Effects of Delay on the Hold-In and Pull-In Range of Quadrature and Binary Costas Loops for Ultrawideband Receiver Synchronization

Analog implementations of Costas loops can be used for efficient, digital signal-processing (DSP)-free receiver synchronization, achieving data rates of multiple Gbit/s. This article shows that the inherent delay in such phase-locked loops (PLLs) significantly impacts loop characteristics. It demonstrates that the delay is crucial to account for, as it can become a limiting factor. We evaluate the ideal and the delay-affected hold-in range, as well as the delay-affected pull-in range, as two design parameters of Costas loops. Costas loops that operate without ideal integrating filters, like zero-pole filters, experience a finite hold-in range. Based on derived linearized models, we demonstrate that they follow the same approaches and theory as common PLLs in terms of the hold-in range, which is essentially delay-independent. Equations for binary and quadrature Costas loops are found and verified by measurement. A nonlinear model of a binary Costas loop in the unlocked state, extended by delay, reveals a substantial limitation of the pull-in range caused by delay. Unlike for PLLs, a range exists for which the pull-in range loses gain dependency. We assess the extension of the model to quadrature and verify both by system simulation and measurement. A custom-designed ultrawideband Costas loop receiver with a measured delay of 45ns, capable of demodulating quadrature data in the X-band with a bandwidth of 1.7 GHz, is employed for experimental validation of the found equations.