Independent AC-DC combined power supplies (IADCPS) are widely used on vehicles, ships and aircraft. The AC line voltage distortion and the DC voltage ripple are of special interest, but they are rather difficult to calculate. This paper presents a mathematical model based on the multi-loop method for a synchronous generator with two sets of windings on the stator to provide AC power and rectified DC output at the same time. The model accurately evaluates the effect of the air gap magnetic field harmonics. Computer simulation results agree with the experimental waveform.