Background and Objective: The electrocardiogram (ECG) plays a crucial role in the diagnosis and treatment of various cardiac diseases. ECG signals suffer from low-resolution (LR) due to the use of convenient acquisition devices, as well as internal and external noises and artifacts. Classical ECG super-resolution (ECGSR) methods adopt an open-loop architecture that converts LR ECG signals to super-resolution (SR) ones. According to the theory of automatic control, a closed-loop framework exhibits superior dynamic and static performance compared with its open-loop counterpart. Methods: This paper proposes a closed-loop approach, termed circular ECGSR (CECGSR), which models the degradation process from SR ECG signals to LR ones. The negative feedback mechanism of the closed-loop system is based on the differences between the LR ECG signals. A mathematical loop equation is constructed to characterize the closed-loop infrastructure. The Taylor series expansion is employed to demonstrate the near-zero steady-state error of the proposed method. A Plug-and-Play strategy is considered to establish the SR unit of the proposed architecture, leveraging any existing advanced open-loop ECGSR methods. This paper also presents Transformer model based open-loop ECGSR and closed-loop CECGSR algorithms. Results: Simulation experiments on both noiseless and noisy subsets of the Physikalisch-Technische Bundesanstalt-Extra Large (PTB-XL) datasets demonstrate that the proposed CECGSR outperforms state-of-the-art open-loop ECGSR algorithms in the reconstruction performance of ECG signals. Conclusions: The proposed method will efficiently enrich ECG signal details and remove ECG signal artifacts in clinical applications.