This brief leads the synthesis of fractional‐order memristor (FOM) emulator circuits. To do so, a novel fractional‐order integrator (FOI) topology based on current‐feedback operational amplifier and integer‐order capacitors is proposed. Then, the FOI is substituting the integer‐order integrator inside flux‐ or charge‐controlled memristor emulator circuits previously reported in the literature and in both versions: floating and grounded. This demonstrates that FOM emulator circuits can also be configured at incremental or decremental mode and the main fingerprints of an integer‐order memristor are also holding up for FOMs. Theoretical results are validated through HSPICE simulations and the synthesized FOM emulator circuits can easily be reproducible. Moreover, the FOM emulator circuits can be used for improving future applications such as cellular neural networks, modulators, sensors, chaotic systems, relaxation oscillators, nonvolatile memory devices, and programmable analog circuits.

This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis.

A new nullor-based model to describe the behavior of Operational Transresistance Amplifiers (OTRAs) is introduced.The new model is composed of four nullors and three grounded resistors. As a consequence, standard nodal analysis can be applied to compute fully-symbolic small-signal characteristics of OTRA-based analog circuits, and the nullorbased OTRAs model can be used in CAD tools. In this manner, the fully-symbolic transfer functions of several application circuits, such as filters and oscillators can easily be approximated.