We report our studies to compare energy consumption of a CDI cell in constant voltage (CV) and constant current (CC) operations, with a focus on understanding the underlying physics of consumption patterns. The comparison is conducted under conditions that the CV and CC operations result in the same amounts of input charge and within identical charging phase durations. We present two electrical circuit models to simulate energy consumption in charging phase: one is a simple RC circuit model, and the other a transmission line circuit model. We built and tested a CDI cell to validate the transmission line model, and performed a series of experiments to compare CV versus CC operation under the condition of equal applied charge and charging duration. The experiments show that CC mode consumes energy at 33.8 kJ per mole of ions removed, which is only 28% of CV mode energy consumption (120.6 kJ/mol), but achieves similar level of salt removals. Together, the models and experiment support our major conclusion that CC is more energy efficient than CV for equal charge and charging duration. The models also suggest that the lower energy consumption of CC in charging is due to its lower resistive dissipation. (C) 2016 Elsevier B.V. All rights reserved.