First‐Order Step Response of RC and RL Circuits

Summary

Step response is one form of zero‐state response. This chapter summarizes several different first‐order circuit topologies and their voltage and current response to a step input in the time domain. It considers a series RC circuit driven by a voltage step function. The intuitive analysis shows how to visually inspect a first‐order circuit and determine whether the current and voltage waveforms are rising or decaying exponentials, given that the response is already known to be exponential and the time constants are already known and understood. The chapter discusses the step response of the series RL circuit driven by a voltage source step function. In first‐order electrical circuits, step response comes from an applied step function, an ideal instantaneous change with zero rise time. The ideal step function is mathematically significant and it can be handled in the Laplace transform s‐domain.