9.1 Introduction

← Back to Fundamentals of Electric Circuits Overview

9.1 Introduction

Thus far our analysis has been limited for the most part to dc circuits: those circuits e xcited by constant or time-in variant sources. We ha ve restricted the forcing function to dc sources for the sake of simplicity, for pedagogic reasons, and also for historic reasons. Historically, dc sources were the main means of providing electric power up until the late 1800s. At the end of that century, the battle of direct current versus alternating current began. Both had their advocates among the electrical engineers of the time. Because ac is more efficient and economical to transmit over long distances, ac systems ended up the winner . Thus, it is in k eeping with the historical sequence of events that we considered dc sources first.

We now begin the analysis of circuits in which the source v oltage or current is time-v arying. In this chapter , we are particularly interested in sinusoidally time-varying excitation, or simply, excitation by a sinusoid.

A sinusoid is a signal that has the form of the sine or cosine function.

A sinusoidal current is usually referred to as alternating current (ac). Such a current reverses at regular time intervals and has alternately positive and negative values. Circuits driven by sinusoidal current or voltage sources are called ac circuits.

We are interested in sinusoids for a number of reasons. First, nature itself is characteristically sinusoidal. We e xperience sinusoidal v ariation in the motion of a pendulum, the vibration of a string, the ripples on the ocean surface, and the natural response of underdamped secondorder systems, to mention but a few. Second, a sinusoidal signal is easy to generate and transmit. It is the form of v oltage generated throughout the world and supplied to homes, factories, laboratories, and so on. It is the dominant form of signal in the communications and electric power industries. Third, through Fourier analysis, any practical periodic signal can be represented by a sum of sinusoids. Sinusoids, therefore, play an important role in the analysis of periodic signals. Lastly , a sinu soid is easy to handle mathematically . The derivative and integral of a sinusoid are themselve s sinusoids. For these and other reasons, the sinusoid is an extremely important function in circuit analysis.

A sinusoidal forcing function produces both a transient response and a steady-state response, much like the step function, which we studied in Chapters 7 and 8. The transient response dies out with time so that only the steady-state response remains. When the transient response has become negligibly small compared with the steady-state response, we say that the circuit is operating at sinusoidal steady state. It is this sinusoidal steady-state response that is of main interest to us in this chapter.

We begin with a basic discussion of sinusoids and phasors. We then introduce the concepts of impedance and admittance. The basic circuit laws, Kirchhoff’s and Ohm’s, introduced for dc circuits, will be applied to ac circuits. Finally , we consider applications of ac circuits in phaseshifters and bridges.