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Find the output voltage expression for a step down chopper with Vs as the input voltage and α as the duty cycle.

A) $V_{o} = V_{s} \alpha$

B) $V_{o} = V_{s} \times \alpha$

C) $V_{o} = V_{s}^{2} \alpha$

D) $V_{o} = 2 V_{s} \alpha \pi$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower Electronics

Option B

$V_{o} = V_{s} \times \alpha$

Quick Summary:

A step-down chopper (also known as a Buck Converter) converts a fixed DC input voltage $V_s$ into a lower average DC output voltage $V_o$ . The output voltage is directly proportional to the duty cycle $\alpha$ and input voltage $V_s$ , given by $V_o = \alpha V_s$ . Since $\alpha \le 1$ , the output voltage is always less than or equal to the input voltage.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$V_o = \alpha \times V_s$ — Average Output Voltage of Step-Down Chopper

$\alpha = \frac{T_{on}}{T} = \frac{T_{on}}{T_{on} + T_{off}}$ — Duty Cycle

$V_{o(rms)} = \sqrt{\alpha} \times V_s$ — RMS Output Voltage

$P_o = \frac{V_o^2}{R} = \frac{\alpha V_s^2}{R}$ — Output Power for Resistive Load

⚙️ Working Principle

When the chopper switch is turned ON for duration $T_{on}$ , the load receives the supply voltage $V_s$ . When the switch is turned OFF for duration $T_{off}$ , the load voltage becomes zero (assuming a freewheeling diode maintains load current continuity). The average output voltage is computed by integrating the instantaneous voltage over the total switching period $T = T_{on} + T_{off}$ , resulting in $V_o = \frac{T_{on}}{T} \times V_s = \alpha V_s$ .

📌 Key Points

▸
The output voltage of a step-down chopper is always less than or equal to the input voltage ( $V_o \le V_s$ ).
▸
The duty cycle $\alpha$ ranges from $0$ to $1$ ( $0 \le \alpha \le 1$ ).
▸
Chopping frequency is $f = \frac{1}{T} = \frac{1}{T_{on} + T_{off}}$ .
▸
A step-down chopper is also referred to as a Class-A chopper or Buck converter.

✅ Advantages

▸
High efficiency compared to linear voltage regulators.
▸
Precise dynamic control of DC output voltage by adjusting duty cycle $\alpha$ .

❌ Disadvantages / Limitations

▸
Produces harmonic ripples in output current and voltage requiring LC filters.
▸
Requires high-speed semiconductor switching components.

🛠️ Applications / Uses

▸
DC motor speed control in traction drives and electric vehicles.
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Switch Mode Power Supplies (SMPS) and battery chargers.

📄 Additional Information

▸
Option A ( $V_o = \frac{V_s}{\alpha}$ ) represents a hypothetical inverse dependence not used in DC choppers.
▸
Option B ( $V_o = V_s \times \alpha$ ) is correct for a step-down chopper.
▸
Option C ( $V_o = \frac{V_s^2}{\alpha}$ ) is dimensionally incorrect for voltage calculation.
▸
Option D ( $V_o = \frac{2V_s}{\alpha \pi}$ ) incorrectly introduces AC rectification parameters ( $\pi$ ) into a DC-DC converter equation.

📊 Diagram / Illustration

✅

B is correct — For a step-down chopper, the average output voltage $V_o$ is equal to the product of input supply voltage $V_s$ and duty cycle $\alpha$ ( $V_o = \alpha V_s$ ).

Core Concepts Used

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DC-DC Step-Down Chopper Duty Cycle Control (PWM) Buck Converter Voltage Relationship

💡 EXAM TIP

Remember: Step-down chopper gives $V_o = \alpha V_s$ , Step-up chopper gives $V_o = \frac{V_s}{1 - \alpha}$ , and Buck-Boost chopper gives $V_o = \frac{\alpha V_s}{1 - \alpha}$ .

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