A Note on the Generation of Phase Plane Plots on a Digital Computer

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated as a pair of coupled differential equations with phase error and phase error derivative as dependent variables and arc length as the independent variable, which is uniformly distributed along the phase plane trajectory. The sinusoidal phase-locked loop and polarity-type Costas loop are used as illustrations of the proposed method of solution.