Uncertainty analysis for the simultaneous measurement of complex electromagnetic parameters using an open-ended coaxial probe

A differential uncertainty equation is established for the simultaneous measurement of complex electromagnetic (EM) parameters, i.e., permittivity ε and permeability μ, using an open-ended coaxial probe, in the systematical consideration of the error sources associated with computation, modeling, measurements, etc. A numerical analysis is carried out based on the "thickness-varying method" to provide the relations between the uncertainties and sample thicknesses in 3D figures. The comparison between the measured errors and theoretical uncertainty prediction validates the feasibilities of our formulas.