FE Device P+Cap +Loss Polarization aseshift 0 deg FIGURE 49.5 Modern hysteresis circuit. An op amp is used to integrate the charge; loss and static capacitance compensation cluded Remanent (E2 300-200-10 200300 FIGURE 49.6 Idealized hysteresis curve for typical PZT materials. Many PZT materials display m the origin and ive asymmetries with respect to the origin. The curve shows how the remanent polarization the coercive field (Dare defined. While the loop is idealized, the values given for the polarization and field are realistic for typical PZT The measurement of the dielectric constant and the losses is usually very straightforward. a slab with a circular or other well-defined cross section is prepared, electrodes are applied, and the capacity and loss are measured(usually as a function of frequency). The dielectric constant is found from C=8￡ (49.10) where A is the area of the device and t the thickness. In this definition(also used in Table 49. 2)E is the relative dielectric constant and e, is the permittivity of vacuum. Until recently, the dielectric constant, like the polar ion, was measured at 50 or 60 Hz(typical powerline frequencies). Today the dielectric parameters are typically specified at 1 kHz, which is possible because impedance analyzers with high-frequency capability are readily available. To avoid low-frequency anomalies, even higher frequencies such as 1 MHz are often selected. This is especially the case when evaluating PZT thin films. Low frequency anomalies are not included in the equivalent circuit(Fig. 49.3)and are due to interface layers. These layers will cause both the resistive and reactive components to rise at low frequencies producing readings which are not representative of the dielectric properties c 2000 by CRC Press LLC© 2000 by CRC Press LLC The measurement of the dielectric constant and the losses is usually very straightforward. A slab with a circular or other well-defined cross section is prepared, electrodes are applied, and the capacity and loss are measured (usually as a function of frequency). The dielectric constant is found from (49.10) where A is the area of the device and t the thickness. In this definition (also used in Table 49.2) e is the relative dielectric constant and eo is the permittivity of vacuum. Until recently, the dielectric constant, like the polar￾ization, was measured at 50 or 60 Hz (typical powerline frequencies). Today the dielectric parameters are typically specified at 1 kHz, which is possible because impedance analyzers with high-frequency capability are readily available. To avoid low-frequency anomalies, even higher frequencies such as 1 MHz are often selected. This is especially the case when evaluating PZT thin films. Low frequency anomalies are not included in the equivalent circuit (Fig. 49.3) and are due to interface layers. These layers will cause both the resistive and reactive components to rise at low frequencies producing readings which are not representative of the dielectric properties. FIGURE 49.5 Modern hysteresis circuit.An op amp is used to integrate the charge; loss and static capacitance compensation are included. FIGURE 49.6 Idealized hysteresis curve for typical PZT materials. Many PZT materials display offsets from the origin and have asymmetries with respect to the origin. The curve shows how the remanent polarization (PY r) and the coercive field (EY c) are defined. While the loop is idealized, the values given for the polarization and field are realistic for typical PZT materials. C A t = o e e