Designing capacitively coupled microelectromechanical filters

High-quality-factor resonators are ubiquitous in todays communication devices. Macroscopic ceramic, SAW or FBAR filters offer excellent performance but their large size, high cost and unsuitability for IC integration limit their scope of application. In order to reduce the number of these bulky offchip filters, receiver architectures such as direct conversion have been developed. However, high-Q filters remain needed as band-select and channel-select filters. Miniature mechanical resonators, fabricated with microelectromechanical-systems (MEMS) technology, are a potential replacement of off-chip filters as they are compact in size and integratable with IC electronics. The demonstrated quality factors of MEMS resonators, Q> 100000 at 10 MHz [1] and Q> 1000 at 1 GHz [2], are comparable to their macroscopic counterparts. While the mechanical properties of MEMS resonators are very promising, the electrostatically coupled resonators characteristically suffer from low electromechanical coupling that leads to high electrical impedance levels and high insertion loss. In order to obtain lower impedances, very narrow gaps are required leading to nonlinear effects due to the inverse capacitance-displacement relationship. In filter applications, signal intermodulation (IM) due to odd-order nonlinearities is especially detrimental as it can lead to unwanted frequency components within the filter passband. For example, cubic mixing of two fundamental signals having frequencies ω1 and ω2 results in third-order intermodulation (IM3) products at frequencies 2ω1 − ω2 and 2ω2 − ω1 .I f ω1 = ω0 + ∆ω and ω2 = ω0 +2 ∆ω, the IM product at 2ω1 − ω2 is at the passband center frequency ω0 corrupting the desired signal. In this paper, our prior analysis of in-band [3] and out-ofband [4] filter distortion is summarized and a design procedure