The mathematical interpretation of a practical sampler which is useful to obtain small signal models for peak and average current mode controls is proposed. Due to difficulties in applying Shannon's sampling theorem to the analysis of sampling effects embedded in the current mode control, several different approaches have been reported. However, these approaches require information about the inductor current in a discrete expression, which restricts the application of the reported methods to peak current mode control. In this paper, mathematical expressions of sampling effects on a current loop to which Shannon's sampling theorem can be directly applied are newly proposed, and are applied to the modelling of peak current mode control. From newly derived models of a practical sampler, models in a discrete time domain and a continuous time domain are obtained. It is expected that the derived models are useful for the control loop design of power supplies. The effectiveness of the derived models are verified through the simulation and experimental results.