A New Approach to the Linear Design and Analysis of Phase-Locked Loops

Abstract

Using the techniques and philosophy of control systems theory, the phase-locked loop is analyzed as a conventional feedback loop. The root-locus method yields graphs which specify how the transient response changes with signal strength. This method also reveals two thresholds which explain why a small change in signal strength or modulation may cause complete loss of detection. Charts show how the transients vary with various pole-zero patterns for both step and ramp inputs. The feedback equation shows why the phase-locked loop is an FM detector, and simplifies its design analysis to that of a simple audio network. The application of Wiener's criterion is simplified, and a new method of solution for the filter is presented which is applicable to almost any kind of signal. Because the phase-locked loop is nonlinear, there is no known solution for the filter except when the noise is white. The optimum transfer function may easily be reduced to the loop components. When used in an AM detector the phase-locked loop should be designed for minimum phase shift independent of the modulation.