The electrical power consumption in automobiles continues to increase thereby demanding higher power capability of the alternator. The standard alternator today is a claw-pole synchronous machine. The claw-pole alternators have brushes which are maintenance issue; it is not possible to increase power output by increasing the stack length; and the rotor inertia is large due to the steel core and rotor excitation coil. Despite these disadvantages, the claw-pole alternator is still used because of its low cost and ease of manufacturing. An alternator with DC stator excitation, has a laminated salient pole rotor with no excitation coil. Therefore the weight and inertia is less than in the claw-pole alternator. The excitation coil is located in the stator and therefore there are no brushes needed. In this type of alternator, the stator has three-phase output coils evenly shifted in space 120 degrees. This paper discusses the principle of operation and develops the mathematical equations for magnetic flux, electromotive force, and torque for a single-phase alternator, a two-phase alternator, and a three-phase alternator.