A Novel Method for Determining the R-Card Sheet Impedance Using the Transmission Coefficient Measured in Free-Space or Waveguide Systems

Free-space and rectangular waveguide techniques for determining the effective complex permittivity and, ultimately, the effective sheet impedance of an R-card using the forward transmission coefficient are presented. The advantage of using a transmission coefficient method instead of a more traditional reflection-based technique is discussed. The exact transcendental expressions relating the transmission coefficient and effective complex permittivity are derived and approximated using the Maclaurin series for sine and cosine. It is shown that the Maclaurin series expansion leads to simple closed-form solutions to the effective complex permittivity and avoids the use of sensitive and often unstable root search algorithms, which are necessary to solve transcendental equations. The accuracy of the approximations is directly related to the R-card's thickness and wavenumber. Free-space (4-16 GHz) and waveguide (8.2-12.4 GHz) measurements are made using two R-cards of differing thicknesses and impedances to demonstrate the method and regimes of validity. An uncertainty analysis is also performed to demonstrate the robustness of the technique.