ET13.pdf

Cole cole plots and when semicircular provide a quick

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cole-cole plots and when semicircular provide a quick verification that the material is homogeneous and frequency nondispersive. If the dielectric properties of permittivity and conductivity are spatially dependent or dependent on frequency, then the cole-cole plots will deviate from the semicircular shape. To illustrate this effect, consider Fig. 29, which shows the effective properties for a relatively insulating liquid dielectric. 14 In this case, a parallel plate sensor was immersed in a liquid dielectric so that no air gaps would be present between the test material and the electrodes. At high frequencies, the effective permittivity is constant and the effective conductivity is unmeasured because the response is dominated by the capacitive effects. At intermediate frequencies, both the permittivity and conductivity can be determined and are constant with frequency. At very low frequencies, the effective properties show a dependence on frequency and reflect the existence of an electrical double layer at the electrode interfaces. The cole-cole plot of Fig. 30 shows this frequency dependence: the semicircular shape of the response is lost at low frequency and at the elevated temperatures because of the electrical double layer capacitance. In many circumstances, only one side of the test material is accessible or the spatial variations of the material properties may be of interest. In these situations, it is generally impractical to use a parallel plate sensor and one-sided measurement schemes are required. These single-sided sensor schemes can be visualized as parallel plate capacitors that have been opened so that the sensor responds to the material properties through changes in the fringing electric fields between the electrodes. Guard electrodes can also limit unintentional coupling of the fields to the sense electrode. One single-sided electrode format that has an advantage of providing a relatively large sensing response within a given sensor footprint is an interdigitated electrode structure as shown in Fig. 31a. 15-17 The spatial periodicity of the electrodes is determined by the wavelength λ . One set of electrode fingers is driven by a sinusoidally time varying signal V D with known amplitude and frequency whereas the second set of 348 Electromagnetic Testing Legend = permittivity = conductivity F IGURE 29. Representative plots of effective material properties for transformer oil: (a) at 15° C (59° F); (b) at 70° C (158° F). Relative permittivity, ε′ · ε –1 0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Conductivity σ (pS·m –1 ) 10 –2 10 –1 0 10 1 10 2 10 3 10 4 Frequency (Hz) (a) Relative permittivity, ε′ · ε –1 0 70 60 50 40 30 20 10 0 Conductivity σ (pS·m –1 ) 10 –2 10 –1 0 10 1 10 2 10 3 10 4 Frequency (Hz) 40 30 20 10 0 (b) Z imag (G ) 60 50 40 30 20 10 0 Increasing frequency 15 °C (59 °F) 50 °C (122 °F) 0 10 20 30 40 50 60 70 °C (158 °F) 35 °C (95 °F) Z real (G ) F IGURE 30. Representative cole-cole plots of real and imaginary parts of complex impedance Z corresponding to data of Fig. 30.
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interdigitated fingers is capacitively
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  • Fall '19
  • Magnetism, Magnetic Field, Electrical conductivity

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