An optimum phase-locked loop with a non-ideal filter

Abstract

In communications engineering the problem of synchronization is vital. Any loss of synchronism is required to be restored in the shortest possible time. The concept of optimum PLL which utilizes a non-linear, memoryless feedback device was introduced by Ahmed and Cheng (1974). It was shown that this optimum PLL achieves synchronization in the minimum time if the filter were ideal. This paper considers the optimization of the PLL with non-ideal filter. The input sinusoid and the VCO output are assumed to have the same frequency but to differ in phase. The object of this paper is to investigate whether the optimum PLL introduced earlier (Ahmed and Cheng, p. 254) still retains its virtues when the ideal filter is replaced by a non-ideal one. The nonlinear Volterra integro-differential equation governing the PLL performance is solved by two different approaches and the solution indicates that the PLL in the presence of a non-ideal filter is optimal only within a certain range of variation of the parameter def...