Piezoelectric ceramics filters

Thomarm H, Wersing W (1982) Principles of piezoelectric ceramics for mechanical filters. Ferroelectrics... 

In the use of mechanical vibration devices such as filters or oscillators, the size and shape of a device are very important, and both the vibrational mode and the ceramic material must be considered. The resonance frequency of the bending mode in a centimeter-size sample ranges from 100 to 1000 Hz, which is much lower than that of the thickness mode (100 kHz). For these vibrator applications the piezoceramic should have a high mechanical quality factor (Qm) rather than a large piezoelectric coefficient d that is, hard piezoelectric ceramics are preferable. 

Ferroelectric and piezoelectric ceramics, in particular, play an ever-increasing role as materials for electrical and electronic applications that include multilayer capacitors (MLCs), bypass capacitors, dielectric resonators for frequency stabilization of microwave circuits, low-noise oscillators and low-insertion loss bandpass filters for microwave communication components, dielectric waveguide resonators, piezoelectric transducers and sensors, piezomechanical actuators and motors,... 

A filter is required to pass a certain selected frequency band, or to stop a given band. The passband for a piezoelectric device is proportional to k2, where k is the appropriate coupling coefficient. The very low k value of about 0.1 for quartz only allows it to pass frequency bands of approximately 1% of the resonant frequency. However, the PZT ceramics, with k values of typically about 0.5, can readily pass bands up to approximately 10% of the resonant frequency. Quartz has a very high Qm (about 106) which results in a sharp cut-off to the passband. This, coupled with its very narrow passband, is the reason why the frequency of quartz oscillators is very well defined. In contrast PZT ceramics have Qm values in the range 102—103 and so are unsuited to applications demanding tightly specified frequency characteristics. 

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