he capacitance and r the resistance of the dielectric For an applied voltage Vacross the dielectric, the leakage current is I,=VIR and the displacement current is Ic= joCV; since tan8=I/Ic,then ns (558) ORC It is to be emphasized that in Eq (55.8), the quantities R and C are functions of temperature, frequency, and voltage. The equivalence between Eqs. (55.7)and(55.)becomes more palpable if I, and Ic are expressed as oe.V and joe'CoV, respectively. Every loss mechanism will exhibit its own characteristic tan& loss peak, centered at a particular absorption frequency, o, for a given test temperature. The loss behavior will be contingent upon the molecular structure of the material, its thickness, and homogeneity, and the temperature, frequency, and electric field range over which the measurements are performed [Bartnikas C and Eichhorn, 1983]. For example, dipole orientation losses will be manifested only if the material contains permanent molecular or side-link dipoles; a considerable overlap may ccur between the permanent dipole and ionic relaxation T regions. Ionic relaxation losses occur in dielectric structures where ions are able to execute short-range jumps between two or more equilibrium positions. Interfacial or space charge polarization will arise with insulations of multilayered struc- FIGURE 55.1 (a)Parallel equivalent RC circuit ne individual strata or where one dielectric phase is inter persed in the matrix of another dielectric. Space charge traps also occur at crystalline-amorphous interfaces, crystal defects, and oxidation and localized C-H dipole sites in polymers. Alternatively, space charge losses will occur with mobile charge carriers whose movement becomes limited at the electrodes. This type of mechanism takes place often in thin-film dielectrics and exhibits a pronounced thickness effect. If the various losses are considered schematically on a logarithmic frequency scale at a given temperature, then the tan8 and e values will appear as functions of frequency as delineated schematically in Fig. 55. 2. For many materials the dipole and ionic relaxation losses tend to predominate over the frequency range extending from about 0.5 to 300 MHz, depending upon the molecular structure of the dielectric and temperature. For example, the absorption peak of an oil may occur at 1 MHz, while that of a much lower viscosity fluid such as water may appear at pproximately 100 MHz. There is considerable overlap between the dipole and ionic relaxation loses, because the ionic jump distances are ordinarily of the same order of magnitude as the radii of the permanent dipoles. Space charge polarization losses manifest themselves normally over the low-frequency region extending from 10-Hz to 1 MHz and are characterized by very broad and intense peaks; this behavior is apparent from Eq (55.7), which indicates that even small conductivities may lead to very large tand values at very low frequencies The nonrelaxation-type electronic conduction losses are readily perceptible over the low-frequency spectrum nd decrease monotonically with frequency The dielectric loss behavior may be phenomenologically described by the Pellat-Debye equations, relating the imaginary and real values of the permittivity to the relaxation time, t, of the loss process(i. e, the frequency at which the e peak appears: f o= 1/2 T), the low-frequency or static value of the real permittivity, E, and the high-or optical-frequency value of the real permittivity, Ex. Thus, for a loss process characterized by a single relaxation time e=Em+1+02t (559) c 2000 by CRC Press LLC© 2000 by CRC Press LLC the capacitance and R the resistance of the dielectric. For an applied voltage V across the dielectric, the leakage current is Il = V/R and the displacement current is I C = jvCV; since tand = Il/IC , then (55.8) It is to be emphasized that in Eq. (55.8), the quantities R and C are functions of temperature, frequency, and voltage. The equivalence between Eqs. (55.7) and (55.8) becomes more palpable if Il and IC are expressed as we²Co V and jwe¢Co V, respectively. Every loss mechanism will exhibit its own characteristic tand loss peak, centered at a particular absorption frequency, vo for a given test temperature. The loss behavior will be contingent upon the molecular structure of the material, its thickness, and homogeneity, and the temperature, frequency, and electric field range over which the measurements are performed [Bartnikas and Eichhorn, 1983]. For example, dipole orientation losses will be manifested only if the material contains permanent molecular or side-link dipoles; a considerable overlap may occur between the permanent dipole and ionic relaxation regions. Ionic relaxation losses occur in dielectric structures where ions are able to execute short-range jumps between two or more equilibrium positions. Interfacial or space charge polarization will arise with insulations of multilayered struc￾tures where the conductivity and permittivity is different for the individual strata or where one dielectric phase is inter￾spersed in the matrix of another dielectric. Space charge traps also occur at crystalline-amorphous interfaces, crystal defects, and oxidation and localized C-H dipole sites in polymers. Alternatively, space charge losses will occur with mobile charge carriers whose movement becomes limited at the electrodes. This type of mechanism takes place often in thin-film dielectrics and exhibits a pronounced thickness effect. If the various losses are considered schematically on a logarithmic frequency scale at a given temperature, then the tand and e¢ values will appear as functions of frequency as delineated schematically in Fig. 55.2. For many materials the dipole and ionic relaxation losses tend to predominate over the frequency range extending from about 0.5 to 300 MHz, depending upon the molecular structure of the dielectric and temperature. For example, the absorption peak of an oil may occur at 1 MHz, while that of a much lower viscosity fluid such as water may appear at approximately 100 MHz. There is considerable overlap between the dipole and ionic relaxation loses, because the ionic jump distances are ordinarily of the same order of magnitude as the radii of the permanent dipoles. Space charge polarization losses manifest themselves normally over the low-frequency region extending from 10–6 Hz to 1 MHz and are characterized by very broad and intense peaks; this behavior is apparent from Eq. (55.7), which indicates that even small conductivities may lead to very large tand values at very low frequencies. The nonrelaxation-type electronic conduction losses are readily perceptible over the low-frequency spectrum and decrease monotonically with frequency. The dielectric loss behavior may be phenomenologically described by the Pellat-Debye equations, relating the imaginary and real values of the permittivity to the relaxation time, t, of the loss process (i.e., the frequency at which the e² peak appears: fo = 1/2 pt), the low-frequency or static value of the real permittivity, es, and the high- or optical-frequency value of the real permittivity, e`. Thus, for a loss process characterized by a single relaxation time (55.9) tand w = 1 RC FIGURE 55.1 (a) Parallel equivalent RC circuit and (b) corresponding phasor diagram. ¢ = + - + • • e e e e w t s 1 2 2