Abstract: Load-side virtual synchronous machine（LVSM） which introduces the moment of inertia J and damping coefficient Dp enhances the power grid inertia, but its stability in weak grid needs to be explored. Considering the control delay and sampling filters, the wideband dq-frame impedance model of LVSM was established, and the dq-frame impedance characteristics of LVSM and traditional voltage source PWM rectifier（VSR） were compared. Zdd of LVSM behaves the negative resistance within 10 Hz, which is narrower than that of VSR, and is basically inductive above 10 Hz. Secondly, based on the generalized Nyquist criterion, comparative studies found that they all induce oscillations in weak grid: the frequency ranges of oscillations of the LVSM（40～60 Hz） are narrower than that of the VSR（7～200 Hz）. Furthermore, the dc-link voltage controller is the key to their stability. For LVSM, the larger the proportional gain is and the smaller the integral gain is, the more stable the system is, and reducing J and Dp can enhance the system stability. For VSR, the smaller the proportional and integral gains are, the more stable the system is, and removing the voltage feedforward can enhance the system stability. Finally, simulations and experiments verified the correctness of the stability analysis.