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The utilization of Reconfigurable Intelligent Surface (RIS) in a backscatter communication (BackCom) system can increase the flexibility of equipment deployment while extending the communication distance. We concentrate on reducing the transmitting power through the optimization of active and passive beamforming and power allocation, while ensuring that BackCom performance remains uncompromised. Unlike previous studies on RIS neglecting the relationship between amplitude and phase shift of the signal reflected by RIS, our work takes into account the practical phase shift and amplitude response. In order to get solutions for the optimisation problem, we propose an iterative algorithm based on the alternating optimization (AO) and minimization-maximization approaches. We also suggest a nonlinear function fitting technique and a trust region inspection algorithm to reduce the computational complexity.