A quantitative comparison of three Bode straight-line phase approximations for second-order, underdamped systems

Bode straight-line approximations are an extremely useful tool in the study of system frequency response. These approximations give good insight into the frequency variation of the amplitude and the phase of a system response without the use of computer simulation or complex calculations. Three Bode straight-line approximations to the phase of second-order, underdamped systems are subjected to quantitative error analysis. The magnitude of the maximum phase error and root-mean-square phase error are computed for each phase approximation as a function of the system damping coefficient. The results of the analysis indicates superiority of the little-known decade-fraction phase approximation technique.