First‐Order RC and RL Circuits Introduction

Summary

This chapter introduces first‐order circuits in both time and frequency domain. The time domain response from initial conditions is called natural or zero‐input response (ZIR). The time domain response from a step function input is a form of zero‐state response (ZSR). The frequency domain response analyzed here is the sinusoidal steady‐state response. First‐order circuits have one reactive circuit element, such as a capacitor or inductor. First‐order natural response, RC or RL, comes from an initial condition, an initial capacitor voltage v_C(0) or an initial inductor current i_L(0), decaying to zero over time. In contrast to natural response, step response is a ZSR where there are no initial conditions in the circuit. Complete response is both ZIR and ZSR, the response of a circuit to an input signal and any initial conditions which may be present.