Mode-Dependent Effective Dielectric Constants of Inhomogeneous Dielectric Layers for PCB Applications

The dielectric substrate of printed circuit boards (PCBs) generally consists of epoxy or polyurethane resin and fiberglass, which can be modeled as inhomogeneous dielectric layers (IDLs). IDLs are not homogeneous in the perpendicular direction of the layers’ interface, which means that they constitute an anisotropic material. Thus, the effective dielectric constant (Dk) for IDLs is direction dependent, i.e., mode dependent. In this study, the effective Dk values of IDLs are extracted for different modes using three commonly used full-wave simulation models: the transverse electric (TE), transverse magnetic (TM), and equivalent parallel-plate capacitor models. The results for the TE and TM modes showed a 10% discrepancy. The effective Dk of IDLs was efficiently estimated by the parallel-plate capacitor model based on the layers’ dielectric properties and thicknesses. Moreover, the analytical formulas of resonance frequency for a cylindrical cavity resonator filled with IDLs were derived to extract the effective Dk of the IDLs at different resonance modes, which could be used as a guideline of resonator methods for PCB material characterization. These results correlated with the results from the equivalent parallel capacitor model. Finally, the impact of IDL anisotropy on transmission line loss and time-domain reflectometry impedance was analyzed based on full-wave simulation.