Question

Boost converter output \( V_o \) is:

• A. Less than \( V_{\text{in}} \)
• B. Equal to \( V_{\text{in}} \)
• C. Greater than \( V_{\text{in}} \)
• D. Zero

Hint:

Converter Cheat Sheet:
Buck Converter: \( V_o = D V_{\text{in}} \) (Always step-down).
Boost Converter: \( V_o = \frac{V_{\text{in}}}{1-D} \) (Always step-up).
Buck-Boost Converter: \( V_o = \frac{D V_{\text{in}}}{1-D} \) (Step-up or step-down).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to compare the output voltage \( V_o \) of a DC-DC Boost converter with its input voltage \( V_{\text{in}} \).
A boost converter is a switched-mode power supply that steps up an input DC voltage to a higher output DC voltage.

Step 2: Key Formula or Approach:
For a boost converter operating in continuous conduction mode (CCM), the relationship between the input voltage \( V_{\text{in}} \), output voltage \( V_o \), and the switch duty cycle \( D \) is given by:
\[ V_o = \frac{V_{\text{in}}}{1 - D} \] Where:
\( D \) is the duty cycle, defined as the ratio of the switch ON-time to the total switching period (\( D = \frac{T_{\text{on}}}{T} \)).
The value of the duty cycle is bounded by:
\[ 0 \le D < 1 \]

Step 3: Detailed Explanation:
Let us analyze the voltage conversion ratio based on the duty cycle value:

• Duty Cycle Bounds: Since the duty cycle \( D \) is a fraction representing time, its value must lie between 0 and 1.

• Mathematical Evaluation:
- If \( D > 0 \), the term \( 1 - D \) is strictly less than 1.
- Consequently, the denominator term \( \frac{1}{1 - D} \) is strictly greater than 1.
- Substituting this into the voltage transfer equation:
\[ V_o = V_{\text{in}} \times \left(\frac{1}{1-D}\right) > V_{\text{in}} \] - For example, if the duty cycle \( D = 0.5 \) (the switch is ON for \( 50\% \) of the period):
\[ V_o = \frac{V_{\text{in}}}{1 - 0.5} = \frac{V_{\text{in}}}{0.5} = 2 V_{\text{in}} \] - This shows that the output voltage is double the input voltage.

• Conclusion: Because \( V_o \) is always greater than \( V_{\text{in}} \) for any practical duty cycle greater than zero, the converter is classified as a step-up or "Boost" converter.

Step 4: Final Answer:
The output voltage \( V_o \) of a boost converter is always greater than the input voltage \( V_{\text{in}} \).