1.1 The Response of a Second Order Circuit

A circuit containing n energy storage devices (inductors and capacitors) is said to be an nth-order circuit, and the differential equation describing the circuit is an nth-order differential equation. For example, if a circuit contains an inductor and a capacitor, or two capacitors or two inductors, along with other devices such as resistors, it is said to be a second-order circuit and the differential equation that describes it is a second order differential equation. It is possible, however, to describe a circuit having two energy storage devices with a set of two first-order differential equations, a circuit which has three energy storage devices with a set of three first-order differential equations and so on. These are called state equations ^[*] but these will not be discussed here.

The response is found from the differential equation describing the circuit, and its solution is obtained as follows:

1. We write the differential or integrodifferential (nodal or mesh) equation describing the circuit. We differentiate, if necessary, to eliminate the integral.

2. We obtain the forced (steady-state) response. Since the excitation in our work here will be either a constant (DC) or sinusoidal (AC) in nature, we expect the...