Emulation of current excited fractional-order capacitors and inductors using OTA topologies Georgia Tsirimokou a , Costas Psychalinos a , Todd J. Freeborn b,n , Ahmed S. Elwakil c,d a Department of Physics, Electronics Laboratory, University of Patras, Greece b Department of Electrical and Computer Engineering, University of Alabama, Tuscaloosa, USA c Department of Electrical and Computer Engineering, University of Sharjah, Sharjah, UAE d Nile University, Nanoelectronics Integrated Systems Center (NISC), Cairo, Egypt article info Article history: Received 18 April 2016 Received in revised form 17 June 2016 Accepted 17 June 2016 Keywords: Fractional-order capacitor Fractional-order inductor Analog signal processing circuits MOS integrated circuits Fractional-order circuits abstract A novel topology suitable for emulating fractional-order capacitors and inductors using current excitation is achieved using a fractional-order differentiator/integrator block and appropriately configured Opera- tional Transconductance Amplifiers. The scheme is capable of emulating both fractional-order capacitors and fractional-order inductors without any modifications to its structure. This implementation allows for electronic tuning of the order, capacitance/inductance, and bandwidth of operation by modification of only the bias current. Post-layout simulation results of the impedance magnitude and phase confirm the correct emulated behavior of both fractional-order capacitors and inductors. Two examples highlight the applications of this topology in i) realizing a fractional-order bandpass filter and ii) emulating a Cole- impedance model for biological applications. For both examples the characteristics of each circuit are validated in simulation. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction Fractional-order capacitors (FC), also commonly referred to as constant phase elements (CPEs), and fractional-order inductors (FI) are very important elements for implementing fractional-or- der systems [1]. These systems have been used to implement analog filter circuits with precise control of the attenuation char- acteristics [2–4], oscillator circuits with high oscillation fre- quencies independent of capacitance [5,6], and control systems with improved performance [7]. Unfortunately, these elements are not yet commercially available but significant research effort is ongoing to develop FCs as stand-alone two-terminal devices. For example, FCs have been developed utilizing electrolytic processes [8], fractal structures on silicon [9], dipping capacitive type poly- mer-coated probes in a polarizable medium [10,11] and most re- cently using graphene [12]. Each of the aforementioned solutions is not commercially available and also does not offer any possibi- lities of on-the-fly adjustability. Typical techniques for emulating a FC rely on passive RC trees with component values obtained using one of several suitable methods (such as Continued Fraction Ex- pansion) [13–17]. Each technique attempts to emulate the FC impedance given by ()= ^ () α Z s Cs 1/ 1 FC where α ( < < ) 0 1 is the order and ^ C is the pseudo-capacitance expressed in F s α−1 , and ω ω απ απ =( ) = [ ( )+ ( ) ] α α α s j j cos /2 sin /2 . While these approximations are successful at emulating the im- pedance, they are problematic when it is desired to change the characteristics α ( ^ ) C, of the emulated FC; requiring each of the passive components to be changed to a new value. In other words, only a fixed approximation for a specific α ( ^ ) C, valid over a certain pre-specified bandwidth with acceptable magnitude and phase errors is possible with these techniques. Recent works have ex- plored active topologies using Current Feedback Operational Am- plifiers (CFOAs), passive resistors, and capacitors to emulate FCs and FIs [18]. While this scheme is effective at emulating the FC and FI characteristics without any change in its structure, it suffers from the absence of any electronic tuning capabilities. An alter- native solution was introduced in [19], where the employed active elements were Operational Transconductance Amplifiers (OTAs). As a result, in addition to emulating FCs and FIs without any changes in the topology, the proposed scheme allowed electronic tuning of the order, capacitance/inductance, and bandwidth of operation. However, this solution is only capable of emulating a voltage excited FC, and not a current excited FC. Here, we present a method to emulate current excited FCs and FIs using an OTA Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/mejo Microelectronics Journal http://dx.doi.org/10.1016/j.mejo.2016.06.008 0026-2692/& 2016 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: tsirimg@upatras.gr (G. Tsirimokou), cpsychal@physics.upatras.gr (C. Psychalinos), tjfreeborn1@eng.ua.edu (T.J. Freeborn), elwakil@ieee.org (A.S. Elwakil). Microelectronics Journal 55 (2016) 70–81