t_off (off time of the switch) can be also expressed as _________

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$(1-D) 	imes T$

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 $t_{off} = (1 - D) 	imes T$.

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 $t_{on} = D 	imes T$, we arrive at $t_{off} = T - (D 	imes T) = (1 - D) 	imes T$.

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

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

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

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

Applications: Buck and Boost Converters; Motor Speed Control; Inverters

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

Answer: 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 $(1-D) 	imes T$.

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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