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Uncertainty with Various Additives and Primary Materials


The uncertainty in a prospective application can be estimated from the permittivities of the primary material and additive using the standard mixing rule and the known uncertainty of the electrical measurements. Substantially better results are typically obtained by averaging, but for a conservative estimate the standard deviation of the permittivity measurements is taken as 0.01. The calculated uncertainty is low when the permittivity of the additive is different from that of the primary material. This is evident in the figure, in which primary materials are ranked along the horizontal axis in order of increasing permittivity and additives materials are ranked along the vertical axis also in order of increasing permittivity. To evaluate a prospective measurement application, locate a point on the graph horizontally at the relative permittivity of the primary material and vertically at the relative permittivity of the additive and identify the zone in which the point is located. Measurement uncertainties in each of the zones are labeled on the graph.

Successive measurements at a single frequency once every two seconds could be averaged over three minutes to yield nearly one hundred measurements, reducing the uncertainty by a factor of ten. The chart gives conservatively estimated single measurement uncertainties, and a factor of ten better performance is often achieved.

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Last updated August 2000