Electrocardiography (ECG) is the gold standard for monitoring heart function and is crucial for preventing the worsening of cardiovascular diseases (CVDs). However, the inconvenience of ECG acquisition poses challenges for long-term continuous monitoring. Consequently, researchers have explored non-invasive and easily accessible photoplethysmography (PPG) as an alternative, converting it into ECG. Previous studies have focused on peaks or simple mapping to generate ECG, ignoring the inherent periodicity of cardiovascular signals. This results in an inability to accurately extract physiological information during the cycle, thus compromising the generated ECG signals' clinical utility. To this end, we introduce a novel PPG-to-ECG translation model called CATransformer, capable of adaptive modeling based on the cardiac cycle. Specifically, CATransformer automatically extracts the cycle using a cycle-aware module and creates multiple semantic views of the cardiac cycle. It leverages a transformer to capture detailed features within each cycle and the dynamics across cycles. Our method outperforms existing approaches, exhibiting the lowest RMSE across five paired PPG-ECG databases. Additionally, extensive experiments are conducted on four cardiovascular-related tasks to assess the clinical utility of the generated ECG, achieving consistent state-of-the-art performance. Experimental results confirm that CATransformer generates highly faithful ECG signals while preserving their physiological characteristics.