A comprehensive error analysis of free-space techniques for extracting the permeability and permittivity of materials using reflection-only measurements

The electromagnetic characterization of layered materials is applicable to many different applications. In previous work it has been shown that reflection-only techniques — which vary the underlying structure of the sample stack to obtain two independent measurements — are a variation of a single unifying scheme such that there is a single set of closed-form unifying extraction equations for the electric permittivity and magnetic permeability. In this paper, the error propagation method is applied to this single set of closed-form extraction equations in order to derive an accompanying set of closed-form equations to predict the measurement uncertainty of electric permittivity and magnetic permeability. An error analysis is performed on the layer-shift method, and results are compared to a Monte Carlo simulation to prove the viability of the general error analysis equations. © 2021, Electromagnetics Academy. All rights reserved.