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The discontinuous conduction mode (DCM) of the inductor current is an effective way to achieve high efficiency and high power density of inverters because it has the advantages of zero-current switching and small inductance of the filter inductor. Although the DCM can operate at a fixed switching frequency, there has been no linear model for realizing high-performance digital control. This paper provides a solution for this problem. Firstly, a linear first-order charge quantity model (CQM) for a DCM inverter with a fixed switching frequency is established, which uses charge quantities output by the inverter bridge as a control variable. Secondly, a direct charge control (DCC) method is proposed, and the design process is significantly simplified. Finally, the performance of the proposed control method is verified by the experiments using a 1 kW prototype, and a high-quality output voltage waveform with a peak efficiency of above 98% was achieved. The proposed method outperforms existing works because the CQM is a first-order linear model that realizes the high-performance digital control and significantly simplifies the design of controller.