# CHAPTER 14

*The Laplace Transform*

**IN THIS CHAPTER**

**14.1** Introduction

**14.2** Laplace Transform

**14.3** Pulse Inputs

**14.4** Inverse Laplace Transform

**14.5** Initial and Final Value Theorems

**14.6** Solution of Differential Equations Describing a Circuit

**14.7** Circuit Analysis Using Impedance and Initial Conditions

**14.8** Transfer Function and Impedance

**14.9** Convolution

**14.10** Stability

**14.11** Partial Fraction Expansion Using MATLAB

**14.12** How Can We Check … ?

**14.13 DESIGN EXAMPLE**–Space Shuttle Cargo Door

**14.14** Summary

Problems

PSpice Problems

Design Problems

## 14.1 *Introduction*

Circuits that have no capacitors or inductors can be represented by algebraic equations.

- Chapters 1–6 described circuits without capacitors or inductors. We learned many things about such circuits, including how to represent them by mesh current equations or node voltage equations.
- Capacitors and inductors are described in Chapter 7.

Circuits that contain capacitors and/or inductors are represented by differential equations. In general, the order of the differential equation is equal to the number of capacitors plus the number of inductors in the circuit. Writing and solving these differential equations can be challenging.

- In Chapter 8, we analyzed first-order circuits.
- In Chapter 9, we analyzed second-order circuits.

The response of a circuit containing capacitors and/or inductors can be separated into two parts: the steady-state ...