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## Microelectromechanical resonators design: low-frequency resonators

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Low-frequency MEMS resonator device design using a mixed mechanical and electrical coupling scheme is illustrated in this chapter. The closed-form expressions are easier to handle and provide automated analysis before fabrication. The electrical coupling scheme is also useful in suppressing spurious modes due to an increase in the operating temperature of the device by no addition to the responses at the output electrode. Mechanical couplers at equal velocity point aids in minimum variations in mode shapes and resonant frequencies. Thus, mixed electrical and mechanical coupling scheme enhances operation in desired modes and suppresses undesired and spurious modes. The device can be designed using Euler Bernoulli's beam theory. Desirable center frequency and bandwidth can be obtained using well-defined equations and physical parameters. Although resultant frequency and bandwidth can be achieved, other filter parameters such as insertion loss, output power, and stopband rejection which is the function of the transduction gap, the width of the CC beam, and the number of CC beams need careful modeling of the device. A comprehensive model is required that would give complete design automation before fabrication of the device under electrostatic actuation. Filter characteristics, suppression of spurious modes, and thermal stability can be obtained using CC beam array that is anchored to the substrate using rigid contact anchors. These anchors are responsible to dissipate large amounts of energy and reduce Q. Although it is known that a free-free beam achieves high Q. But dual frequency characteristics, desired bandwidth, and suppression of unwanted responses may be difficult to achieve using a free -free beam. Hence it is required to adopt techniques that would reduce anchor losses and enhance Q. RF MEMS resonator filters to be deployed in a transceiver for wireless communication systems needs to satisfy all the stringent specifications given to the filter designer. One of the most important among them is thermal stability. Metals MEMS resonator filter has poor thermal stability hence composite structure using silicon dioxide. To improve further the thermal stability of the device, we suggest fabricating the composite structure of the device using metals and silicon dioxide.

Chapter Contents:

• 3.1 Introduction
• 3.2 Low-frequency RF MEMS resonators
• 3.3 Actuation mechanism
• 3.3.1 Electrostatic actuation
• 3.3.2 Piezoelectric actuation
• 3.3.3 Magnetic actuation
• 3.4 Design of low-frequency MEMS resonator
• 3.4.1 Clamped-clamped beam design
• 3.4.2 Mechanical coupler design
• 3.4.3 Electrical coupling scheme
• 3.4.4 Suppression of spurious responses
• 3.5 Summary
• References

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