The tuning of electrical circuit resonance with a variable capacitor, or varactor, finds wide application with the most important being wireless telecommunication. We demonstrate an electromechanical graphene varactor, a variable capacitor wherein the capacitance is tuned by voltage controlled deflection of a dense array of suspended graphene membranes. The low flexural rigidity of graphene monolayers is exploited to achieve low actuation voltage in an ultra-thin structure. Large arrays comprising thousands of suspensions were fabricated to give a tunable capacitance of over 10 pF/mm$^2$, higher than that achieved by traditional micro-electromechanical system (MEMS) technologies. A capacitance tuning of 55% was achieved with a 10 V actuating voltage, exceeding that of conventional MEMS parallel plate capacitors. Capacitor behavior was investigated experimentally, and described by a simple theoretical model. Mechanical properties of the graphene membranes were measured independently using Atomic Force Microscopy (AFM). Increased graphene conductivity will enable the application of the compact graphene varactor to radio frequency systems.
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