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In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switching frequency is $50$ kHz. Assume ideal components and a very large output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
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