilizing a general immittance converter (GIC) as the core design principle.
• Employing operational transconductance amplifiers (OTAs) as active elements within the GIC structure.
• Leveraging a small set of "seed" FOEs with specific fractional orders to generate a broad spectrum of new FOEs.

Main Results:

• A systematic design concept enabling the creation of FOEs with fractional orders in the range [-n, n].
• Successful generation of 51 distinct FOEs with fractional orders between -2 and 2 using only two "seed" FOEs.
• Demonstration of the proposed GIC's operability, performance optimization, and robustness through post-layout simulations using OTAs in 0.18 μm CMOS technology.

Conclusions:

• The proposed GIC-based concept offers an efficient method for designing a wide range of fractional-order elements.
• This approach effectively addresses the commercial unavailability of FOEs, enabling their use in sensor applications and analog signal processing.
• The design is validated through simulations, confirming its performance and robustness for practical implementation.