Dielectric material properties of printed circuit boards (PCBs) are needed by designers working in various areas such as signal integrity, antennas, and embedded RF components. Among many methods to extract the material properties, the full sheet resonance technique is commonly used on PCBs due to its simplicity. The disadvantage of this method is that an analytical equation is used to extract the dielectric constant, which is accurate only for lossless dielectrics. In this paper, a new method is presented to solve the inaccuracy issue of the extraction of the dielectric constant by applying customized electromagnetic simulation based on a new rapid plane solver instead of analytical equations. For PCB dielectrics, the loss tangent tends to be flat over several decades. The dielectric constant then varies as a function of frequency based on the Kronig-Kramers relations. This paper introduces a new Debye type of a model for the complex permittivity of such dielectrics. The parameters of the Debye model can be obtained analytically without requiring any curve fitting. The resulting Debye model can then be easily integrated in SPICE or a finite-difference time-domain simulator.