The shapes of Nyquist plots [Lecture Notes]

The Nyquist criterion is a valuable design tool with applications to control systems and circuits. In this paper, it was shown that many Nyquist plots are classical plane curves. Surprisingly, this connection seems to have gone unnoticed. It was determine that the precise shapes of several Nyquist curves and relate them to the shapes of the classical plane curves. Some classical plane curves are related to exactly proper or improper loop transfer functions, which do not roll off at high frequencies and thus are not physical.