Dielectric Loss Tangent Extraction Using Modal Measurements and 2-D Cross-Sectional Analysis for Multilayer PCBs

Frequency-dependent electrical properties of dielectric materials are one of the most important factors for high-speed signal integrity design. To accurately characterize material's dielectric loss tangent (tanδ) after multilayer printed circuit board fabrication a novel method was proposed recently to extract tanδ using coupled striplines' measured S-parameters and cross-section geometry. By relating modal attenuation factors to the ratio between the differential and common mode per-unit-length resistances, the surface roughness contribution is eliminated and the contributions of dielectric and conductor loss are separated. Here, we specifically decided to avoid using any physical dielectric model in the extraction algorithm in order to eliminate a need for any a priori information about dielectric behavior. Further analysis and improvement of the tanδ extraction approach is presented in this article. To evaluate the accuracy of the extraction, the impact of errors due to de-embedding, vector network analyzer measurement, and two-dimensional solver's calculation are taken into account by a statistical error model. A confidence interval of extracted tanδ is provided. To describe the frequency dependence of tanδ, a two-term Djordjevic model is proposed to fit the extracted tanδ curve, which guarantees causality and gives better agreement with measured insertion loss compared to the traditional Djordjevic model.