Digitally Controlled Fractional-Order Elements Using OTA-C Structures

Abstract

This article presents an active realisation of an electronically controlled FO capacitor or a constant phase element (CPE) and an FO inductor (FOI) in the form of an integrated circuit. The realisation is demonstrated using an OTA-C structure in AMS 0.35 μm C35B4C3 technology. The same core is used for both realisations of CPE and FOI, and the angles can be realised in all four quadrants. The realisation of active constant-phase elements using OTAs with MOS transistors in the saturation region is proposed. The operating frequency is in the high range of 7–350 kHz, with a centre frequency of 50 kHz. A tuning method is proposed using different bias currents of the OTAs, which in turn are digitally controlled to obtain the desired parameters such as impedance and angle of an element. The linearisation of the individual OTAs is achieved by source degeneration. The newly introduced minimax approximation is used to design three non-integer orders of 1/3, 1/2, and 2/3. The integrated circuit was designed with a total area of 710 × 1127 µm2. The power consumption of the entire system is 12.37 mW.