In this paper, the influence of the rotor circuit on the characteristics of the Brushless Doubly-Fed Induction Machine (BDFIM) is investigated. For this purpose, a dynamic model is provided for the nested-loop BDFIM. The model is based on the coupled circuits of the stator windings and the rotor loops. By using the winding function method, the self- and mutual-inductances of the coupled circuits are obtained as functions of the rotor position and design parameters. This model is used as a fast tool to predict the dynamic performance of the BDFIM and is verified by means of time-stepping Finite Element Analysis (FEA). Using the provided dynamic model, some characteristics of BDFIM such as the Joule loss and the magnetic coupling between the power and control windings at no-load condition is studied. Using the developed model, the effect of the number and the arc span of the rotor loops on the no-load characteristic of the BDFIMs is studied.