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Slow thickness shear vibrations in AT-cut quartz plates driven by a lateral electric field produced by surface electrodes are analyzed theoretically. Mindlin's first-order theory of piezoelectric plates is used. Through an electrically forced vibration analysis, the motional capacitance and mode shapes near resonances are obtained. The effects of the electrode gap, the electrode/plate mass ratio R...
In the design and optimization of quartz crystal resonators, the finite element method has been adopted for the analysis of quartz crystal plates with complications for the vibration frequency and mode shapes. Further extension of such analysis can be made by using complex solutions to extract the electrical parameters of quartz crystal resonators because it is a typical electronic component in circuit...
The thickness-shear vibrations of a quartz crystal plate serve as the functioning mode of a resonator with strong couplings to many other modes of vibrations, which can affect the frequency and mode shape, consequently the resonator properties. For applications, it is always desired to have pure thickness-shear vibrations that only exist in an infinite plate. With the three-dimensional equations of...
Quartz crystal resonators of circular type are widely used for frequency control and detection functions with the quartz crystal plate vibrating at the thickness-shear mode. Naturally, vibrations of circular quartz crystal plates are of great interests in the design and optimization of resonators. We have derived the Mindlin plate equations for the thickness-shear vibrations of circular plates in...
A novel compact CPW-fed slotted patch antenna for quad-band operation is proposed. The antenna is printed on a 25 × 20 mm FR4 substrate with thickness of 1.6 mm and relative permittivity of 4.6 which has three L-shaped slots and a rectangular slot as additional resonators to achieve multi-band operation. As the four resonant frequencies of antenna are related to certain parts of the patch, one resonant...
Mindlin plate equations have wide applications in engineering fields with piezoelectric crystal resonators in particular due to its accurate prediction of high frequency vibrations of plates in the vicinity of thickness-shear mode. As a linear theory based on the assumption of infinitesimal deformation, its applications have been limited mainly to vibration frequency analysis. Many important properties...
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