Interdisciplinary Applied Mathematics

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17.2.2 Description Languages

Even though the equivalent circuit approach is popular, there are several drawbacks to using an equivalent circuit representation, the most important one being that not all microdevices can be represented by equivalent circuits, and even if an equivalent circuit representation exists, its construction may    not be    trivial.    Besides,    the    physical    meaning    of    the    problem gets

complicated due to representation of nonelectrical quantities such as force and velocity in terms of electrical quantities such as current and voltage. As a result, it may not be easy to understand how well the model captures the physics of the device.

Several other methods have also been developed which are based directly on the algebraic-differential equations that describe the device behavior. Suitable languages are used to describe the equations, with hardware description language being one of them. Simulations using description languages are, however, slower. The speed can be increased by using built-in libraries (stamps) for some standard structures or devices. Nodal analysis is another method, where the differential equations are solved directly. These two techniques are summarized below.

Element Stamps

One way of building coupled systems of equations in the electrical and mechanical domain is through the use of element stamps. Element stamps are the building blocks of conventional circuit simulators. They are derived from lumped-constant models of individual microdevices, and built into the circuit simulator (Casinovi, 2002). The use of element stamps for the constitutive elements allows one to simulate a system in a faster and more efficient way compared to models written in hardware description languages. Lumped constant models are sufficiently accurate for many applications. Ordinary circuit simulators use lumped constant models for electronic devices. This approach enables the simulation of complex mixed technology systems starting from their constitutive elements. Like Kirchhoff’s laws for electrical components, the equations governing the dynamics of constrained rigid bodies are additive with respect to the number of elements in the system. As a consequence, models of microdevices can be represented by stamps, which contain all the terms that contribute to the global system of equations.

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