Synchronous machines can be applied to a variety of pulsed power systems ranging from single pulse to continuous duty operation. Each application places its own set of design constraints on the alternator, but the underlying principles of operation are the same for all designs. This paper explains these basic principles and provides background for the design of alternators for pulsed power applications. The transient operation of a synchronous machine is described in terms of inductively-coupled circuits with a physical description of the machine crosssection and the magnetic fields involved. Some examples are considered that represent the range of operation for a pulsed alternator.