The open-ended coaxial probe with lift-off is studied using a full-wave analysis, and an uncertainty analysis is presented. The field equations for the following terminations are worked out: (1) the sample extends to x in the positive axial direction, (2) the sample is backed by a well-characterized material, and (3) the sample is backed by a short-circuit termination. The equations are valid for both dielectric and magnetic materials. The model allows the study of the open-ended coaxial probe as a nondestructive testing tool. The analysis allows a study of the effects of air gaps on probe measurements. The reflection coefficient and phase are studied as a function of lift-off, coaxial line size, permittivity, permeability, and frequency. Numerical results indicate the probe is very sensitive to lift-off. For medium to high permittivity values and electrically small probes, gapson the order of fractions of a millimeter strongly influence the reflection coefficient. In order for the field to penetrate through the air gap, larger size coaxial line or higher frequencies need to be used. A comparison of the theory to experiment is presented. The results are in close agreement. A differential uncertainty analysis is also included.
This letter presents a new transmission line method for measuring the complex permittivity of dielectric materials using propagation constant measurements. In contrast to previous methods, a network analyzer calibration is unnecessary since calibrated scattering parameters are not required. We use measurements in X-band waveguide to show that this technique compares well with the transmission/reflection and cylindrical cavity methods.
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