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anuradha / Art No. eme308 1^20

PERMITTIVITY AND MEASUREMENT
V. KOMAROV S. WANG J. TANG
Washington State University

Mechanisms that contribute to the dielectric loss in heterogeneous mixtures include polar, electronic, atomic, and Maxwell–Wagner responses [7]. At RF and microwave frequencies of practical importance and currently used for applications in material processing (RF1–50 MHz and microwave frequencies of 915 and 2450 MHz), ionic conduction and dipole rotation are dominant loss mechanisms [8]: e00 ¼ e00 þ e00 ¼ e00 þ d s d s e0 o ð2Þ

1. INTRODUCTION Propagation of electromagnetic (EM) waves in radiofrequency (RF) and microwave systems is described mathematically by Maxwell’s equations with corresponding boundary conditions. Dielectric properties of lossless andlossy materials influence EM field distribution. For a better understanding of the physical processes associated with various RF and microwave devices, it is necessary to know the dielectric properties of media that interact with EM waves. For telecommunication and radar devices, variations of complex dielectric permittivity (referring to the dielectric property) over a wide frequency range areimportant. For RF and microwave applicators intended for thermal treatments of different materials at ISM (industrial, scientific, medical) frequencies, one needs to study temperature and moisture content dependencies of the permittivity of the treated materials. Many techniques have been developed for the measurement of material permittivity. Some general descriptions of those methods are providedin the literature [1–4]. The measurement results for diverse dielectric media are compiled in the literature [5–7]. The objective of this article is to provide a brief description of basic physical theory for the measurement of permittivity associated with three popular experimental methods and to review the permittivities for different materials. Most of these data are taken from the literature,but some of permittivity data were measured in Biological Systems Engineering Department of Washington State University. The measurements were conducted by means of open-ended coaxial probe method with commercial instrumentation. 2. THEORY OF PERMITTIVITY Permittivity is a quantity used to describe dielectric properties that influence reflection of electromagnetic waves at interfaces and theattenuation of wave energy within materials. In frequency domain, the complex relative permittivity eà of a material to that of free space can be expressed in the following form: eà ¼ e0 À je00 ð1Þ

where subscripts ‘‘d’’ and s stand for contributions due to dipole rotation and ionic conduction, respectively; s is the ionic conductivity in S/m of a material, o is the angular frequency in rad/s, and e0is the permittivity of free space or vacuum (8.854 Â 10–12 F/m). Dielectric lossy materials convert electric energy at RF and microwave frequencies into heat. The increase in temperature (DT) of a material can be calculated from [9] rCp DT ¼ 5:563 Â 10À11 f E2 e00 Dt ð3Þ

where Cp is the specific heat of the material in J kg À 1 1 C À 1, r is the density of the material in kg/m3, E is theelectric field intensity in V/m, f is the frequency in Hz, Dt is the time duration in seconds, and DT is the temperature rise in the material in 1C. It is clear from Eq. (3) that the rise in temperature is proportional to the material’s dielectric loss factor, in addition to electric field intensity squared, frequency, and treatment time. In dielectric materials, the electric field strength decreases withdistance z from the surface and is written as E ¼ E0 eÀaz ð4Þ

The attenuation factor a depends on the dielectric properties of the material [5] and is given by 2 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 131=2  00 2 2p 41 0 @ e e 1þ 0 À 1A5 a¼ l0 2 e

ð5Þ

where l0 is the free-space wavelength. Substituting Eq. (4) into power equation Eq. (3), one obtains P ¼ P0 eÀ2az ð6Þ

The real part e0 is...