Phasors

In the next chapter we shall see that Maxwell's equations are a system of first-order partial differential equations in four independent variables: three space coordinates and time. The solution of these equations is often quite complicated, and it may be advantageous to eliminate the dependence of the field quantities upon one or more of the independent variables by applying a Fourier (or Laplace) transform to Maxwell's equations, solving the resulting equations in the transform domain, and then obtaining the original field quantities by an inverse transformation. Obviously, the main advantage of a transform technique with respect to an independent variable is to change the dependence of the equations on that variable from a differential one to an algebraic one. As the reader may already know from a course on circuits or on transmission lines, the variable that is usually selected for elimination is time; the procedure involves either a one-dimensional Fourier transform from the time domain to the frequency domain, or the introduction of phasors; the latter is the approach followed in this text.