Abstract
We present an online tool for calculating the capacitance between two conductors represented as simply-connected polygonal geometries in 2D with Dirichlet boundaries and homogeneous dielectric. Our tool can be used to model the so-called 2.5D geometries, where the 3rd dimension can be extruded out of plane. Micro-electro-mechanical systems (MEMS) with significant facing surfaces may be approximated with 2.5D geometry. Our tool compares favorably in accuracy and speed to the finite element method (FEM). We achieve modeling accuracy by treating the corners exactly with a Schwarz-Christoffel mapping. And we achieve fast results by not needing to discretize boundaries and subdomains. As a test case, we model a MEMS torsional actuator. Our tool computes capacitance about 1000 times faster than FEM with 4.7% relative error.
Highlights
mechanical systems (MEMS) technology has been rapidly developed and expanded in the past 30 years in various industries such as automobile, consumer electronic, health, and telecommunication
We present an online tool for calculating the capacitance between two conductors represented as -connected polygonal geometries in 2D with Dirichlet boundaries and homogeneous dielectric
When conformal mapping is used for modeling capacitance, it is usually done by mapping an arbitrary geometry configuration that is difficult to solve to a configuration that is easy to solve
Summary
MEMS technology has been rapidly developed and expanded in the past 30 years in various industries such as automobile, consumer electronic, health, and telecommunication. Some popular methods used for computing the capacitance in MEMS include parallel-plate approximation, conformal mapping, and distributed element methods. When conformal mapping is used for modeling capacitance, it is usually done by mapping an arbitrary geometry configuration that is difficult to solve to a configuration that is easy to solve Such arbitrary geometries are transformed to truly infinite parallel plate configuration, which is accurate, unlike the partial parallel-plate approximation mentioned above. Such geometric transformations can be quite extreme, the capacitance is invariant during one or more conformal mappings [7].
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