An automated frequency domain technique for dielectric spectroscopy of materials

Transmission

“…The terms e~""' relate to relaxation and the terms e"-'''"' relate to resonant phenomena. Since the Laplace transform of eq (3.4) is G{s) = J2Ar, 1 S -\-an -\-jbn (3.5) for stability (no increasing time domain exponentials) there can be no poles or zeros in the right half-side of the 5-plane [37], [38] The approach for determining the complex parameters Aj, Bj is to minimize the sum of the squares of the differences between the predicted and observed S-parameters, mm E4-4II , (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) where the measured vectors are denoted by S^j = {Sij{L0-i),Sij{uj2), , Sij{uJn)) and where [7] or Weir [6]. The most significant input parameters for modeling permittivity [26] and only the most essential details will be presented here.…”

“…Due to their relative simplicity, the off-resonance waveguide and coaxial line transmis- Most of the present transmission-line techniques [2,3,4], with some variations, are based on the procedure developed by Nicolson and Ross [5] and Weir [6] for obtaining 2-port, off-resonance, broadband measurements of permeability and permittivity. In the Nicolson-Ross-Weir (NRW) procedure the equations for the scattering parameters are combined in such a fashion that the system of equations can be decoupled.…”

Transmission

“…Equation (4.8) transforms Then for independent measurements on the two samples we havê 11(1) = ffj^> (4)(5)(6)(7)(8)(9)(10)(11)(12) and Port1…”

“…In these cases we have four unknown quantities (complex permittivity and permeability) and therefore require four independent real equations to solve for these variables. These equations can be generated by Most of the present transmission-line techniques [2,3,4], with some variations, are based on the procedure developed by Nicolson and Ross [5] and Weir [6] for obtaining 2-port, off-resonance, broadband measurements of permeability and permittivity. In the Nicolson-Ross-Weir (NRW) procedure the equations for the scattering parameters are combined in such a fashion that the system of equations can be decoupled.…”

Synthesis of All Known Analytical Permittivity Reconstruction Techniques of Nonmagnetic Materials From Reflection and Transmission Measurements

“…The reflection and transmission measurements have to be compensated (moved from the measuring planes to the interface of the material), in one way or an other [2], [5]- [7], [9], and then different reconstruction formulas can be used to reconstruct the permittivity: the Nicolson-Ross, Weir, and Stuchly-Matuszewsky equations [1], [3], [4]. When a calibrated model of the line is available, it can be computed directly from the measured S-parameters with the propagation matrices method [10].…”