Dielectric Loss

the portion of the energy of an alternating electrical field in a dielectric medium that is converted into heat. When the value and direction of the field intensity E change, the dielectric polarization also varies in value and direction; during one cycle of an alternating field the polarization is established twice and disappears twice. If the dielectric is made up of molecules that are dipoles themselves (polar molecules) or contain weakly bound ions, the orientation or displacement of these particles in an electrical field (orientation polarization) requires a definite time (relaxation time). As a result, the polarization maximum does not occur simultaneously with the maximum of the field intensity—that is, there is a phase shift between field intensity and polarization. Because of this there is also a phase difference between the field intensity E and the electrical induction D, which causes the energy loss W_∊. In a vector representation of the variables, it is possible to say that the electrical induction vector lags behind the electrical field vector by a certain angle 8, which is known as the dielectric loss angle. When molecules or ions are oriented by the field, they collide with other particles, thus dissipating energy. If the relaxation time T many times greater than the period T of the alternation of the applied field, polarization is barely able to develop and the dielectric loss is very small. At low frequencies, where the relaxation time T is considerably less than the period T, the polarization follows the field and the dielectric loss is also small because the number of reorientations per unit time is small. The dielectric loss is highest when the equality ω = 1/τ is satisfied, where ω the circular frequency of the electrical field: ω = 2π/T.

The mechanism described for the relaxation dielectric loss takes place in solid and liquid dielectrics that contain polar molecules or weakly bound ions. The magnitude of the relaxation dielectric loss in a liquid depends on its viscosity, the temperature, and the frequency of the applied field. For non-viscous liquids (water or alcohol) this loss appears in the centimeter wavelength range. In polymers that contain polar groups it is possible to orient both individual polar radicals and the longer or shorter molecular chains.

In dielectrics with ion and electron polarization, matter can be regarded as a set of oscillators experiencing induced oscillations, accompanied by energy dissipation, in an alternating electrical field (see Figure 1). However, if the frequency of

Figure 1. Model of a dielectric consisting of oscillators that are elastically bound electrical charges

the electrical field is much higher or lower than the natural frequency of the oscillators, the energy dissipation—and therefore the dielectric loss—is negligible. At frequencies comparable to the natural frequency of the oscillators, the energy dissipation and the dielectric loss W_∊ are high; a maximum occurs when these frequencies are equal, ω = ω_n (Figure 2). For electron polarization the maximum loss corresponds to the optical frequency range. In dielectrics that are made up of ions (for example, alkaline-halide crystals) the polarization is due to the elastic displacement of the ions, and the maximum loss occurs in the infrared frequency range (10¹²-10¹³Hz).

Figure 2. The function W_∊ (ω) for a dielectric consisting of the identical oscillators shown in Figure 1

Since real dielectrics have some electrical conductivity, there are energy losses that are caused by the electrical current flow in them (Joule loss) and are not frequency-dependent.

The dielectric loss in a dielectric placed between the plates of a capacitor is found from the relation

W_∊ = U²ωC tan δ

where U is the voltage on the capacitor plates, C is the capacitance of the capacitor, and tan 8 is the tangent of the dielectric loss angle. The loss for 1 cu cm of a dielectric in a uniform field E is

W_∊ = E²ω∊ tan δ

where ∊ is the dielectric constant.

The product ∊ tan δ is called the dielectric loss factor. A reduction of the dielectric loss is very important for the production of capacitors and in the technology of electrical insulation. High dielectric loss is used for dielectric heating in a high-frequency electrical field.