Dielectric Spectroscopy: Choosing the Right Approach - Pharmaceutical Technology

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Dielectric Spectroscopy: Choosing the Right Approach
This tutorial paper is meant to aid in dielectric-sensor selection
 Sep 2, 2008 Pharmaceutical Technology Volume 9, Issue 32, pp. 8293

 Table I: Results of the ranking algorithm showing the top three frequencies ranked by mean error and standard deviation. Error values are normalized.
in which T is the thickness of the coating, C f1 is the capacitance measured at frequency f 1, and K 1, K 2, and K 3, respectively, are the quadratic, linear, and offset coefficients.

To determine these coefficients and the frequency to be used, a simple algorithm is performed. First, the measured capacitances are averaged over the four samples for each of the coating levels. For each frequency, the minimum capacitance is subtracted to remove offset errors. Then the values are divided by the maximum capacitance at each frequency to remove the linear errors. The resulting capacitance ratios at each frequency are individually fitted to the quadratic equation above, and the resulting error in estimation is computed. The mean of the estimation errors and the standard deviation is tabulated for each frequency. The frequencies are ranked on the basis of least mean error and the least standard deviation. The product of these rankings is used as a figure of merit for selection of the frequency f 1. Table I shows the results obtained from the algorithm detailed above. It shows that the measurements at 100 kHz are the most suitable for the estimation process. The coefficients K 1, K 2, and K 3 were determined by least square methods. The resulting equation for estimation of coating thickness is

 Figure 6 (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
in which C 100k is the mean compensated and normalized capacitance at 100 kHz. Figure 6 shows the comparison between the actual coating thickness and estimated coating thickness. This process of estimation must be further validated by conducting experiments with many more coating levels and samples. Therefore, for inline process measurements, a selected frequency of excitation can be ascertained with some postprocessing of off-line data.

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