Measurement of Planar Substrate Uniaxial Anisotropy

A new technique to measure uniaxial anisotropy in planar substrates is described. The technique uses a single dual-mode resonator. Each mode of the resonator has a different distribution of horizontal (parallel to the substrate surface) and vertical (perpendicular to the substrate surface) directed fields. Using an electromagnetic analysis of the dual-mode resonator, the resonant frequencies of the modes are space mapped to the horizontal and vertical dielectric constants. The space mapping allows the anisotropic dielectric constants to be extracted from the measured resonant frequencies. It is also suggested that this technique can be applied to magnetic uniaxial anisotropy as well as to magnetic and electric loss tangent anisotropy. The dual and quad "RA" resonators are introduced in this paper. A measurement of FR4 (a common anisotropic epoxy-glass weave composite substrate) with a detailed error analysis illustrates the technique.