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In this paper, we demonstrate full closed-loop control of electrostatically actuated double-gimbaled MEMS mirrors and use them in an optical cross-connect. We show switching times of less than 10 ms and optical power stability of better than 0.2 dB. The mirrors, made from 10-[micro]m-thick single-crystal silicon and with a radius of 400-450 [micro]m, are able to tilt to 8[degrees] corresponding to 80% of touchdown angle. This is achieved using a nonlinear closed-loop control algorithm, which also results in a maximum actuation voltage of 85 V, and a pointing accuracy of less than 150 [micro]rad. This paper will describe the MEMS mirror and actuator design, modeling, servo design, and measurement results. Index Terms--Electrostatic actuator, microelectromechanical systems (MEMS), nonlinear closed-loop control, optical cross-connects, snap-down, torsional spring.

Microstrip elements of arbitrary shape are modeled in multilayered media. The Green's function for the multilayered structure is developed in a form useful for efficient computation for interacting microstrip elements, which may be located at any substrate layer and separated by an arbitrarily large distance. This result is of significant value to a variety of applications in wave propagation besides those discussed in this paper. The mixed-potential integral-equation (MPIE) method is developed in the spatial domain. Examples for regularly/arbitrarily shaped geometries in single and multilayered media are presented. These involve the optimization of an open-end microstrip, a radial-stub microstrip, a five-section overlay-gap-coupled filter, and a circular-patch proximity-coupled microstrip antenna. Very good agreement with measurement and other published data is observed.

A methodology for the design of multiple via-hole and air-bridge transitions of arbitrary shape in multilayered multiport microstrip circuits is presented in this paper. Application of multiple via holes to the design of microstrip filters and other devices will be discussed. To properly describe the current along the vertical post, the simple pulse function with a triangular cross section is used in the moment method analysis. Circularly and rectangularly shaped vertical transitions are analyzed for several practical applications. Comparisons of numerical results with experimental and available analytical data show good agreement.

The introduction of printed aperture into multiport microstrip circuits as a vertical transition proves to be practical in the design as well as manufacturing process of multilayered circuits. With the mixed-potential integral equation-based moment method, it becomes possible to analyze and optimize the performance of this arbitrary shape aperture transition for multiport circuit applications. Bandwidth enhancement is obtained by changing the shape of the slot for two-port and three-port microstrip transitions. Also, the influence of slot size, orientation, and mutual coupling have been thoroughly studied in order to reach an optimal circuit performance. Using this transition, a three-port power divider with 180 degree phase difference and a directional coupler with various degree of coupling have been designed.