Design, synthesis and simulation of fractional-order element using MOS transistors as distributed resistive capacitive devices

The article presents a synthesis method to design electrical circuit elements with fractional-order impedance, referred to as a Fractional-Order Element (FOE) or Fractor, that can be implemented by Metal-Oxide-Semiconductor (MOS) transistors. This provides an approach to realize this class of device using current integrated circuit manufacturing technologies. For this synthesis MOS transistors are treated as uniform distributed resistive-capacitive layer structures. The synthesis approach adopts a genetic algorithm to generate the MOS structures interconnections and dimensions to realize an FOE with user-defined constant input admittance phase, allowed ripple deviations, and target frequency range. A graphical user interface for the synthesis process is presented to support its wider adoption. We synthetized and present FOEs with admittance phase from 5 to 85 degrees. The design approach is validated using Cadence post-layout simulations of an FOE design with admittance phase of 74 ± 1 degrees realized using native n-channel MOS devices in TSMC 65 nm technology. Overall, the post-layout simulations demonstrate magnitude and phase errors less than 0.5% and 0.1 degrees, respectively, compared to the synthesis expected values in the frequency band from 1 kHz to 10 MHz. This supports that the design approach is appropriate for the future fabrication and validation of FOEs using this process technology.