The current flow within a salient pole brushless exciter with polygon-connected winding is calculated. The winding is connected to a rectifier, which causes transients in the winding during switching. Brushless exciters are over-dimensioned for their rated operation. During ceiling conditions the required voltage may be two times higher and the exciter is strongly saturated. Therefore the normal asynchronous circuit theory is no longer applicable for a detailed study within the exciter itself. A nonlinear finite difference time stepping method with rotating rotor and diode circuits is applied instead. Basic theories for the combination between the circuit theory and field theory are summarized in one mathematical model. Calculation results are compared to measurements on a real power plant exciter for different operation conditions.