Extended and Generic Higher-Order Elements for MEMS Modeling

State-dependent resistors, capacitors, and inductors are a common part of many smart engineering solutions, e.g., in MEMS (Micro-Electro-Mechanical Systems) sensors and actuators, Micro/NanoMachines, or biomimetic systems. These memory elements are today modeled as generic and extended memristors (MR), memcapacitors (MC), and meminductors (ML), which are more general versions of classical MR, MC, and ML from the infinite set of the fundamental elements of electrical engineering, known as Higher-Order Elements (HOEs). It turns out that models of many complex phenomena in MEMS cannot be constructed only from classical and state-dependent elements such as R, L, and C, but that other HOEs with generalized behavior should also be used. Thus, in this paper, generic and extended versions of HOEs are introduced, overcoming the existing limitation to MR, MC, and ML elements. The relevant circuit theorems are formulated, which generalize the well-known theorems of classical memory elements, and their application to model complex processes of various physical natures in MEMS is shown.