In this article, a robust Lyapunov demodulator (LD) based on orthogonal signal generation (OSG) approach for single/three-phase application is proposed. Conventionally, LD is not capable of rejecting the DC-offset in the grid signal. Thus, an additional estimation loop is required which may affect the dynamic performance. Nevertheless, an application of harmonically polluted grid voltage signal to LD may severely affect the steady-state performance of the estimated parameters. To address these issues, an enhanced LD based-OSG is proposed, wherein a moving average filter is incorporated in the LD-OSG structure. Thus, rapid rejection of DC-offset and harmonics is easily achieved without any additional loop. The proposed structure may accurately estimate the fundamental in-phase and the quadrature components. However, these orthogonal components may suffer from amplitude imbalance and errors in the phase information under off-nominal frequency conditions. Additionally, the errors in the amplitude and the phase information are eliminated using an open-loop frequency deviation detector and a feed-forward curve fitting approach. The dynamic performance of the proposed scheme has been validated by numerical and hardware studies. It is reported that, with the less sensitivity toward phase angle jump and good immunity to fundamental negative sequence, the proposed scheme is a potential technique for synchronization of single/three-phase grid connected power electronic equipment.