A unified modeling approach for characterization of fractional‐order memory elements

Abstract

SummaryA generalized mathematical model for current‐controlled fractional‐order memory elements is introduced in this work. The model characterizes constant‐phase elements (CPEs) when its nonlinearity parameter is zero ( ); otherwise ( ), it characterizes three main types of fractional‐order memory elements (memristor, meminductor, and memcapacitor). Time‐domain analyses of the voltage and energy relations of the model are derived and verified via numerical and circuit simulations. Some new deductions on the effects of the respective fractional‐order values are recorded: Each fractional‐order element transposes into their corresponding resistive or memristive properties as their fractional‐order values are varied; the meminductor's voltage response have undesired initial trails due to the fractional differentiator; the hysteresis loop of the meminductor is only pinched when its fractional‐order values are unequal. A new CPE emulator circuit is designed, and a generalized memelement emulator is also designed and verified in PSpice circuit simulator: Circuit simulation results confirm the numerical analysis in all cases.