Temperature coefficient permittivity

The temperature coefficient of the natural logarithm of the relative permittivity of water is -0.0046, and insertion into equation (2.39) gives ... 

Class I dielectrics usually include low- and medium-permittivity ceramics with dissipation factors less than 0.003. Medium-permittivity covers an sr range of 15-500 with stable temperature coefficients of permittivity that lie between +100 and -2000 MK-1. 

Low-loss materials can be obtained with relative permittivities exceeding 500 but accompanied by high negative temperature coefficients, generally exceeding... 

High-power transmitter capacitors for the frequency range 0.5-50 MHz for which the main requirement is low loss a negative temperature coefficient of permittivity is tolerable since it limits the power through the unit when its temperature increases. 

For a number of dielectrics with e, > 30, TC is negative and within 15% of —aLer as illustrated by the examples given in Table 5.6. Eq. (5.34) suggests that the temperature variation of polarizability is small compared with the volume expansion coefficient in these cases. Lower-permittivity oxides have positive TC s and in their case the temperature coefficient of polarizability can be assumed to exceed the volume expansion coefficient. However, the extent to which the Clausius-Mosotti equation can be applied to ionic solids is open to debate. 

Table 5.6 Temperature coefficient of permittivity of Class I dielectrics...

A parallel-plate capacitor at 25 °C comprises a slab of dielectric of area 10 4 m2 and thickness 1 mm carrying metal electrodes over the two major surfaces. If the relative permittivity, temperature coefficient of permittivity and linear expansion coefficient of the dielectric are respectively 2000, — 12MK 1 and 8MK 1, estimate the change in capacitance which accompanies a temperature change of + 5 °C around 25 °C. [Answer — 0.035 pF]... 

A ceramic of relative permittivity 37 is in the form of a cylindrical DR for use at 1 GHz. Estimate the overall dimensions of the DR. The ceramic has a temperature coefficient of linear expansivity of 5MK-1 and a temperature coefficient of permittivity of — 16MK-1. Estimate by how much the resonance frequency will change for a 5°C change in temperature. [Answer diameter 2.5 cm 15 kHz]... 

The contribution E(ds/dT) (Eq. (7.3)) can be made by all dielectrics, whether polar or not, but since the temperature coefficients of permittivity of ferroelectric materials are high, in their case the effect can be comparable in magnitude with the true pyroelectric effect. This is also the case above the Curie point and where, because of the absence of domains, the dielectric losses of ferroelectrics are reduced, which is important in some applications. However, the provision of a very stable biasing field is not always convenient. 

In ferroelectrics the major contributor to tan 3 is domain wall movement which diminishes as the amplitude of the applied field diminishes the value applicable to pyroelectric detectors will be that for very small fields. The permittivity is also very sensitive to bias field strength, as is its temperature coefficient. The properties of some ferroelectrics - the relaxors - are also frequency dependent. It is important, therefore, to ensure that when assessing the suitability of a ferroelectric for a particular application on the basis of measured properties that the measurements have been made using values of the parameters (frequency, field strength etc.) appropriate to the application. This is not always done. 

A defined temperature coefficient of permittivity either close to zero (for capacitors with a capacity independent of temperature), or variable with negative or positive values (for the capacity compensation in circuits). 

Estimate the entropy of solvation of K in NM given that the temperature coefficient of the permittivity is —0.161 K. Use both the Born model and the MSA. Compare these with the experimental estimate of — 181 JK mol at 25°C. What are the contributions to long-range interactions which depend on dEs/dr, and local interactions which depend on dSs/dr, in this estimate ... 

It should be mentioned that even in the absence of dipolar, polarizable, or ionic reaction partners, high electric fields may cause shifts in chemical distributions. Such a field effect requires, however, that the solvent phase has a finite temperature coefficient of the dielectric permittivity or a finite coefficient of electrostriction an additional condition is that the chemical reactions proceed with a finite reaction enthalpy (AH) or a finite partial volume change (A V). Electric field induced temperature and pressure effects of this type are usually very small they may, however, gain importance for isochoric reactions in the membrane phase. 

Permittivity of mixtures at different temperatures can be calculated with high accuracy from absolute temperature coefficients of permittivity and their values using equations identical in form to [9.24]- [9.26]. For example, the calculation of temperature coefficients... 

Dielectric data for microwave dielectric materials, namely, the relative dielectric permittivity (e,), the product of the quality factor Q and the frequency (Q x/), the frequency of the measurement (/), and the temperature coefficient of the resonance frequency (xf) based on rare earth aluminates are listed in Table 30. Measurements carried out using low-frequency (MHz) impedance methods are... 

Ferroelectric materials, especially polyciystalhne ceramics, are utihzed in various devices such as high-permittivity dielectrics, ferroelectric memories, pyroelectric sensors, piezoelectric transducers, electrooptic devices, and PTC (positive temperature coefficient of resistivity) components. 

The well-known Cockbain relation (Cockbain and Harrop, 1968) between e and Ts, that is, as e increases the temperature coefficient of the dielectric permittivity decreases to strongly negative values. 

Several strategies for the design of dielectric microwave ceramics with high permittivities, high Q-factors, and a close to zero temperature coefficient of the resonance frequency, are Usted in Table 8.5. 

---