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This paper introduces an efficient and passive discrete modeling technique for estimating signal propagation delays through on-chip long interconnects that are represented as distributed RLC transmission lines. The proposed delay model is based on a less frequently used numerical approximation technique, called the differential quadrature method (DQM). The DQM can compute the partial derivative of a function at any arbitrary point located within a prespecified closed domain of the function by quickly estimating the weighted linear sum of values of the function at a relatively small set of well-chosen grid points within the domain. By using the fifth-order DQM, a new approximation framework is constructed in this paper for discretizing the distributed RLC interconnect and thereafter modeling its delay. Due to high efficiency of DQM approximation, the proposed framework requires only few grid points to achieve good accuracy. The presented equivalent-circuit model appears like the ones derived by the finite difference (FD) method. However, it has higher accuracy and less internal nodes than generated by the FD-based modeling. The fifth-order DQM modeling technique is shown to preserve passivity. It has linear forms that are compatible with the passive order-reduction algorithm for linear network. Numerical experiments show that the proposed modeling approach leads to high accuracy as well as high efficiency.