The brushless exciter is now widely used in alternator excitation systems as it offers the advantage of reduced maintenance. An accurate modelling of the exciter-alternator set is important for design and operation engineers. In the paper, an accurate detailed model of the set is presented. The exciter is modelled as a synchronous machine in the direct phase reference frame, to comply with the nature of the rectifier circuit. Kron's tensor method for analysis of electrical circuits is utilised, and a variable connection matrix is developed to suit the variable topology of the exciter circuit. A complete mathematical model that covers all the modes of operation of the rotating bridge rectifier circuit is developed. Short circuit transient results are computed and compared with test results.