Difference Between the Method of Moments and the Finite Element Method for Estimation of Complex Permittivity in Liquids Using a Coaxial Probe

In this study, the method of moments (MoM; a technique based on transverse electromagnetic (TEM) mode analysis) was applied for estimation of complex permittivity in liquids. This represents an inverse problem based on a combination of the coaxial probe approach (which facilitates measurement of liquid dielectric constants over a broad frequency range) and comparison of S 11 measurement values with calculated values based on electromagnetic (EM) analysis for periods of contact with an unknown material. The dielectric constants of certain liquid types were estimated assuming contact between the sample and the flange based on an inverse problem using the 2D Newton-Raphson method to coincide with S 11 values calculated using the MoM and the finite element method (FEM) at frequencies of 0.50, 1.5 and 3.0 GHz. The results of complex permittivity estimation using the MoM were also compared with set dielectric property values associated with S11 calculation using the FEM. The difference between each value in the material constant relating to S 11 calculation was then quantitatively calculated. Sample results include differences of 0.374 to 1.238% for the real part and 0.107 to 0.837% for the imaginary part in the permittivity of pure water with MoM application using the coaxial-probe approach as compared to FEM application.