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Title: DIMENSIONAL ANALYSIS OF A PERMITTIVITY MEASUREMENT PROBE

Author
item BARTLEY, PHILIP - NORFOLK, VA
item Nelson, Stuart
item MCCLENDON, RONALD - UGA ATHENS, GA

Submitted to: IEEE Transactions on Instrumentation and Measurement
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/3/2002
Publication Date: 6/1/2002
Citation: BARTLEY, P.G., NELSON, S.O., MCCLENDON, R.W. DIMENSIONAL ANALYSIS OF A PERMITTIVITY MEASUREMENT PROBE. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. VOL. 51(6). P. 1312-1315. 2002.

Interpretive Summary: Dielectric properties of materials are the characteristics of materials, which are relatively poor conductors of electricity, that determine how they interact with electromagnetic fields. For example some foods heat rapidly in a microwave oven and some heat slowly depending on their dielectric properties. The dielectric properties are also useful, for example, in measuring the moisture content of grain, because instruments can sense the dielectric properties, and those properties are highly correlated with moisture content. Thus, rapid moisture measurements are possible for grain and other products with electronic moisture meters. In research on improving moisture measurement, microwave heating of foods, etc., measurement of the dielectric properties of these materials is important. One technique for measuring dielectric properties is the use of an open coaxial-line probe. For reliable measurements, the electromagnetic characteristics of the probe must be accurately determined. This paper presents a new application of a technique known as dimensional analysis, which is a powerful tool for many analytical mechanical problems, to an electrical description of an open coaxial probe that might be used for measuring dielectric properties of materials. The dimensional analysis approach simplifies the problem compared to the very complicated electric field computations which are normally required, thus enabling easier modeling of new ideas in probes for dielectric properties measurements on various materials.

Technical Abstract: Open-ended coaxial-line probes provide a convenient means of determining the dielectric properties of many materials over a relativity wide frequency range. Because of this, much attention has been given to understanding the interaction of the probe and the material which it is inserted into. In this paper a dimensional analysis was performed on a generalized open-ended coaxial-line probe. Applying the Buckingham Pi-theorem revealed that the admittance of the probe/dielectric interface, scaled by the frequency, is a function of a single dimensionless variable. This fact greatly simplifies the modeling of the probe. The problem is reduced from fitting a model of two variables, frequency and permittivity, to one dimensionless variable. In addition the dimensional analysis also revealed that the same results hold for any permittivity measurement probe where the admittance of the probe is a function of permittivity, frequency, and any number of linear dimensions.