Elmore's approximations based explicit delay and rise time model for distributed RLC on-chip VLSI global interconnect

In this work, simple explicit delay and rise time expressions for uniformly distributed RLC on-chip interconnect line are derived based on Elmore's approximations. Here, an n-cell RLC ladder network with capacitive load is used. Transfer function for the n-cell RLC ladder network is obtained by using the transmission line parameter matrix for each cell. In order to deduce the transfer function, the transmission line is modelled by a lumped parameter network. From this transfer function, explicit delay and rise time expressions are derived by using Elmore's definitions. The calculated delay and rise times by the proposed closed form expressions are compared with the results obtained by SPICE simulation for n=2, 3, 4, 5, 6, 7 cell ladder networks with capacitive load.