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Wireless sensor networks are developed to be applied in hazardous or inaccessible places, where hundreds to thousands of sensor nodes are uniformly distributed for long-term data. It has been proved that, to maximize network lifetime, the best position for a sink is the center of the circular deployment area. However, the featured communication pattern, converge cast, brings unbalanced spatial distribution of energy consumption and greatly reduces network lifetime. To quantitatively analyze this phenomenon, an analytical method is proposed with respect to geographic greedy routing. Average energy consumption of sensor nodes in a variable annular region is put forward as the metric of energy efficiency. The optimal case of energy consumption is given by a decreasing concave function of the distance to the sink, which well fits to the simulation results. At last, we study the impact of transmit power on energy efficiency. The unbalanced energy consumption becomes more serious as the deployment area expands. All studies are based upon the CC2420 transceiver.