Macro-Modeling Library in Simscape for MEMS Pressure Sensors Based on Energy-Flow Paradigm

A definitory feature of MEMS devices is the coupling at microscale between multiple energy domains. Reduced order macro-models (ROM) can be built using either signal flow or energy flow paradigms. While easier conceptually, reducing the device to a dynamical system defined by a set of differential equations, the so-called causal signal flow paradigm is nevertheless less portable, because the macro-models embed as well the excitation, or boundary conditions. The energy flow paradigm, on the other side, is an acausal modeling methodology that reduces the physical system to an equivalent generalized, Spice-like, network, based on across-through (power complementary) variables. The circuit-like representation makes it easier to interface with read-out or actuation electronics systems, for complete microsystems design, simulation and optimization. Besides existing standard behavioral modeling languages like VHDL-AMS and Modelica, MathWorks Simscape language has evolved in the past years to the point where it offers an alternative for the implementation of advanced MEMS macro-models; its seamless interface with Matlab and Simulink offers a strong framework for developing complex hybrid microsystems models, that mix Simulink (signal flow) models with Simscape (energy flow) ones. We have built a generic Simscape library for parameterized MEMS pressure sensors for two distinct categories, piezoresistive and capacitive sensing. The behavior of Simscape macro-models (e.g. sensitivity and frequency response) was validated against models of the same devices extracted in Coventor MEMS+ (a dedicated software for the design and simulation of MEMS devices) and finite element analyses (FEA).