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# 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 16 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 ...

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