Design Issues in Electromechanical Filters with Piezoelectric Transducers

The concept of filtering analog signals was first introduced almost one hundred years ago, and has seen tremendous development since then. The majority of filters consist of electrical circuits, which are relatively easy to work with since the signals themselves are usually electrical, although there has been a great deal of interest in electromechanical filters. Electromechanical filters consist of transducers that convert the electrical signal to mechanical motion, which is then passed through a vibrating mechanical system, and then transduced back into electrical energy at the output. In either type of filter, electrical or electromechanical, the key component is the resonator. This is a two-degree-of-freedom system whose transient response oscillates at its natural frequency. In electrical filters, resonators are typically inductor-capacitor pairs, while in mechanical filters they are spring-mass systems. By coupling the resonators correctly, the desired filter type (such as bandpass, band-reject, etc.) or specific filter characteristics (e.g. center frequency, roll-off, ripple, etc.) can be realized. Even though mechanical filters are in general more complex than electrical filters, given the required transducers and the additional fabrication steps, they are desirable because of the extremely good resonator characteristics of mechanical systems, which can result in superior filter characteristics. Existing mechanical filter technology could be considered to be "macro-scale" (centimeters and up) and the design process has been somewhat of an art. There is interest in developing micro-scale filters that are well-integrated with electronics. This thesis discusses the overall design process of mechanical filters, bringing together information from the filter design literature that is somewhat spread out. An example of the design and analysis of a narrow-band mechanical filter with piezoelectric transducers is offered. This design was constructed and tested, and the results are also presented. Finally, the thesis also presents implications for designing mechanical filters at the micro-scale