Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits

A closed form expression for the propagation delay of a CMOS gate driving a distributed RLC line is introduced that is within 5% of dynamic circuit simulations for a wide range of RLC loads. It is shown that the traditional quadratic dependence of the propagation delay on the length of an RC line approaches a linear dependence as inductance effects increase. The closed form delay model is applied to the problem of repeater insertion in RLC interconnect. Closed form solutions are presented for inserting repeaters into RLC lines that are highly accurate with respect to numerical solutions. An RC model as compared to an RLC model creates errors of up to 30% in the total propagation delay of a repeater system. Considering inductance in repeater insertion is also shown to significantly save repeater area and power consumption. The error between the RC and RLC models increases as the gate parasitic impedances decrease which is consistent with technology scaling trends. Thus, the importance of inductance in high performance VLSI design methodologies will increase as technologies scale.