Basic Chopper Problems (Buck and Boost Converter)
Here are 5 basic, step-by-step solved problems on Buck (Step-Down) and Boost (Step-Up) converters in power electronics.
🔹 Problem 1 – Buck Converter
Given: \( V_{in} = 240~V \), duty cycle \( \alpha = 0.25 \)
Find: Average output voltage \( V_{out_{avg}} \)
Solution:
Formula: \( V_{out} = \alpha \, V_{in} \)
Compute: \( V_{out} = 0.25 \times 240 = 60~V \)
Answer: \( \boxed{V_{out} = 60~V} \)
🔹 Problem 2 – Buck Converter
Given: \( V_{in} = 120~V \), desired \( V_{out} = 36~V \)
Find: Duty cycle \( \alpha \)
Solution:
\( \alpha = \dfrac{V_{out}}{V_{in}} = \dfrac{36}{120} = 0.3 \)
Answer: \( \boxed{\alpha = 0.3~(30\%)} \)
🔹 Problem 3 – Buck Converter (Inductor Ripple)
Given: \( V_{in} = 100~V \), \( \alpha = 0.4 \), \( f_s = 20~kHz \), \( L = 2~mH \)
Find: Peak-to-peak inductor current ripple \( \Delta I_L \)
Solution:
\( V_{out} = \alpha V_{in} = 0.4 \times 100 = 40~V \)
Inductor voltage during ON: \( V_L(on) = V_{in} - V_{out} = 100 - 40 = 60~V \)
Switching period: \( T = \dfrac{1}{f_s} = 50~\mu s \)
ON time: \( t_{on} = \alpha T = 0.4 \times 50~\mu s = 20~\mu s \)
\( \Delta I_L = \dfrac{V_L(on) \, t_{on}}{L} = \dfrac{60 \times 20 \times 10^{-6}}{2 \times 10^{-3}} = 0.6~A \)
Answer: \( \boxed{\Delta I_{L(pp)} = 0.6~A} \)
🔹 Problem 4 – Boost Converter
Given: \( V_{in} = 48~V \), \( \alpha = 0.4 \)
Find: Average output voltage \( V_{out} \)
Solution:
Formula: \( V_{out} = \dfrac{V_{in}}{1 - \alpha} \)
\( V_{out} = \dfrac{48}{1 - 0.4} = \dfrac{48}{0.6} = 80~V \)
Answer: \( \boxed{V_{out} = 80~V} \)
🔹 Problem 5 – Boost Converter (Inductor Ripple)
Given: \( V_{in} = 24~V \), \( \alpha = 0.5 \), \( f_s = 50~kHz \), \( L = 100~\mu H \)
Find: Peak-to-peak inductor ripple \( \Delta I_L \)
Solution:
Switching period: \( T = \dfrac{1}{f_s} = 20~\mu s \)
ON time: \( t_{on} = \alpha T = 0.5 \times 20~\mu s = 10~\mu s \)
During ON, \( V_L = V_{in} = 24~V \)
\( \Delta I_L = \dfrac{V_{in} \, t_{on}}{L} = \dfrac{24 \times 10 \times 10^{-6}}{100 \times 10^{-6}} = 2.4~A \)
Answer: \( \boxed{\Delta I_{L(pp)} = 2.4~A} \)
Chopper in Power Electronics – Basic Concepts
A chopper is a DC to DC converter used to obtain a variable DC output voltage from a fixed DC input voltage. It acts like a high-speed ON–OFF switch that controls the average output voltage by changing the ON time and OFF time of the switching device.
🔹 Definition
A chopper is a static device that converts fixed DC input voltage to variable DC output voltage. It is also called a DC-DC converter or DC chopper.
🔹 Basic Principle
When the semiconductor switch (such as a transistor, MOSFET, IGBT, or SCR) is turned ON, the supply voltage \( V_{in} \) appears across the load. When the switch is OFF, the load voltage becomes zero or is maintained by the energy stored in inductors and capacitors.
If the switch is ON for \( t_{on} \) seconds and OFF for \( t_{off} \) seconds, then the total switching period \( T \) is given by:
\[ T = t_{on} + t_{off} \]
The duty cycle \( \alpha \) is defined as:
\[ \alpha = \frac{t_{on}}{T} \]
The average output voltage is:
\[ V_{out} = \alpha \, V_{in} \]
Thus, by controlling the duty ratio \( \alpha \), we can vary the average output voltage from 0 to \( V_{in} \).
🔹 Classification of DC Choppers
| Type | Description |
|---|---|
| Type A – Step-Down Chopper | Output voltage is less than input voltage. Operates in the first quadrant only. |
| Type B – Step-Up Chopper | Output voltage is higher than input voltage. Operates in the second quadrant. |
| Type C – Two-Quadrant Type-A and Type-B | Allows current in both directions while voltage remains positive. |
| Type D – Two-Quadrant Type-C | Both current and voltage can reverse direction. |
| Type E – Four-Quadrant Chopper | Allows operation in all four quadrants (for reversible drives). |
🔹 Step-Down (Buck) Chopper
When the switch is ON, \( V_{out} = V_{in} \). When the switch is OFF, \( V_{out} = 0 \). Average output voltage:
\[ V_{out} = \alpha \, V_{in} \]
Applications: DC motor speed control, battery charging, regulated DC power supply.
🔹 Step-Up (Boost) Chopper
When the switch is ON, energy is stored in the inductor. When the switch is OFF, the energy stored in the inductor is released to the load, increasing the voltage.
\[ V_{out} = \frac{V_{in}}{1 - \alpha} \]
Applications: Electric vehicles, renewable energy systems (solar PV), and DC voltage boosters.
Read also: Voltage source inverter
🔹 Control Techniques
- Time Ratio Control (TRC): Varying the ON/OFF time of the chopper switch.
- Current Limit Control (CLC): Turning ON/OFF depending on current limits.
🔹 Advantages of Chopper
- High efficiency (typically 90–95%)
- Compact and light weight
- Fast and smooth DC voltage control
- Regenerative braking possible in advanced types
🔹 Applications
- DC motor speed control
- Battery-operated vehicles
- DC power supplies
- Solar and wind energy conversion
- Traction control in electric trains
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