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This paper reports on the design of a new analog MEMS varactor that uses electrostatic fringing-field actuation and is based on a single-crystal silicon movable structure coated with a thin metallic layer. Electrostatic fringing-field actuation allows for an analog displacement with no pull-in instability that yields a much larger tuning ratio compared to conventional electrostatic designs. In addition, total lack of dielectric layers and the use of single crystal silicon for the moving membrane significantly enhances the robustness of our proposed varactor by making it devoid of dielectric charging and stiction, insensitive to process variations, amenable to high yield manufacturing and less susceptible to hysteresis and creep. Based on this idea, we present example designs and the associated fabrication processes for varactors that exhibit a tuning ratio of 4.5:1 with capacitance values in the range of 43-200 fF achieved with DC voltages of 0-55 V. Such varactors are key elements in MEMS matching networks, tunable filters and reconfigurable antennas in the K/Ka/W-bands.