Design of Spring Coupling for High- Q High-Frequency MEMS Filters for Wireless Applications

This paper presents the design optimization of the coupling beam of wine glass (WG) mode micromechanical disk filters using the simulated annealing algorithm. The filter under consideration consists of two identical wine-glass mode disk resonators, mechanically coupled by a flexural mode beam. Such coupled two-resonator system exhibits two mechanical resonance modes with closely spaced frequencies that define the filter passband. The frequencies of the constituent resonators determine the center frequency of the filter, while the bandwidth is determined by the stiffness and location of attachment of the coupling beam. The goal is to design a filter with a commonly used bandwidth, namely 100 kHz. The design variables that control the bandwidth value are the beam length, the beam width, and the location of attachment of the coupling beam from the center. The simulated annealing algorithm is used to solve the optimization problem, since the governing dynamic equations of the resonator-coupling system are highly nonlinear. The resulting optimum design is simulated using the finite element method, which confirms the achievement of the desired center frequency and bandwidth. INTRODUCTION Frequency selective and generating components namely filters and oscillators are inherent building blocks in any modern wireless transceiver system as they play a key role in determining the overall system performance and sensitivity [1][2]. In today’s systems, off-chip mechanically resonant components, such as crystal resonators and filters [3], surface acoustic wave (SAW) filters [4][5], and film bulk acoustic resonators (FBAR’s) [6][7], are used to realize high-Q bandpass filters, commonly used in the radio frequency (RF) and intermediate frequency (IF) stages of heterodyne transceivers [4]. These mechanical components have higher quality factors compared to their transistor based counterparts [8][9]; as a result, they greatly outperform comparable filters implemented using transistor technologies [2][4]. On the other hand, these mechanical devices are bulky, and cannot be integrated on chip due to their non CMOS compatible fabrication technology. In addition, the insertion loss associated with these off chip components affect the system performance and reduces the battery life time if additional amplification stages are to be used [8][9]. For these reasons, research on how to implement MEMS based filters and oscillators is currently an active area of research [10][11]. The remainder of this paper is organized as follows. The next section presents the earlier work done related to the context of this paper. Then, the theory behind high-frequency μmechanical resonators design and μmechanical filter design is presented. Simulated annealing is then used to tune the coupling beam dimensions and coupling location to a certain desired bandwidth. Finally, the fabrication process is described. RELATED WORK Advances in surface micromachining technologies made it possible to fabricate on-chip high-Q micromechanical resonators and filters [12][13][14]. Vibrating Micro Electro Mechanical (MEMS) Wine Glass mode disk resonators fabricated using poly-silicon as the structural material first demonstrated by Abdelmoneum et al. [15][14] exhibited Q’s of more than 96,000 under vacuum and 8,600 in atmosphere and center frequency around 71 MHZ [14]. Later, resonators with Q’s in the excess of 145,000 in vacuum [16] were incorporated in demonstrating reference oscillators with phase noise performance surpassing GSM requirements. At this point, it appears that micromechanical resonators (abbreviated “μresonators”) can potentially serve well as miniaturized substitutes for crystals in a variety of high-Q oscillator and filtering applications. MF (eg., 455 kHz) MEMS filters were demonstrated early in literature [17][18]. Later, higher frequency MEMS filters, with frequencies around 7.8 MHz and percent bandwidths from 0.2% to 2.5% (Q from 40 to 450) were demonstrated by Bannon, et al. [19]. Unfortunately, filters at much higher