Correct Answer

Concept & PrincipleElectricalPower Electronics

Option D

$(1-D) \times T$

Quick Summary: In a Pulse Width Modulated (PWM) switching circuit, the total time period $T$ is the sum of the switch's ON time ($t_{on}$) and OFF time ($t_{off}$). Since the duty cycle $D$ is defined as the ratio of $t_{on}$ to $T$, the OFF time can be mathematically expressed as $t_{off} = (1 - D) \times T$.

💡 Explanation

In a Pulse Width Modulated (PWM) switching circuit, the total time period $T$ is the sum of the switch's ON time ( $t_{on}$ ) and OFF time ( $t_{off}$ ). Since the duty cycle $D$ is defined as the ratio of $t_{on}$ to $T$ , the OFF time can be mathematically expressed as $t_{off} = (1 - D) \times T$ .

🔢 Key Formulas

$T = t_{on} + t_{off}$ — Total period definition

$D = \frac{t_{on}}{T}$ — Duty cycle definition

$t_{off} = (1-D)T$ — Complementary switching time

⚙️ Working Principle

The switching frequency is $f = \frac{1}{T}$ . The switch operates in a repeating cycle where it conducts for a fraction of the time $D$ (duty cycle). Because the cycle is either ON or OFF, the sum of these times equals the total duration of one cycle $T$ . Consequently, $t_{off} = T - t_{on}$ . Substituting $t_{on} = D \times T$ , we arrive at $t_{off} = T - (D \times T) = (1 - D) \times T$ .

📌 Key Points

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Duty cycle $D$ is dimensionless and ranges between 0 and 1.
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$t_{off}$ represents the interval where the semiconductor switch is in a blocking state.
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Increasing $D$ results in a shorter $t_{off}$ for a constant switching frequency.

✅ Advantages

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Allows control of output voltage in DC-DC converters
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Provides a simple linear relationship between load and timing

❌ Disadvantages / Limitations

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Switching losses occur during the transitions
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High frequency switching can introduce EMI

🛠️ Applications / Uses

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Buck and Boost Converters
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Motor Speed Control
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Inverters

📄 Additional Information

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Standard switching frequency range for power MOSFETs is typically 20 kHz to 500 kHz.
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Option A ( $DT$ ) represents $t_{on}$ , not $t_{off}$ . Option B is the definition of $D$ . Option C is dimensionally incorrect.

📊 Diagram / Illustration

✅

D is correct — The off time of a switch is the remaining portion of the time period $T$ not occupied by the on time, calculated as $(1-D) \times T$ .

Core Concepts Used

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Duty Cycle Pulse Width Modulation Switching Regulators

💡 EXAM TIP

Always verify units when dealing with time-based expressions; $D$ is dimensionless, so $(1-D)T$ correctly results in units of time.

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