Electrocardiograms (ECG) record the heart activity and are the most common and reliable method to detect cardiac arrhythmias, such as atrial fibrillation (AFib). Lately, many commercially available devices such as smartwatches are offering ECG monitoring. Therefore, there is increasing demand for designing deep learning models with the perspective to be physically implemented on these small portable devices with limited energy supply. In this paper, a workflow for the design of small, energy-efficient recurrent convolutional neural network (RCNN) architecture for AFib detection is proposed. However, the approach can be well generalized to every type of long time series. In contrast to previous studies, that demand thousands of additional network neurons and millions of extra model parameters, the logical steps for the generation of a CNN with only 114 trainable parameters are described. The model consists of a small segmented CNN in combination with an optimal energy classifier. The architectural decisions are made by using the energy consumption as a metric in an equally important way as the accuracy. The optimization steps are focused on the software which can be embedded afterwards on a physical chip. Finally, a comparison with some previous relevant studies suggests that the widely used huge CNNs for similar tasks are mostly redundant and unessentially computationally expensive.