The average battery energy consumption per bit is now used as performance metric for research on energy constraint in wireless sensor networks (WSNs). This paper proposes an on-off keying (OOK) transmitter with an instaneous discharge current (IDC) based battery utilization factor (BUF) model or an average discharge current (MDC) based BUF model, and derives the analytical expression of the battery energy consumption per bit for the two models under Rayleigh channel with specified symbol error rate (SER). On this basis,the impact of the battery parameter and distance on the energy consumption per bit is analyzed through a theoretical approach. Simulation results indicate that the energy consumption per bit for both models increases as battery parameter and distance increase and that theIDCbased BUF model corresponds to larger battery energy consumption per bit. When the battery parameter and distance are large, the energy consumption per bit of the two models is significantly higher than that of the ideal battery. When $\gamma $=0.015 and $d$=90 m, the energy consumption per bit for theIDCbased BUF model is nearly 60% higher than that of ideal battery, while the energy consumption per bit forMDCbased BUF model is about 25% higher.