The Elmore delay as a bound for RC trees with generalized input signals

The Elmore delay is an extremely popular timing-performance metric which is used at all levels of electronic circuit design automation, particularly for resistor-capacitor (RC) tree analysis, The widespread usage of this metric is mainly attributable to it being a delay measure that is a simple analytical function of the circuit parameters, The only drawback to this delay metric is the uncertainty of its accuracy and the restriction to it being an estimate only for the step response delay. In this paper, we prove that the Elmore delay measure is an absolute upper bound on the actual 50% delay of an RC tree response, Moreover, we prove that this bound holds for input signals other than steps and that the actual delay asymptotically approaches the Elmore delay as the input signal rise time increases, A lower bound on the delay is also developed using the Elmore delay and the second moment of the impulse response, The utility of this bound is for understanding the accuracy and the limitations of the Elmore metric as we use it as a performance metric for design automation.