  This letter theoretically compares the active reconfigurable intelligent
surface (RIS)-aided system with the passive RIS-aided system. For fair
comparison, we consider that these two systems have the same overall power
budget that can be used at both the base station (BS) and the RIS. For active
RIS, we first derive the optimal power allocation between the BS's transmit
signal power and RIS's output signal power. We also analyze the impact of
various system parameters on the optimal power allocation ratio. Then, we
compare the performance between the active RIS and the passive RIS, which
demonstrates that the active RIS would be superior if the power budget is not
very small and the number of RIS elements is not very large.
