Concerning the Nyquist plots of rational functions of nonzero type

The Nyquist plots of rational functions of type one or higher are often represented with branches that tend to infinity while approaching either the real or imaginary axis. It is shown that this fails to be true in general, a fact that appears to have little, if any, impact on the usual analysis. However, it has pedagogical interest since it explains the discrepancy between the shape of the Nyquist plots obtained analytically, or with the help of computer programs in the classroom, and the plots found in many standard textbooks. The discrepancy is most clear when the system type is at least two, in which case the branches may move infinitely further from both axes.