In order to achieve early diagnosis for inter-turn short circuit fault of field winding（ISFFW）， electrical quantities under fault conditions， such as currents of stator and rotor winding， must be calculated accurately. An extended multi-loop math model for ISFFW is established， which considers the spatial harmonics of air-gap magnetic field， the unbalanced currents inside the phase windings， and changes of topological structure in excitation circuits due to rotor faults. It may accurately evaluate inductances of the field winding with the model under ISFFW and facilitate numerical simulation of all branch currents in stator and rotor windings during the whole fault transient. ISFFW experiments have been carried out on a 12 kW model synchronous generator with three non-salient pole-pairs. The experiment data of both transient and steady-state processes coincide well with the simulation results obtained from the above math model， which verifies correctness of the math model and accuracy of the simulation program. Based on the simulation and experiment results， a summary is given on the steady-state characteristics of the faults， which may serve as the basis for the protection against ISFFW.