Circuit Analysis For Dummies

Chapter 16

Predicting Circuit Behavior with Laplace Transform Techniques

In This Chapter

Switching domains with the Laplace and inverse Laplace transforms

Defining poles and zeros

Working out a circuit response with Laplace methods

Analyzing the behavior of circuits consisting of resistors, capacitors, and inductors can get complicated because it involves differential equations. Although the classical differential equation approach using calculus is straightforward, the Laplace approach has the advantage of using simpler algebraic techniques. Also, the Laplace transform uncovers properties of circuit behavior you don’t normally see using calculus.

In this chapter, I introduce you to the Laplace transform, show you how to find the inverse Laplace transform, and explain how to use the Laplace transform to predict a circuit’s behavior.

Getting Acquainted with the Laplace Transform and Key Transform Pairs

The Laplace transform allows you to change a tough differential equation requiring calculus into a simpler problem involving algebra in the s-domain (also known as the Laplace domain). After finding the transform solution in the s-domain, you use the inverse Laplace transform to find ...