Analysis and optimisation of the convergence behaviour of the single channel digital tanlock loop

The mathematical analysis of the convergence behaviour of the first-order single channel digital tanlock loop (SC-DTL) is presented. This article also describes a novel technique that allows controlling the convergence speed of the loop, i.e. the time taken by the phase-error to reach its steady-state value, by using a specialised controller unit. The controller is used to adjust the convergence speed so as to selectively optimise a given performance parameter of the loop. For instance, the controller may be used to speed up the convergence in order to increase the lock range and improve the acquisition speed. However, since increasing the lock range can degrade the noise immunity of the system, in a noisy environment the controller can slow down the convergence speed until locking is achieved. Once the system is in lock, the convergence speed can be increased to improve the acquisition speed. The performance of the SC-DTL system was assessed against similar arctan-based loops and the results demonstrate the success of the controller in optimising the performance of the SC-DTL loop. The results of the system testing using MATLAB/Simulink simulation are presented. A prototype of the proposed system was implemented using a field programmable gate array module and the practical results are in good agreement with those obtained by simulation.