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Energy efficiency (EE) is undoubtedly an important criterion for designing power-limited systems, and yet in a context of global energy saving, its relevance for power-unlimited systems is steadily growing. Equally, resource allocation is a well-known method for improving the performance of cellular systems. In this paper, we propose an EE optimization framework for the downlink of planar cellular systems over frequency-selective channels. Relying on this framework, we design two novel low-complexity resource allocation algorithms for the single-cell and coordinated multi-cell scenarios, which are EE-optimal and EE-suboptimal, respectively. We then utilize our algorithms for comparing the EE performance of the classic non-coordinated, orthogonal and coordinated multi-cell approaches in realistic power and system settings. Our results show that coordination can be a simple and effective method for improving the EE of cellular systems, especially for medium to large cell sizes. Indeed, by using a coordinated rather than a non-coordinated resource allocation approach, the per-sector energy consumption and transmit power can be reduced by up to 15% and more than 90%, respectively.