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measurement configuration Fig. 1(i), (k), and (1) are suit- able. ——e An equivalent circuit for all the configurations is shown in Fig. 2(a), and its simplified more useful version in (b). Z(e*) represent this part of the impedance terminating the line, which depends on the permittivity of the test sample. Fig. 2(b) applies to all configurations but 1(b). It is applicable when d is small compared to the wavelength. Z or Cy represent the part of impedance which is independent from the dielectric sample. For the configuration shown in Fig. 1(a) Z = ©. The capaci- tance C(e*) in Fig. 2(b) for a lossy dielectric also includes the conductance due to the losses. However, such simplified rep- resentation is convenient for analytical treatment and accurate with restrictions discussed later.

Figure 1 measurement configuration Fig. 1(i), (k), and (1) are suit- able. ——e An equivalent circuit for all the configurations is shown in Fig. 2(a), and its simplified more useful version in (b). Z(e*) represent this part of the impedance terminating the line, which depends on the permittivity of the test sample. Fig. 2(b) applies to all configurations but 1(b). It is applicable when d is small compared to the wavelength. Z or Cy represent the part of impedance which is independent from the dielectric sample. For the configuration shown in Fig. 1(a) Z = ©. The capaci- tance C(e*) in Fig. 2(b) for a lossy dielectric also includes the conductance due to the losses. However, such simplified rep- resentation is convenient for analytical treatment and accurate with restrictions discussed later.

Related Figures (5)

Fig. 1. Sample configurations for measuring the permittivity using reflection methods.
Fig. 1. Sample configurations for measuring the permittivity using reflection methods.
PARALLEL PLATE, FRINGE FIELD, AND TOTAL CAPACITANCES FOR THE TEST CAPACITOR TERMINATING A COXIAL LINE (FIG. | (c)) TABLE | tively large changes in the reflection coefficient. Measurements of various sample thicknesses may be necessary before an optimum thickness is selected. The greatest accuracy is ob- tained when the sample thickness d is equal to an odd number of quarter wavelengths in the dielectric for low-loss dielectrics and one-quarter wavelength for high-loss dielectrics. Another disadvantage is the necessity for solving a transcendental equation. For liquid samples a window has to be placed at the interface A — A. Unless the window is thin and made of a low dielectric constant and low-loss material, it may cause a sig- nificant error in the measurement.
PARALLEL PLATE, FRINGE FIELD, AND TOTAL CAPACITANCES FOR THE TEST CAPACITOR TERMINATING A COXIAL LINE (FIG. | (c)) TABLE | tively large changes in the reflection coefficient. Measurements of various sample thicknesses may be necessary before an optimum thickness is selected. The greatest accuracy is ob- tained when the sample thickness d is equal to an odd number of quarter wavelengths in the dielectric for low-loss dielectrics and one-quarter wavelength for high-loss dielectrics. Another disadvantage is the necessity for solving a transcendental equation. For liquid samples a window has to be placed at the interface A — A. Unless the window is thin and made of a low dielectric constant and low-loss material, it may cause a sig- nificant error in the measurement.
OPTIMUM CAPACITANCE AS A FUNCTION OF FREQUENCY FOR WATER, MUSCLE TISSUE, AND FAT TISSUE where C(€*) = Coe* (Co is the capacitance of the air-filled parallel plate capacitor). It is assumed that an introduction of the test dielectric to the parallel plate capacitor causes only a negligibly small variation in the fringe field capacitance Cy. Both Co and Cy can be either calculated from (7) or deter- mined experimentally ¢ as s will be discussed later. re nt , re er ee a ee a ee: Sac. a a er oe TABLE II
OPTIMUM CAPACITANCE AS A FUNCTION OF FREQUENCY FOR WATER, MUSCLE TISSUE, AND FAT TISSUE where C(€*) = Coe* (Co is the capacitance of the air-filled parallel plate capacitor). It is assumed that an introduction of the test dielectric to the parallel plate capacitor causes only a negligibly small variation in the fringe field capacitance Cy. Both Co and Cy can be either calculated from (7) or deter- mined experimentally ¢ as s will be discussed later. re nt , re er ee a ee a ee: Sac. a a er oe TABLE II
Fig.4. An accurate equivalent circuit of an open-ended coaxial line (propagation). Fig. 5. Total capacitance versus frequency for three standard coaxial lines open into semi-infinite space.
Fig.4. An accurate equivalent circuit of an open-ended coaxial line (propagation). Fig. 5. Total capacitance versus frequency for three standard coaxial lines open into semi-infinite space.
! Only frequency range 0.1-10 GHz is considered here; some methods are also suitable for f < 0.1 GHz.
! Only frequency range 0.1-10 GHz is considered here; some methods are also suitable for f < 0.1 GHz.
Related topics:
Instrumentation and Measurement ScienceElectrical and Electronic EngineeringDielectric Losses
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