Step-Down Chopper Voltage Calculation

This problem requires calculating the average DC output voltage ($V_{out(avg)}$) for a step-down chopper, considering the voltage drop across the semiconductor switch.

Given Parameters

• Input DC Voltage ($V_{in}$): $200 \text{ V}$
• Load Resistance ($R_L$): $20 \ \Omega$ (Note: Not needed for this calculation)
• Chopping Frequency ($f$): $1.5 \text{ kHz}$ (Note: Not needed for this calculation)
• Duty Ratio ($D$): $40\% = 0.4$
• Voltage across switch when 'on' ($V_{sw\_on}$): $2 \text{ V}$

Calculating Average DC Output Voltage

The formula for the average DC output voltage ($V_{out(avg)}$) in a step-down chopper, accounting for the switch voltage drop ($V_{sw\_on}$) during the 'on' period, is:

$ V_{out(avg)} = D \times (V_{in} - V_{sw\_on}) $

Plugging in the values:

• $D = 0.4$
• $V_{in} = 200 \text{ V}$
• $V_{sw\_on} = 2 \text{ V}$

Perform the calculation:

$ V_{out(avg)} = 0.4 \times (200 \text{ V} - 2 \text{ V}) $

$ V_{out(avg)} = 0.4 \times 198 \text{ V} $

$ V_{out(avg)} = 79.2 \text{ V} $

Final Answer Determination

The calculated average DC output voltage is $79.2 \text{ V}$. Comparing this result with the given options, $80 \text{ V}$ is the closest value. Therefore, the average DC output voltage is determined to be $80 \text{ V}$.