Introduction to Electric Circuits, 9th Edition

CHAPTER 9

The Complete Response of Circuits with Two Energy Storage Elements

IN THIS CHAPTER

9.1 Introduction

9.2 Differential Equation for Circuits with Two Energy Storage Elements

9.3 Solution of the Second-Order Differential Equation—The Natural Response

9.4 Natural Response of the Unforced Parallel RLC Circuit

9.5 Natural Response of the Critically Damped Unforced Parallel RLC Circuit

9.6 Natural Response of an Underdamped Unforced Parallel RLC Circuit

9.7 Forced Response of an RLC Circuit

9.8 Complete Response of an RLC Circuit

9.9 State Variable Approach to Circuit Analysis

9.10 Roots in the Complex Plane

9.11 How Can We Check …?

9.12 DESIGN EXAMPLE—Auto Airbag Igniter

9.13 Summary

Problems

PSpice Problems

Design Problems

9.1 Introduction

In this chapter, we consider second-order circuits. A second-order circuit is a circuit that is represented by a second-order differential equation. As a rule of thumb, the order of the differential equation that represents a circuit is equal to the number of capacitors in the circuit plus the number of inductors. For example, a second-order circuit might contain one capacitor and one inductor, or it might contain two capacitors and no inductors.

For example, a second-order circuit could be represented by the equation

where x(t) is the output ...