To Charge a 120 V battery from a 600 V DC source using a DC chopper, The average battery current should be 20 A, with a peak to peak ripple of 2 A. If the chopper frequency is 200 Hz, calculate the duty cycle.  

Explanation:

Charging a 120 V Battery Using a DC Chopper

Problem Statement: A 120 V battery is to be charged from a 600 V DC source using a DC chopper. The average current supplied to the battery should be 20 A, with a peak-to-peak ripple of 2 A. The chopper operates at a frequency of 200 Hz. The task is to calculate the duty cycle of the chopper.

Solution:

To solve this problem, let us break it into steps:

Step 1: Understanding the DC Chopper Operation

A DC chopper is a power electronics device that steps down or steps up the voltage by controlling the duty cycle (D). The duty cycle is defined as the ratio of the ON time (T_ON) of the chopper to the total time period (T).

The average output voltage (V_out) of a step-down chopper is given by:

V_out = D × V_in

Where:

• V_in = Input voltage (600 V in this case).
• D = Duty cycle (value between 0 and 1).

Rearranging the formula to find the duty cycle:

D = V_out / V_in

Step 2: Calculate the Duty Cycle

Here, the output voltage V_out is equal to the battery voltage, which is 120 V. The input voltage V_in is the source voltage, which is 600 V. Substituting these values into the formula:

D = V_out / V_in

D = 120 / 600

D = 0.2

Thus, the duty cycle of the chopper is 0.2, or 20%.

Step 3: Verify Additional Parameters

The problem also specifies an average battery current of 20 A and a peak-to-peak ripple of 2 A. These parameters are consistent with the design of a DC chopper circuit operating at 200 Hz, where the ripple current is minimized by the use of a suitable inductor in the circuit. However, the calculation of the duty cycle is independent of the current values in this case, as it is determined solely by the voltage ratio.

Conclusion:

The duty cycle of the chopper required to charge the 120 V battery from a 600 V DC source is 0.2 (20%).

Correct Option: Option 1 (0.2)

Additional Information

To further understand the analysis, let’s evaluate why the other options are incorrect:

Option 2 (0.1): This option would imply a much lower duty cycle, resulting in an output voltage of:

V_out = 0.1 × 600 = 60 V

This value is far below the required battery voltage of 120 V, making this option incorrect.

Option 3 (0.5): A duty cycle of 0.5 would result in an output voltage of:

V_out = 0.5 × 600 = 300 V

This value exceeds the battery voltage of 120 V, which would overcharge the battery and potentially damage it. Hence, this option is also incorrect.

Option 4 (0.6): A duty cycle of 0.6 would result in an output voltage of:

V_out = 0.6 × 600 = 360 V

This output voltage is even higher than the one in Option 3, making it completely unsuitable for charging a 120 V battery. Thus, this option is incorrect as well.

Conclusion:

Among the given options, only Option 1 provides the correct duty cycle of 0.2, which ensures the proper output voltage of 120 V for charging the battery. The other options result in either an insufficient or excessive output voltage, making them invalid choices.