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 traditio...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on instrumentation and measurement 2009-07, Vol.58 (7), p.2228-2233
Main Authors: Hyde, M.W., Havrilla, M.J., Crittenden, P.E.
Format: Article
Language:English
Subjects:
Approximation
Closed-form solution
Coefficients
Complex permittivity
Equations
Impedance
Impedance measurement
MacLaurin series
Material measurements
Mathematical analysis
Microwave frequencies
Optical waveguides
Performance analysis
permittivity
Permittivity measurement
Probes
R-card
Rectangular waveguides
Robustness
sheet impedance
Studies
Thickness measurement
transmission coefficient
Waveguides
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2009.2013673