Chopper Output Voltage Calculation

A step-up chopper, also known as a boost chopper, is a power electronic converter that produces an output voltage greater than its input DC voltage. It achieves this voltage step-up by rapidly switching a semiconductor device (like a MOSFET or IGBT) to store energy in an inductor and then release it to the load at a higher voltage.

Step-Up Chopper Principle

The operation of a step-up chopper relies on the energy stored in an inductor. When the switch is ON, the inductor stores energy from the source. When the switch is OFF, the inductor's polarity reverses, and its stored energy adds to the source voltage, resulting in a higher output voltage across the load. The amount of voltage step-up is controlled by the duty cycle of the chopper.

Key Formula for Step-Up Chopper

The average output voltage (\(V_o\)) of a step-up chopper is determined by the input source voltage (\(V_s\)) and the duty cycle (\(\alpha\)). The formula for the average output voltage of a step-up chopper is:

Where:

• \(V_o\) is the average output voltage
• \(V_s\) is the source voltage
• \(\alpha\) is the duty cycle (ratio of ON time to total switching period)

Given Parameters

From the problem statement, we have the following values:

• Source voltage (\(V_s\)) = 200 V
• Duty cycle (\(\alpha\)) = 50%

Detailed Step-by-Step Solution

To find the average output voltage of the step-up chopper, we will follow these steps:

1. Convert Duty Cycle to Decimal: The duty cycle is given as a percentage, which needs to be converted into a decimal for use in the formula.
\[\alpha = 50\% = \frac{50}{100} = 0.50\]
2. Apply the Step-Up Chopper Formula: Substitute the given source voltage and the calculated decimal duty cycle into the average output voltage formula for a step-up chopper.
\[V_o = \frac{V_s}{1 - \alpha}\] \[V_o = \frac{200}{1 - 0.50}\] \[V_o = \frac{200}{0.50}\]
3. Calculate the Average Output Voltage: Perform the division to find the final output voltage.
\[V_o = 400 \text{ V}\]

Final Result

Based on the calculations, the average output voltage of the step-up chopper is 400 V.