In a chopper circuit, duty cycle is represented as:

Explanation:

Chopper Circuit Duty Cycle

Definition: In the context of power electronics, a chopper circuit is a type of electronic switch that controls the voltage by rapidly connecting and disconnecting the load to the power supply. The duty cycle is a crucial parameter in such circuits and is defined as the ratio of the time the switch is ON to the total time of one switching cycle. It is usually expressed as a percentage.

Mathematical Representation: The duty cycle (D) is represented by the formula:

D = TON / (TON + TOFF)

where:

• TON is the duration for which the switch is ON.
• TOFF is the duration for which the switch is OFF.

Correct Option Analysis:

The correct option is:

Option 2: TON / (TON + TOFF)

This option correctly represents the duty cycle of a chopper circuit. The duty cycle is the fraction of time the switch is ON during a single switching period, which includes both the ON time and the OFF time. This is critical in determining the average voltage and power delivered to the load.

Additional Information

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

Option 1: TON / TOFF

This option is incorrect because it represents the ratio of the ON time to the OFF time, not the duty cycle. The duty cycle must account for the total period of the cycle, which includes both the ON and OFF times.

Option 3: TOFF / TON

This option is also incorrect as it represents the inverse of the ON/OFF time ratio. It does not provide the duty cycle, which specifically requires the ratio of ON time to the total cycle time.

Option 4: TOFF / (TON + TOFF)

This option is incorrect because it represents the fraction of the cycle for which the switch is OFF. This is essentially the complement of the duty cycle and does not directly provide the information about the ON time ratio.

Conclusion:

Understanding the duty cycle is fundamental in the design and analysis of chopper circuits. The correct mathematical representation, as given in option 2 (TON / (TON + TOFF)), accurately defines the duty cycle. This parameter is essential in controlling the output voltage and power delivered to the load, impacting the efficiency and performance of the chopper circuit.