Analytical design of MEMS variable capacitors based on shaped-finger comb-drives
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A variable capacitor is one of the widely used components in radio frequency (RF) circuits. Variable capacitors can benefit from the microelectromechanical systems (MEMS) technology, to be equipped with attractive characteristics such as high quality factor and wide tuning range. One of the design goals for MEMS varactors has been to realize linear capacitance-voltage (C-V) characteristics, for which a design method is proposed in this paper, based on shaped-finger comb-drive actuators. The shaped-finger design method, originally developed for a tunable optical filter application by the author, is redeveloped in this work for a linear C-V varactor. Moreover, the conformal mapping method is employed in calculation of capacitances, making the whole design process more time-efficient, being almost all-analytical with the minimum usage of numerical analysis methods. Effects of sense capacitor finger shapes to the optimized drive capacitor finger shapes and the corresponding C-V characteristics are investigated as well. Variable capacitors with the shaped-finger design show linearity factor (LF)-defined as the maximum deviation from the perfect linear relationship-as good as 0.4%, enormously improved from that of the conventional constant-finger-gap devices (LF: 49.9%). Further probed by 3-D numerical analysis, the C-V characteristics of the designed variable capacitor show LF better than 2.62% in the case of constant-gap sense capacitors, and as good as 0.77% in the case of shaped-finger sense capacitors. Versatility of the design method is further demonstrated by presenting a varactor for linear resonant frequency-voltage (f-V) characteristics in voltage-controlled oscillator (VCO) applications. Finally, effects of etch bias, one of common fabrication imperfections, to the linearity of C-V characteristics are studied. The developed analytical design method with shaped fingers can find a wide range of applications where comb-drive actuators are used.