Bode Plots Revisited: a Software System for Automated Generation of Piecewise Linear Frequency Response Plots

Abstract

The paper presents an algorithm for automatic generation of piecewise linear Bode plots. The algorithm is complete in the sense it covers for all posible locations of poles and zeros of transfer functions, including unstable poles and poles and zeroes at the imaginary axis. The starting transfer function is factored into a canonical form, and thirteen elementary transfer function types are defined by their canonical forms. The thirteen elementary transfer function types are shown to be derived from just five generic transfer function types, and piecewise linear Bode plots are defined and depicted for all five of the generic types. For all thirteen elementary transfer function types the nodes they introduce in the piecewise linear plots are specified, as well as the algorithms how they affect the node altitudes. Finally, a three stage algorithm that produces both the Bode plots and the exact numerically computed frequency response plots is described. The algorithm is implemented in a command line based program, illustrated in a filter example, and future work directions are indicated, aiming a graphical user interface and integration of the program to a linear system symbolic analysis software suite.