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Answer :
When the duty cycle is 0.25, the output voltage is approximately 5.333 V, and when the duty cycle is 0.75, the output voltage is 36 V.
To determine the output voltage of a buck-boost converter, we need to consider its operating principles and equations.
The buck-boost converter operates by periodically switching an inductor between the input voltage source and the output load. The duty cycle (D) represents the ratio of time the switch is turned on compared to the total switching period. The duty cycle can vary between 0 and 1, where 0 means the switch is always off, and 1 means the switch is always on.
Assuming ideal components and continuous mode operation, we can use the following equation to calculate the output voltage of a buck-boost converter:
V_out = V_s * D / (1 - D)
Where:
V_out is the output voltage
V_s is the input voltage
D is the duty cycle
Let's calculate the output voltage for the given duty cycle values:
When the duty cycle (D) is 0.25:
V_out = 12 V * 0.25 / (1 - 0.25)
V_out = 12 V * 0.25 / 0.75
V_out = 4 V / 0.75
V_out ≈ 5.333 V
When the duty cycle (D) is 0.75:
V_out = 12 V * 0.75 / (1 - 0.75)
V_out = 12 V * 0.75 / 0.25
V_out = 9 V / 0.25
V_out = 36 V
Therefore, when the duty cycle is 0.25, the output voltage is approximately 5.333 V, and when the duty cycle is 0.75, the output voltage is 36 V.
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