Numerical treatment of the first-order pll equation with sinusoidal phase detector characteristic

Abstract

We discuss a powerful method depending on complex continued fractions to obtain and to solve a nonlinear equation for all eigenvalues of the underlying boundary value problem of the first-order phase locked loop equation. Furthermore we give several numerical examples and - for the sake of comparison - we list the first unverified and verified eigenvalues for a relevant signal-to-noise ratio.

Keywords:

• Pli equation
• cycle slip rate
• eigenvalues
• continued fractions
• vertification