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A novel effective surface impedance is proposed for accurate modeling of the frequency-dependence of field penetration inside thick strip conductors. The proposed effective surface impedance is obtained through the rigorous modeling of the frequency-dependent cross-sectional field distribution in the interior of the lossy conductor, and is a function of both frequency and position along the perimeter of the cross section of the conductor. Availability of such an effective surface impedance enables the use of a surface integral equation formulation for the electromagnetic analysis of on-chip interconnects and integrated passives structures. Such formulations are much more efficient than volumetric ones without sacrificing accuracy in the modeling of the impact of conductor internal impedance and skin effect loss on the electromagnetic response. The validity of the proposed model is demonstrated through comparisons with measured scattering parameters for on-chip interconnect structures.