of of

The behavior of the amplification factor G also can be determined by graphical methods. Equation (10.45) can be written in the form

G = (I - 2d) + 2d cos () (10.49) In the complex plane, Eq. (10.49) represents an oscillation on the real axis, centered at (I - 2d + fO), with an amplitude of 2d, as illustrated in Figure 10.14. The stability boundary, IGI = 1, is a circle of radius unity in the complex plane. For G to remain on or inside the unit circle, -I S IGI s I, as () varies from -00 to +00, 2d S 1. The graphical approach is very useful when G is a complex function.