In recent years, field programmable gate array (FPGA) have been used in many internet of things (IoT) devices and are equipped with cryptographic circuits to ensure security. However, they are exposed to the risk of cryptographic keys being stolen by side-channel attacks. Countermeasures against side-channel attacks have been developed, but they are becoming more of a threat to IoT devices due to the diversity of attacks. Therefore, it is necessary to understand the basic characteristics of side-channel attacks. Therefore, this study clarifies the relationship between two timing issues, the clock period of the circuit and the power sampling interval, and the amount of side-channel leakage. We design seven advanced encryption standard (AES) circuits with different clock periods and conduct empirical experiments using logic simulations to clarify the correlation between the two timings and the amount of side-channel leakage. T-test is used to evaluate the leakage amount, which is evaluated based on four metrics. From the results, we argue that the clock period and sampling interval do not interfere with each other in the side-channel leakage amount.