TABLE OF CONTENTS Since introducing energy-storage elements we have focused upon two particular but practically interesting responses, namely, the transient response and the ac response. The transient response, which is the response to a dc forcing signal of the type x( t) = X m, was investigated using time-domain techniques. The ac response, which is the response to an ac forcing signal of the type x( t) = X m cos ( ? t + ?), was investigated using frequency-domain techniques (time-domain techniques are possible but generally much more laborious).
In the present chapter we expand our scope by investigating the response to a more general class of forcing signal, namely, complex exponential signals of the type x( t) = X e st, where X and s are complex variables. Though these signals cannot, in general, be duplicated in the laboratory because of these complex variables, they nonetheless constitute a most powerful analytical tool for the following reasons:
The study of the response to complex exponentials evidences important information that is characteristic of the circuit, regardless of the applied signals or the internal stored energy. This information, expressed in the form of parameters known as the natural, characteristic, or critical frequencies of the circuit, or just the roots, is contained in a function arising in the study of complex exponential responses called the network function. Since design...
