The values of duty cycle (α) lies between.

Question

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$0 \leq \alpha \leq 1$

Explanation: The duty cycle ($\alpha$) of a chopper represents the ratio of the 'ON' time to the total time period of a pulse width modulation signal. Since the switch cannot be 'ON' for more than the total period or 'OFF' for less than zero time, the range is mathematically bounded between 0 and 1 inclusive.

Working Principle: In a DC-to-DC converter (chopper), the duty cycle is defined as $\alpha = \frac{T_{ON}}{T}$, where $T_{ON}$ is the conduction time and $T$ is the total period ($T_{ON} + T_{OFF}$). If $\alpha = 0$, the switch is always OFF (output is 0V), and if $\alpha = 1$, the switch is always ON (output is $V_{source}$).

Key Formulas: $\alpha = \frac{T_{ON}}{T}$ — Definition of Duty Cycle; $V_{o} = \alpha V_{s}$ — Average output voltage of a step-down chopper

Key Points: Duty cycle is a dimensionless quantity ranging from 0 to 1.; A value of $\alpha = 0$ corresponds to 0% duty cycle.; A value of $\alpha = 1$ corresponds to 100% duty cycle.; In practice, extreme values of 0 and 1 may be limited by switching frequency and circuit losses.

Advantages: Allows for precise control of average output voltage.; High efficiency as the switch operates in fully ON or OFF states.

Disadvantages: Requires high-frequency switching which can cause EMI issues.; Non-linearities at very low or very high duty cycles.

Applications: DC Motor speed control.; Switch-mode power supplies (SMPS).; Battery chargers.

Additional Info: Option B is incorrect because duty cycle cannot be negative.. Option D is incorrect as values exceeding 1 imply a duty cycle greater than 100%, which is physically impossible for a single switch period.

Answer: C is correct — The duty cycle represents the proportion of the period the switch is closed, physically constrained to the range $0 \leq \alpha \leq 1$.

Exam Tip: Always verify if the question asks for percentage duty cycle (0-100%) or decimal duty cycle (0-1); in most technical exams, the decimal range is implied unless specified otherwise.

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