A Novel FDTD Approach Considering Frequency Dispersion of FR-4 Substrates for Signal Transmission Analyses at GHz Band

High-speed digital signaling can cause various signal integrity and electromagnetic interference problems. Signal attenuation and distortion can be observed in the gigahertz band owing to the frequency dispersion of substrates. In this article, we propose a frequency-dependent finite-difference time-domain (FDTD) approach for the numerical analyses of flame-retardant type-4 (FR-4) substrates. The proposed FDTD approach provides accurate broadband solutions because it can take into account the frequency dispersion of the substrate. First, the broadband complex permittivity of FR-4 substrates was measured using a balanced-type circular disk resonator and fitted into a Djordjevic model for the FR-4 substrates. Second, we adapted the fast inverse Laplace transform and Prony methods to find the
z
-domain expressions and incorporate them into the FDTD formulation.The validity of the proposed approach was demonstrated by comparing the numerical and experimental results of the differential insertion loss and phase constant of differential microstrip lines. Both results were in good agreement, indicating the validity and usefulness of the proposed approach for simulations of broadband signal transmission in FR-4 substrates.