An alternator has a field coil that produces a magnetic field which induces electricity in a coil arrangement. A field coil excitation system includes a generator with an output coil assembly for producing alternating electricity. A rectifier converts the alternating electricity into voltage and direct current at two nodes. A capacitor, between the nodes, has capacitance that forms a resonant circuit with inductance of the output coil assembly. Due to that resonant circuit, the voltage and direct current oscillate in a predefined phase relationship. A switch and the field coil are connected in series between the nodes. A controller renders the switch conductive for a time period specified by a received control signal. The switch is rendered non-conductive at the first occurrence of a minimum current level after the time period ends. The predefined phase relationship enables the minimum current level to be detected by sensing the voltage.