Kevin Coakley, Jolene Splett
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
where the resonant frequency fo is approximately 10 GHz and the additive noise at frequency f is . 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 fo.
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
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
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