If T is the time period for a chopper circuit and α is its dut... | Electrical MCQ | Examoogle

Back to Practice Questions

ElectricalPower Electronics

Prev Next

If T is the time period for a chopper circuit and α is its duty cycle, then the chopping frequency is_____.

$T o n \alpha$

$T o f f \alpha$

$\alpha T o f f$

$\alpha T o n$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower Electronics

Option D

$\alpha T o n$

Quick Summary:

The duty cycle $\alpha$ of a chopper is defined as the ratio of on-time $T_{on}$ to the total time period $T$ , i.e., $\alpha = \frac{T_{on}}{T}$ . Rearranging this gives $T = \frac{T_{on}}{\alpha}$ . Since chopping frequency $f$ is the reciprocal of the time period ( $f = \frac{1}{T}$ ), substituting $T$ yields $f = \frac{\alpha}{T_{on}}$ .

⚙️TETechnical SolutionConcept & Principle

📜 Standard Reference & Code Clause

IEEE 519 / IEC 60146 (Uninterruptible Power Systems & Power Converters)

💡 Explanation

🔢 Key Formulas

$\alpha = \frac{T_{on}}{T}$ — Duty cycle of the chopper

$T = T_{on} + T_{off}$ — Total time period of switching

$f = \frac{1}{T} = \frac{\alpha}{T_{on}}$ — Chopping frequency in terms of duty cycle and conduction time

$f = \frac{1 - \alpha}{T_{off}}$ — Chopping frequency in terms of off-time

⚙️ Working Principle

A chopper acts as a high-speed semiconductor switch that connects and disconnects the DC source to the load. By controlling the switch on-time ( $T_{on}$ ) relative to the total switching period ( $T$ ), the average output voltage is varied. The chopping frequency determines how many switching cycles occur per second.

📌 Key Points

▸
The chopping frequency $f$ is inversely proportional to $T_{on}$ for a constant duty cycle $\alpha$ .
▸
In Constant Frequency Control (PWM), $T$ and $f$ remain fixed while $T_{on}$ and $\alpha$ vary.
▸
In Variable Frequency Control (FM), either $T_{on}$ or $T_{off}$ is kept constant while changing $f$ to vary $\alpha$ .

✅ Advantages

▸
High efficiency due to low switching power loss.
▸
Fast dynamic response compared to conventional phase-controlled converters.

❌ Disadvantages / Limitations

▸
Generates high-frequency electromagnetic interference (EMI).
▸
Requires smoothing inductors or filters to reduce output current ripples.

🛠️ Applications / Uses

▸
DC motor speed control in electric traction and vehicles.
▸
Switched-Mode Power Supplies (SMPS) and DC-DC converters.

📄 Additional Information

▸
Option A ( $\frac{T_{on}}{\alpha}$ ) represents the time period $T$ , not the frequency $f$ .
▸
Option B ( $\frac{T_{off}}{\alpha}$ ) is mathematically incorrect because $T_{off} = (1 - \alpha)T$ , which gives $\frac{T_{off}}{1 - \alpha} = T$ .
▸
Option C ( $\frac{\alpha}{T_{off}}$ ) is incorrect; the correct expression involving $T_{off}$ is $f = \frac{1 - \alpha}{T_{off}}$ .

📊 Diagram / Illustration

✅

D is correct — Since $\alpha = \frac{T_{on}}{T}$ , rearranging gives $T = \frac{T_{on}}{\alpha}$ , and substituting into $f = \frac{1}{T}$ yields $f = \frac{\alpha}{T_{on}}$ .

Core Concepts Used

Click any tag to open in AI Tutor

DC-DC Chopper Circuits Duty Cycle Control Pulse Width Modulation (PWM)

💡 EXAM TIP

Remember that $T_{on} = \alpha T$ and $T_{off} = (1 - \alpha)T$ . Converting between frequency and period expressions is a common trap in GATE/ESE numericals.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)