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# DK2041_03 - Thou nature art my goddess to thy laws My...

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Thou, nature, art my goddess; to thy laws My services are bound. . . - Carl Friedrich Gauss DIELECTRIC LOSS AND RELAXATION-I T he dielectric constant and loss are important properties of interest to electrical engineers because these two parameters, among others, decide the suitability of a material for a given application. The relationship between the dielectric constant and the polarizability under dc fields have been discussed in sufficient detail in the previous chapter. In this chapter we examine the behavior of a polar material in an alternating field, and the discussion begins with the definition of complex permittivity and dielectric loss which are of particular importance in polar materials. Dielectric relaxation is studied to reduce energy losses in materials used in practically important areas of insulation and mechanical strength. An analysis of build up of polarization leads to the important Debye equations. The Debye relaxation phenomenon is compared with other relaxation functions due to Cole-Cole, Davidson-Cole and Havriliak-Negami relaxation theories. The behavior of a dielectric in alternating fields is examined by the approach of equivalent circuits which visualizes the lossy dielectric as equivalent to an ideal dielectric in series or in parallel with a resistance. Finally the behavior of a non-polar dielectric exhibiting electronic polarizability only is considered at optical frequencies for the case of no damping and then the theory improved by considering the damping of electron motion by the medium. Chapters 3 and 4 treat the topics in a continuing approach, the division being arbitrary for the purpose of limiting the number of equations and figures in each chapter. 3.1 COMPLEX PERMITTIVITY Consider a capacitor that consists of two plane parallel electrodes in a vacuum having an applied alternating voltage represented by the equation

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where v is the instantaneous voltage, F m the maximum value of v and co = 2nf is the angular frequency in radian per second. The current through the capacitor, ij is given by ~) ( 3 - 2 ) 2 where m (3.3) z In this equation C 0 is the vacuum capacitance, some times referred to as geometric capacitance. In an ideal dielectric the current leads the voltage by 90° and there is no component of the current in phase with the voltage. If a material of dielectric constant 8 is now placed between the plates the capacitance increases to CQ£ and the current is given by (3.4) where (3.5) It is noted that the usual symbol for the dielectric constant is e r , but we omit the subscript for the sake of clarity, noting that & is dimensionless. The current phasor will not now be in phase with the voltage but by an angle (90°-5) where 5 is called the loss angle. The dielectric constant is a complex quantity represented by E* = e'-je" (3.6) The current can be resolved into two components; the component in phase with the applied voltage is l x = vcos"c 0 and the component leading the applied voltage by 90° is I y = vo>e'c 0 (fig. 3.1). This component is the charging current of the ideal capacitor.
The

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