Nonlinear dynamics of a class of digital tan-lock loops with non-ideal phase detector

• The unequal propagation time in two arms of tan-lock phase detector is modeled as fractional delay.
• Dynamics of digital tan-lock loop (DTL) with fractional delay is examined analytically and numerically.
• Fractional delay of proper magnitude broadens stable zone and frequency acquisition range of the loop.
• Inclusion of deliberate fractional delay may be an useful technique of high performance DTL design.

The consequences of unequal propagation delay of the sampled control signals along the two arms of a class of digital tan-lock loops (DTLs) have been studied in this paper. The said delay is considered as a fraction of the basic sampling period and it is modeled by including a discrete time version of a unit-amplitude pure phase shift network in one of the arms of the tan-lock phase detector (PD). The DTL with such unbalanced fractional delay (named as FD-DTL) is studied through bifurcation analysis and time domain numerical simulation of the system equation. Obtained results indicate that for a FD-DTL loop gain values could be taken higher and frequency acquisition ranges (FARs) are wider compared to those for a conventional DTL (CDTL). Thus a deliberate inclusion of a fractional time delay network in one of the arms of a CDTL is a novel technique to improve its dynamical responses.