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This paper presents investigations of dc-link voltages balance with the use of a passive RLC circuit in a single-phase diode-clamped inverter composed of two three-level legs. Application of the balancing circuit in the diode-clamped inverter needs proper PWM generation but the modulation method is the same for both in the balanced and unbalanced state. This method of dc-link voltages balance does not need any measurements or additional control, and this ensures fast response and low energy losses. This paper also presents mathematical analysis of the PWM modulation method and the inverter operation, and an analytical description of the natural balancing process with contribution of the load current and the balancing circuit current. Simulations and experimental results of the inverter with FPGA-based control are presented to confirm the effectiveness of the natural balancing process.