Transformers, piezoelectric

Medical Ultrasound Micro-positioning and Micro-motors Piezoelectric Transformers Active Noise and Vibration Damping SUGGESTED READING References on Silicon Devices Problems for Chapter 6... 

Fig. 6.22 (a) Simple form of piezoelectric transformer (b) transformer incorporating multilayered primary (c) transformer with multilayered primary and secondary. 

In addition to suitability to cheap mass production, piezoelectric transformers offer the advantage of a low profile when mounted on printed circuit boards. Over recent years they have found a commercially significant application for powering fluorescent lamps for back-lighting the screen in lap-top computers and electronic notebooks with liquid crystal displays. For these applications the output voltage and power are typically approximately 1 kV (rms) and 5 W, respectively. 

Longtu, Li. et al. (1990) Lead zirconate titanate ceramics and monolithic piezoelectric transformer of low firing temperature, Ferroelectrics, 101, 193-200. 

There are essentially three parts to the sensor. One is the mechanical part, the second is the piezoelectric transformation, and the last one is the electronics necessary to produce the amplification. The oscillating mass is a second-order mass, damper, stiffness system. Let us consider now the models of each of these sections with the aim at putting them together as a multidisciplinary mechatronics model. 

The piezoelectric transformation is a direct relation between the displacement of the mass and the charge generated in the capacitor so that it would yield... 

This represents the piezoelectric transformation between the velocity of the oscillating mass and the current, which is the input to the operational amplifier. This equation in bond graph notation is represented by a transformer element, which transforms the input force into voltage proportional to the acceleration. This can be represented in (Fig. 11.39)... 

The effort variables of the mechanical section represent the forces and the effort variables of the piezoelectric transformation represent the relation between the forces, which the sensor is subjected to and the voltage produced because of the piezoelectric effect. These variables in the electrical section represent the distinct voltages at any node in the circuit. Respectively, the flow variables represent the velocities and the currents involved. This approach considers the system as a whole so that the state matrix involves all three sections of the sensor, a mechanical section, a piezoelectric, and an electrical, a complete mechatronics system. CAMPG can obtain the desired transfer functions using the computer-generated state matrices derived in symbolic form. The Laplace transform is applied to the state space form and the transfer functions are obtained in symbolic and also in numeric form for... 

To realise these decentralized control systems, it is necessary to realise small signal processing and actuator driving units. In the case of piezoelectric actuators, the high driving voltage also has to be supplied, preferably generated from the common 12 VDC vehicle electrical system. Concepts based on piezoelectric transformers have been examined as potential solutions for this task [145]. 

Uchino, K. (et. al.) High-Power Piezoelectric Transformers. Proc. 13 Int. Conf. Adaptive Structures Tech. (ICAST) (2002)... 

The brothers Jacques and Pierre Curie are credited with the discovery of piezoelectricity in a number of hemiedric crystals (Curie and Curie, 1880). Today, piezoelectrics are utiUzed in acousto-electronic devices and sensors based on bulk and surface acoustic waves, piezomechanical sensors to monitor pressure, power, and acceleration, as actuators for micropositioning devices, band pass filters with low insertion losses, as electro-optic devices for optical memories, displays for high-definition televisions, and possibly as transparent piezoelectric speaker membranes as well as miniaturized piezoelectric transformers and motors. As the classic piezoelectric material is a-quartz, the basic relationships are detailed below using it as a model structure. Further details on the piezoelectric properties of quartz, and of its history, discovery and utilization, are available elsewhere (Ballato, 2009). 

Figure 8.41 Working principle of a piezoelectric transformer (after Ichinose, 1987). Reprinted with permission from Wiley-Blackwell Ltd, Oxford, UK.

Timability of perovskites is defined according to the dielectric nonlinearity of as functions of electric field above the Ciuie temperature. Ferroelectries for applications in electrically tunable devices are generally in the paraelectric phase [3,4,7-10,13]. The reason is that most of the ferroelectries in polar phase are also piezoelectric. Piezoelectric transformations cause large losses at relatively low microwave frequencies, and additional losses in polar phase are associated with the domain wall movements. Another reason hindering the applications of a ferroelectric in a polar phase is the hysteresis in field-dependent dielectric characteristics [7]. 

In this chapter studies of physical effects within the elastic deformation range were extended into stress regions where there are substantial contributions to physical processes from both elastic and inelastic deformation. Those studies include the piezoelectric responses of the piezoelectric crystals, quartz and lithium niobate, similar work on the piezoelectric polymer PVDF, ferroelectric solids, and ferromagnetic alloys which exhibit second- and first-order phase transformations. The resistance of metals has been investigated along with the distinctive shock phenomenon, shock-induced polarization. 

Tantalum and niobium are added, in the form of carbides, to cemented carbide compositions used in the production of cutting tools. Pure oxides are widely used in the optical industiy as additives and deposits, and in organic synthesis processes as catalysts and promoters [12, 13]. Binary and more complex oxide compounds based on tantalum and niobium form a huge family of ferroelectric materials that have high Curie temperatures, high dielectric permittivity, and piezoelectric, pyroelectric and non-linear optical properties [14-17]. Compounds of this class are used in the production of energy transformers, quantum electronics, piezoelectrics, acoustics, and so on. Two of... 

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

Finally, ferroelectricity is manifest in asymmetrical crystals producing domains of spontaneous polarization whose polar axis direction can be reversed in an electric field directed opposite the total dipole moment of the lattice. The two (or more) directions can coexist in a crystal as domain structures comprising millions of unit cells which contain the same electric orientation. The symmetry elements are temperature sensitive in ferroelectric materials [27]. At a particular temperature called the Curie Point the values of the piezoelectric coefficients reach particularly high values. Above the Curie Point the crystal transformation is to a less polar form and the ferroelectric nature disappears. 

Naturally, the fixed composition phase transformations treated in this section can be accompanied by local fluctuations in the composition field. Because of the similarity of Fig. 17.3 to a binary eutectic phase diagram, it is apparent that composition plays a similar role to other order parameters, such as molar volume. Before treating the composition order parameter explicitly for a binary alloy, a preliminary distinction between types of order parameters can be obtained. Order parameters such as composition and molar volume are derived from extensive variables any kinetic equations that apply for them must account for any conservation principles that apply to the extensive variable. Order parameters such as the atomic displacement 77 in a piezoelectric transition, or spin in a magnetic transition, are not subject to any conservation principles. Fundamental differences between conserved and nonconserved order parameters are treated in Sections 17.2 and 18.3. 

The simplest SAW sensor is a two-terminal transmission (delay) line in which the acoustic (mechanical) wave is piezoelectrically launched in one oscillator, called the transmitter. It travels along the surface of the substrate and is then transformed back into an electrical signal by the reverse piezoelectric effect at the receiving oscillator (Fig. 4.18). 

In comparison to ordinary dielectrics, the permittivities of the so-called ferroelectric materials are about 103 times larger. The ferroelectric material can be transformed into a new type of material called piezoelectric material by heating the ferroelectric above its Curie temperature and then cooling it in a powerful electric field. A piezoelectric crystal changes its polarization once subjected to a mechanical strain. As a result, it can deform mechanically under an electric field or produce electric impulses as a result of mechanical impulses. Currently, piezoelectric materials are widely used as force or pressure transducers with fast response times and very sensitive output. Permittivities of common dielectric and ferroelectric materials are given in Table 1.9. 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

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