Equivalent Elmore delay for RLC trees

Closed-form solutions for the 50% delay, rise time, overshoots, and settlin g time of signals in an RLC tree are presented, These solutions have the sa me accuracy characteristics of the Elmore delay for RC trees and preserves the simplicity and recursive characteristics of the Elmore delay. Specifica lly, the complexity of calculating the time domain responses at all the nod es of an RLC tree is linearly proportional to the number of branches in the tree and the solutions are always stable. The closed-form expressions intr oduced here consider all damping conditions of an RLC circuit including the underdamped response, which is not considered by the Elmore delay due to t he nonmonotone nature of the response. The continuous analytical nature of the solutions makes these expressions suitable for design methodologies and optimization techniques. Also, the solutions have significantly improved a ccuracy as compared to the Elmore delay for an overdamped response, The sol utions introduced here for RLC trees can be practically used for the same p urposes that the Elmore delay is used for RC trees.