As power generation shifts towards cleaner energy, there is a growing effort to reduce the reliance on traditional fossil fuel-operated synchronous generators by adopting modern inverter-based resources. This rapid integration of inverter-based resources with the power grid has necessitated the development of advanced inverter controls. Existing controls of power electronic converter-based resources may not be sufficient to ensure grid stability in a future inverter-dominated power system. The grid-forming inverters have been considered as a potential solution to this emerging problem. Droop control is a widely used methodology in grid-forming inverters, especially due to its capabilities to enable power-sharing, frequency control, and voltage control. Recent advancements in droop control have incorporated filtering techniques (especially low pass filters) to mitigate AC harmonic noise injected into the control loops, thereby enhancing the overall response of the system. This research introduces the mathematical significance of the low pass filter used with droop control and establishes its necessity to enable grid-forming characteristics. Furthermore, an enhanced droop control is proposed with an integrated synchronous machine emulator using an error correction term. This enhanced droop control retains the benefits of conventional droop control but with the additive benefits of emulating the synchronous generator's response. These mathematical justifications are verified using bode plots, step responses, and eigenvalue analysis. The performance of the proposed controller and the grid-forming characteristics are verified using MATLAB simulations. These simulation results and the proposed controller's performance are verified by a controller hardware-in-loop experiment.