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The choice of switching frequency for pulsewidth modulation single-phase inverters, such as those used in grid-connected photovoltaic application, is usually a tradeoff between reducing the total harmonic distortion (THD) and reducing the switching loss. This paper discusses an approach to minimize the switching loss while meeting a given THD requirement using variable switching frequency schemes (switching schemes with the switching frequency varying within a fundamental period). An optimal switching scheme is proposed based on time-domain current ripple analysis and the calculus of variations. The analysis shows that, to meet the same THD requirement, the optimal scheme has a significant saving on switching loss, compared to the fixed switching frequency scheme and the hysteresis control scheme, in addition to other benefits such as reduced peak switching loss and a spread spectrum of the current harmonics. The optimal scheme has been implemented in a prototype and the experimental results have verified the theoretical analysis. Also, a straightforward design method for designing filter inductors for single-phase converters is provided based on the time-domain current ripple analysis.