The influence by trapezoidal conductor shapes on ring-resonator based material characterization up to 110 GHz

Material characterization by ring-resonator based measurements is well established since the early 20th century. Since then, the demand on spectral complex permittivity characterizations of RF materials and dielectric covers at higher microwave frequencies rises. Nowadays, both free space applications, e.g. 77 GHz automotive radar systems, and dielectrics for microchip packages require accurate knowledge of the relative permittivity in order to optimize RF circuit designs. With increasing frequencies, the conductor shape of photochemically etched ring-resonators gets more influence on the effective ring radius, and therefore the measured resonance frequencies, which results in an error for the relative permittivity determination. This paper provides correction factors for the ring radii up to 110 GHz, compensating the altered field distribution due to trapezoidal edges.