3.2.2 Characterizing Dielectric Materials

Kevin Coakley, Jolene Splett
Statistical Engineering Division, ITL

Mike Janezic
Radio Frequency Technology Division, 813.01

Dielectric materials have wide application throughout the electronics, microwave, communication and aerospace industries including: printed circuit boards, substrates, electronic and microwave components, sensor windows, antenna radomes and lenses, and microwave absorbers. NIST is developing new measurement methods for characterizing the complex permittivity of dielectric materials. In collaboration with EEEL staff, Statistical Engineering Division staff are developing statistical methods for the design and analysis of experiments in which the permittivity of a dielectric material is estimated. The goal is to develop dielectric Standard Reference Materials (SRMs).

The proposed SRM is a batch of cylindrical Rexolite samples. We estimate permittivity by placing each sample in a radio frequency cavity. The permittivity estimate depends, in part, on the observed Q factor and resonant frequency of the empty cavity and the observed Q factor and resonant frequency of the cavity when occupied by the sample. The estimate also depends on the mean height of the Rexolite sample.

We developed two statistical methods for estimation of surface roughness and the mean height of Rexolite samples. The first method models surface roughness as a polynomial surface, while a second technique models surface roughness using a nonparametric method. For both the parametric and nonparametric models, the estimated mean heights were in very close agreement. To estimate the resonant frequency of the cavity and the corresponding Q factor, we developed a nonlinear parameter estimation algorithm. Our model for the observed resonant curve at frequency fis

$$\begin{eqnarray*}T(f) = \frac{T(f_o)} { 1 + Q^2 ( f/f_o - f_o/ f )^2 } ~+~ (\alpha_1 + \alpha_2 f) + \epsilon(f) \end{eqnarray*}$$

where the resonant frequency f_o is approximately 10 GHz and the additive noise at frequency f is $\epsilon(f)$. In this model, we assume a background which varies linearly with frequency. In studies involving both real and simulated data, our nonlinear estimation procedure outperformed current state of the art methods used for estimating Q and f_o.

Given a model for the variance of the additive noise, we can compute the asymptotic standard deviation of the estimates of Q and the resonant frequency. In the actual experiment, resonance curves are sampled at a fixed number of frequencies. However, the frequency spacing is adjustable. As a first step in a study to determine the optimal data collection strategy, we compute the asymptotic standard error of the estimates as a function of frequency spacing. In this preliminary study, we assume that the additive noise variance is constant over all frequencies. Based on repeat measurements of resonance curves, the additive noise variance clearly depends on frequency. In future work, we plan to characterize the frequency dependency of the additive noise variance.

Figure 6: The top graph displays a nonparametric model estimate of surface height for a cylindrical Rexolite sample, while the bottom graph shows an observed (dots) and predicted (line) resonance curve.

       

Date created: 7/20/2001
Last updated: 7/20/2001
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