Micromachined Energy Harvesting Device for EM Application

We perform reduced ordered modeling simulation through the System Model Extraction (SME). It is a means by which a full three-dimensional meshed numerical model of a multi-conductor electromechanical device can be converted into a reduced-order analytical macromodel that can be inserted as a black-box element into a mixed-signal circuit simulator. This process is based on the energy method approach. We construct analytical models for each of the energy domains of the system and determine all forces as gradients of the energy.

 

The energy method has the advantage of making this process modular, enabling us to incorporate other energy domains into our models in the future. In addition, our energy methods are guaranteed to be energy conserving, because each stored energy shall be constructed as an analytical function, and all forces shall be computed directly from analytically computed gradients. The advantage of using SME is that the user shall construct the model and all necessary parameters of the model are considered during the simulation. Above all, this process has the ultimate benefit of constructing computationally efficient models, allowing their use in a dynamical simulator.

 

Initially, we reduce the degrees of freedom of the system. Rather than allow each node in a finite element model to be free to move in any direction, we constrain the motion of the system to a linear superposition of a selected set of deformation shapes. This set will act as our basic set of motion. The positional state of the system will hence be reduced to a set of generalized coordinates and each coordinate being the scaling factor by which its corresponding basis shape will contribute. Next, we construct an analytical macromodels of each of the energy domains of the system. In the case of conservative capacitive electromechanical systems, these consist of the electrostatic and kinetic energy domains. These macromodels will be the analytical functions of the generalized coordinates. (As we will see in Section Using Mode Shapes as a Basis Set, some of these energy domains will be determined as a by-product of modal analysis, avoiding the need for explicit calculation). We can then use Lagrangian mechanics to construct the equations of motion of the system in terms of its generalized coordinates. Finally, we can translate these equations of motion into an Analog hardware description language (HDL), thereby constructing a black-box model of the electromechanical system that can be inserted into an Analog circuit simulator.