Analytical design of linear variable capacitors with shaped-finger comb-drive actuators

Variable capacitors have a broad usage in radio frequency (RF) circuits. Microelectromechanical systems (MEMS) technology can provide variable capacitors with high quality factor and wide tuning range characteristics. One of the design goals for MEMS varactors has been linear capacitance- voltage (C-V) characteristics. To design a linear C-V varactor, a shaped-finger comb-drive actuator is proposed in this paper. The shaped-finger design method, originally developed to obtain linear wavelength-voltage relationships in a tunable optical filter, is modified in this work for a linear C-V varactor, which involves development of a new governing equation. Moreover, conformal mapping is employed in calculation of capacitances, making the whole design process almost all-analytical with the minimum usage of numerical analysis methods. Variable capacitors with the shaped-finger design show linearity factor (LF) - defined as the maximum deviation from the perfect linear relationship - as low as 0.4%, tremendously improved from that of the conventional constant-finger-gap devices (LF: 49.9%). The characteristics of the designed variable capacitor are further investigated through 3-D numerical analysis, and show LF better than 11.5% for the finger thickness in the range between 1 and 10 micrometers. Versatility of the design method is further demonstrated by design of a varactor with linear resonant frequency-voltage (f-V) characteristics for voltage-controlled oscillator (VCO) applications. The developed analytical design method with shaped fingers can find a wide range of applications where comb-drive actuators are used.