Under weak grid conditions, the number of oscillation accidents caused by the impedance mismatch between the power grid and the grid-tied inverters is on the rise, which makes the accurate identification of the broadband impedance characteristics of the power grid that can sense the current operating state of the system an urgent problem to be solved. This article theoretically analyzes the discrepancy between the impedance characteristics of the conventional purely inductive grid impedance and the generalized grid impedance by comparing the amplitude-phase characteristic curves of both, which in turn affects the analytical results of stability. Subsequently, in order to accurately recognize the GGI, a signal-to-noise ratio (SNR) design scheme based on the active impedance identification technique is proposed, which investigates the impact of SNR on the identification accuracy from the perspective of a grid-tied inverter, with the GGI including transmission lines and grid-tied devices external to the inverter as the identification target. Moreover, current disturbances at different characteristic harmonic frequency points are injected into the grid in the MATLAB/Simulink platform to verify the accuracy of the SNR design scheme with the help of the sweep results of GGI. Finally, the significance of generalized grid impedance as the main form of the grid is further revealed through comparative experiments on the RT-BOX platform.