properties can also be expressed in termsof the complex permittivity ε*:(18)Typical excitation frequencies range fromless than 1 mHz for insulating materialsup to several megahertz forsemiconducting materials. The sensorgeometry is accurately captured by theratio of the area to the gap (A·d–1) whenthe electrode widths are much larger thanthe gap so that the fringing fields at theelectrode sides can be neglected. Placingguard electrodes around the senseelectrode with their voltage the same asthe sense electrode voltage helpsminimize the effects of the fringing fieldsas illustrated in Fig. 27b. A guardelectrode can also be placed behind thesense electrode to further reduceextraneous coupling from the fringingfields. The final use of thesedielectrometry measurements is to inferrelated physical properties such asmoisture content, density, porosity andimpurities. Empirical measurements thencan generally map values of the physicalvariable to values of the materialpermittivity and conductivity.For simple systems (as in Fig. 28),measurements at a single excitationfrequency can be used to determine boththe permittivity and conductivity of thematerial. Most materials are dispersive,however, so the effective propertiesdepend on the excitation frequency.Dispersiveness can be attributed toheterogeneous material properties, such asparticles embedded in a matrix ormultiple layers of different materialproperties, or can be attributed tomultiple physical processes, such asmultiple conduction mechanisms.Different techniques or models are thenused to determine the properties ofinterest. As examples for multiple layeredmaterials, equivalent circuits andexpressions for the terminal capacitanceor conductance (Eqs. 14 and 15) thataccount for the properties of each layerεεεεσω*=′ −′′=−jjYZGjC==+1ωRC=εσGRAd==1σCAd=ε347Electromagnetic Techniques for Material IdentificationFIGURE27.Parallel plate electrode sensor: (a) basic sensor;(b) sensor with guard electrodes.(a)V0cos(ωt)SampleFringing fieldsElectrodesI(b)V0cos(ωt)DriveSensing electrodeGuard electrode driven atpotential of sensing electrodeILegendI= terminal currentt= time (second)V= voltageω= angular frequencyGuard electrode driven atpotential of sensingelectrodeFIGURE28.Equivalent circuit for parallel plateelectrode sensor and homogeneousdielectric material.Impedance ZAdmittance YCapacitance C
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can be used.12For two-phase compositematerials, the effective dielectricproperties of the composite can be relatedto the dielectric properties and geometryof the constituent materials.13The effects of material heterogeneitycan also be displayed graphically. Ifexcited by a sinusoidal voltage in time, asthe frequency is varied from zero toinfinity, a plot of the imaginary part ofthe impedance or admittance versus thereal part of the impedance or admittancetraces out a semicircle for the equivalentcircuit of Fig. 28. Such plots are called
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