OVERVIEW

Having devoted the previous two chapters to the study of the transient response, we now turn our attention to the other basic response type, the ac steady-state response. As we know, this is the response to a sinusoidal forcing function after all transients have died out.

There are many reasons for selecting the sine wave as the forcing function. One of these is just a practical one. To begin with, alternators generate electric power in sinusoidal form, and this is also the form in which power is most efficiently transmitted and distributed to households and industries. For reasons of efficiency, sinusoidal waves are also used in commercial radio and television broadcasting. Here, electromagnetic energy is radiated by means of a sinusoidal wave called the carrier. In AM broadcasting the carrier amplitude is changed or modulated according to the information signal to be broadcast; in FM broadcasting the parameter being modulated is the carrier frequency. Finally, in dial-tone telephones information is transmitted in sinusoidal form as, for instance, when computers are linked together via modems. Considering the importance of the utility power and electronic communications in modern life, this reason alone would suffice to justify our study of the ac response.

There is, however, another deeper reason for studying the ac response, namely, because nature itself seems to have a decidedly sinusoidal character. For instance, the natural response of an underdamped second-order circuit is a damped sinusoid, just like the vibration of a guitar string, the...