Implementing Inductor Function with Vibrating Capacitor Structures

Abstract

One of the most common uses of inductors is in filtering electrical signals to remove oscillations over selected frequency ranges. In this application, they are combined with capacitors to build resonant circuits to either block or dissipate signals at the unwanted frequencies. Similar, but larger current capacity filters are used to eliminate oscillatory ripple voltages from DC power supply outputs. Inductors are also essential components in buck converter type power supplies in which they store energy supplied by an oscillatory source to power a circuit, which generates a constant voltage. Inductors of various constructions have proven highly successful in all of these applications, but their performance is not ideal. For one, they dissipate the energy that is stored in them via a number of mechanisms. The conductivity of the wire comprising their windings is finite, so they suffer Ohmic losses. Their magnetic fields induce eddy currents within their cores and dissipative currents in surrounding circuit elements. Inductors also exhibit parasitic capacitance between their windings, which can give rise to dielectric losses. Because of these loss mechanisms, the quality factor of an inductor, which is its time average ratio of stored to dissipated energy, is typically less than a few hundred. By contrast, mechanical resonators, fabricated from single crystal silicon, attain quality factors that are orders of magnitude higher. Hence, mechanical filters could be made with sharper roll offs and smaller bandwidths than inductor based filters. They would also be more efficient in power supply applications. Inductors are also relatively heavy components, when compared to capacitors, resistors and integrated circuits, due to their high content of copper and iron. A mechanical oscillator could be made significantly lighter than an inductor that is capable of storing the same amount of energy. We have been investigating mechanical oscillators that use flat beams, suspended at both ends above substrates with electrode patterns that form a capacitive dive to excite oscillations in the beam. We are examining a number of configuration variables, including beam geometry, mass distribution and excitation loading. We use finite element analysis and lumped parameter models to characterize beam deflection and MatLab scripts to predict performance in electrical circuits. We are also preparing to fabricate our first design for testing.