Converse magnetoelectric sensors enable the detection of low-frequency and low-amplitude magnetic fields over a bandwidth of several kilohertz by combining the electrical excitation of a magnetoelectric resonator via a piezoelectric layer with an inductive readout. Here, a comprehensive sensor model is presented to further foster the development of this promising sensor concept. The model relates the output signal to the device characteristics, taking into account the magnetoelastic and electromechanical properties, the resonator geometry, and operating conditions. The sensor system is thoroughly experimentally analyzed to validate the model. Based on the analysis, the sensor concept is explained in detail, including the origin of its loss and bandwidth and their connection with the magneto-mechanical loss in the magnetostrictive layer. Significant advances have been made in the comprehensive understanding of converse magnetoelectric sensors, providing a solid basis for future improvements in magnetoelectric sensor systems.