Circuit timing and power analysis are important in various aspects of circuit optimization. In order to solve the problem of finding input vectors to activate worst-case timing or power, a concept called timed characteristic function (TCF) was proposed, which can characterize logical and temporal conditions simultaneously. Traditionally TCF assumes the (one-vector) floating mode of operation. In this paper we extend TCF for the (two-vector) transition mode and propose an efficient way to construct transition-mode TCF. Also, we apply the TCF concept to the analysis of the maximum instantaneous current (MIC) of a circuit, where transition-mode TCF is used to formulate gates? switching conditions. The experimental results show that on average, the TCF technique can derive about 30% more accurate MIC results than random simulation does for combinational circuits.