Answer :
Final answer:
The negative sign in the duty cycle formula for a buck-boost converter is due to the inversion of output (output is of opposite polarity to input), not because the output voltage is negative. The magnitude alone is considered in calculations.
Explanation:
The buck-boost converter is a type of DC-DC converter that has a magnitude of output voltage more or less than the input voltage and is primarily used in power management applications. The formula for finding the duty cycle (D) in a buck-boost converter is vout=-vinD/(1-D), where vin is the input voltage to the converter and vout is the output voltage.
The negative sign is due to the inverse nature of the buck-boost converter. That is, the output is negative with respect to the input; the input and output are of opposite polarities. The magnitude of the output voltage vout is determined by the duty cycle (D), which is the ratio of the time that the switch is on to the total period of the wave. The negative sign does not necessarily indicate a negative voltage, but the inversion of output. In order to find a specific duty cycle D that would result in a particular output voltage relative to the input voltage, the magnitude alone is considered and thus the negative sign is not typically part of the calculation.
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