Permittivity measurement of disk and annular dielectric samples using coaxial transmission line fixtures. part I: theory and formulation

One way of measuring the permittivity of circularly shaped dielectric samples is to measure the S-parameters of a two-port coaxial transmission line fixture into which the samples are placed. Among the sample forms that can be fitted into coaxial waveguides are (1) circular disks and (2) annular rings. The former type is sandwiched between two disjointed inner conductors of the coaxial line, whereas the latter dielectric form is snug-fitted to become the insulation layer of an intermediate coaxial section. Each type of sample requires a different coaxial configuration; this work studies both fixtures. The investigation of the first type is based on a previously studied technique that treats the sandwiched circular disk as a parallel-plate capacitor. Because of inaccuracies in the original form of that method, a modified version that offers improved accuracy is devised here. In addition, a new, independently developed technique for accurately characterizing dielectrics of the second form (annular-ring samples) using quadratic curve fitting is proposed. The experimental fixture, comprising a connected series of coaxial waveguide sections, is numerically treated with the method of moments and mode-matching technique. Details of the theoretical groundwork are presented in this paper, which constitutes the first of two parts of this work. Part II, also appearing in this issue, describes the measurement technique in detail and presents simulation results of the experimental procedure based on the formulation presented herein. In addition, the method that treats circular disks is also investigated in Part II and is used to make comparative performance studies.