In the course of analyzing linear response of some electrical and mechanical systems, I noticed that the complex plot of their impedance,i.e.parametric plot of impedance with frequency as a real-valued parameter, is often a circle. The examples of such plots are shown in the image:
The neccessary condition seems to be that there should be a pole away from the real axis. On the other hand the function (impedance vs. frequency) does not have to be rational.
I am curious what is the mathematical/physical significance of ubiquitousness of the circle?