Transmission/reflection and short-circuit line methods for measuring permittivity and permeability

The transmission/reflection and short-circuit line methods for measuring complex permittivity and permeability of materials in waveguides and coaxial lines are examined. Equations for complex permittivity and permeability are developed from first principles. In addition, new formulations for the determination of complex permittivity and permeability independent of reference plane position are derived. For the one-sample transmission/reflection method and two-position short-circuit line measurements, the solutions are stable for frequencies corresponding to integral multiples of one-half wavelength in the sample. For two-sample methods, the solutions are unstable for frequencies where both samples resonate simultaneously. Criteria are given for sample lengths to maintain stability. An optimized solution is also presented for the scattering parameters. The solution is stable over all frequencies and is capable of reducing scattering parameter data on materials with higher dielectric constants. An uncertainty analysis for the various techniques is developed and the results are compared. The errors incurred due to the uncertainty in scattering parameters, length measurement, and reference plane position are used as inputs to the uncertainty models.