Range of the Duty Ratio is ________________

Question

Examoogle · Accepted Answer

0 to 1

Explanation: The duty ratio (or duty cycle) is defined as the ratio of the pulse duration (on-time) to the total time period of a signal. Since the pulse duration $T_{on}$ cannot be negative and cannot exceed the total period $T$, the range is bounded between 0 and 1 (inclusive).

Working Principle: In pulse-width modulation (PWM) and switching converters, a periodic signal alternates between two states, typically high and low. If $T_{on}$ is the time the switch is closed and $T_{off}$ is the time it is open, the total period is $T = T_{on} + T_{off}$. The duty ratio $D$ is $D = \frac{T_{on}}{T_{on} + T_{off}}$.

Key Formulas: $D = \frac{T_{on}}{T}$ — Definition of Duty Ratio; $V_{out} = D \cdot V_{in}$ — Output voltage of a Buck converter in terms of duty ratio

Key Points: Duty ratio is a dimensionless quantity.; A duty ratio of 0 represents a signal that is always OFF (0% duty cycle).; A duty ratio of 1 represents a signal that is always ON (100% duty cycle).; In power electronics, varying the duty ratio is the primary method for controlling voltage in DC-DC converters.

Advantages: Allows efficient voltage regulation without significant resistive losses.; Enables precise control of power delivery to loads.

Disadvantages: Extreme duty ratios (very close to 0 or 1) can cause control stability issues.; High switching frequencies associated with duty cycle control can increase electromagnetic interference (EMI).

Applications: DC-DC Converters (Buck, Boost, Buck-Boost); Motor Speed Control (PWM control); LED Dimming circuits

Additional Info: In industry, duty cycle is often expressed as a percentage, meaning the range 0 to 1 corresponds to 0% to 100%.. Option B (0 to 100) is technically a percentage representation, but the standard scientific definition for the duty ratio variable itself is 0 to 1.

Answer: A is correct — The duty ratio is mathematically defined as the ratio of on-time to total period, constraining its range to the interval [0, 1].

Exam Tip: Remember that while duty ratio ranges from 0 to 1, the duty percentage ranges from 0% to 100%; always clarify the units in competitive exams.

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