TABLE OF CONTENTS The objective of ac analysis is to find the steady-state response y(t) to an ac forcing function x( t). Chapter 10 focused on time-domain ac analysis, so called because it deals with functions of time. This type of analysis requires the formulation and solution of differential equations and is illustrated diagrammatically in the left column of Table 11.1. Though it can in principle be applied to the study of any circuit, it is tedious and lengthy, requiring extravagant trigonometric manipulations. As circuit complexity increases, this approach becomes prohibitive both in terms of time and effort, and we need a more efficient method to obtain the ac response of a circuit.
| Time Domain | Frequency Domain |
|---|---|
| x ( t) | X( ?) |
| ? | ? |
| Differential eqns. | Algebraic eqns. |
| ? | ? |
| y( t) | Y( ?) |
The answer is provided by phasor analysis, an ingenious technique developed by the German-born American mathematician and engineer Charles P. Steinmetz (1865-1923). Instead of dealing with sinusoidal functions of time, this technique deals directly with their phasors, and it achieves the goals of ac analysis via algebraic equations rather than differential equations. Moreover, it uses the circuit theorems and techniques of resistive circuits, indicating that we can extend the experience acquired in earlier chapters to the analysis of ac circuits as well. Also called frequency-domain ac analysis because phasors are, in general, functions of...
