Dielectric-phase angle

Dielectric loss tangent The difference between 90° and the dielectric phase angle for a material. 

Dielectric phase angle n. The angular difference in phase between the alternating voltage (usually sinusoidal) applied to a dielectric and the resulting current. The angle is often symbolized by 9, the cosine of which is the power factor. Ku CC, Liepins R (1987) Electrical properties of polymers. Hanser Publishers, New York. 

DIELECTRIC POWER FACTOR The cosine of the dielectric phase angle (or sine of the dielectric loss angle). 

Dielectric Loss Angle. (Dielectric Phase Difference) The difference between 90 deg and the dielectric phase angle. 

The variations of dielectric constant and of the tangent of the dielectric-loss angle with time provide information on the mobility and concentration of charge carriers, the dissociation of defect clusters, the occurrence of phase transitions and the formation of solid solutions. Techniques and the interpretation of results for sodium azide are described by Ellis and Hall [372]. 

The tangent of the capacitance phase angle has been shown to be a measure of the completeness of the anneal (2.) Based on this technique, we have data which would predict 30 minutes at 300°C is sufficient to obtain optimum dielectric properties. However, we have found chronogravimetric analysis of polyimide films to be more useful in defining optimum anneal conditions. 

Polarizability Permeability Poisson s ratio Dielectric polarization Phase angle between stress and strain Specific resistance Polyamide (nylon)... 

Figure 13.5 Amplitude and phase angle of the third harmonic of the field induced strain and dielectric displacement of a 60/40 PZT thin film.

The effectiveness of these instruments for dielectric cure studies depends on sensitivity and accuracy. The sensitivity is related to the minimum resolvable phase angle, which for general cure studies, should ideally be less than about 0.10. Unfortunately, actual sensitivity in use depends strongly on the measurement frequency, on the admittance of the sample, on the details of the cabling and shielding, and on the electrical noise level of the environment. Therefore, analysis of published sensitivity specifications is difficult. It is easier to evaluate intrinsic instrument accuracy, which can be expressed in terms of either the tan8x accuracy or the conductivity accuracy. An example is useful. 

Dielectric monitoring can be accomplished in a variety of ways as illustrated in Figure 14. Here, phase angle (phase meter), tan 6 (dielectrometer) and DC resistivity (iongraphing) are plotted as a function of a simple cure cycle, a fixed rate of heating... 

An impedance response can be interpreted graphically as a vector on the complex plane. The imaginary axis is the out-of-phase response (Z"), and the real axis is the in-phase response (Z ). The magnitude of the impedance response Z is the length of the vector, and the phase angle (]) describes its direction (Fig. 3). Each point on the plane defines an impedance response at a particular frequency. Such representations are commonly referred to as complex plane plots, Nyquist diagrams, or Cole-Cole plots. However, the Cole-Cole plot is actually the complex plane representation of the dielectric response of a material. 

One of the most characteristic problems in the measurement of low frequency dielectric dispersion is that the ratio between the resistive and capacitive component of Z (tu) is very large. In other words, the phase angle is high. Therefore, accurate measurements of the latter component require an extremely powerful phase-sensitive detector. A second, nagging, problem, is electrode polarization, which may become particularly troublesome at low co. There are two options to avoid, or suppress, electrode polarization ... 

In the 1920s, impedance was applied to biological systems, including the resistance and capacitance of cells of vegetables and the dielectric response of blood suspensions. ° Impedance was also applied to muscle fibers, skin tissues, and other biological membranes. " The capacitance of the cell membranes was found to be a function of frequency, and Fricke observed a relationship between the frequency exponent of the impedance and the observed constant phase angle. In 1941, brothers Cole and Cole showed that the frequency-dependent complex... 

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