Calculate L C values For Buck Converter How to?

In a buck converter, the values of the inductor (L) and capacitor (C) are critical for stable and efficient operation. Their values depend on the desired output voltage, output current, switching frequency, and acceptable levels of ripple in current and voltage.

The circuit diagram of basic buck converter is shown below. 

1. Calculating the Inductor (L):

The inductor value affects the ripple current ($\mathrm{\Delta }{I}_L$) and determines the operation mode (Continuous or Discontinuous Conduction Mode).

Formula:

$$L = \frac{V_{in} - V_{out}}{\Delta I_L \cdot f_{sw}}$$

Where:

• $V_{in}$ = Input voltage
• $V_{out}$ = Output voltage
• $\mathrm{\Delta }{I}_L$ = Inductor ripple current
• $f_{sw}$ = Switching frequency

Key Notes:

• The ripple current ($\mathrm{\Delta }{I}_L$) is typically chosen as a percentage of the maximum output current, usually $20\mathrm{\%}$ to $40\mathrm{\%}$: $$\Delta I_L = 0.2 \times I_{out(max)}$$
• Ensure $L$ is large enough to maintain continuous conduction mode (CCM) if desired.

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2. Calculating the Output Capacitor (C):

The capacitor value affects the output voltage ripple ($\Delta V_{out}$) and smooths the output voltage.

Formula:

$$C = \frac{\Delta I_L}{8 \cdot f_{sw} \cdot \Delta V_{out}}$$

Where:

• $\mathrm{\Delta }{I}_L$ = Inductor ripple current (calculated earlier)
• $f_{sw}$ = Switching frequency
• $\Delta V_{out}$ = Acceptable output voltage ripple

Key Notes:

• Output voltage ripple ($\Delta V_{out}$) is often chosen based on the application's tolerance, typically in the range of 1% to 5% of $V_{out}$.
• Higher capacitance reduces voltage ripple but may slow down the transient response.

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Practical Design Considerations:

1. Inductor Saturation Current:
   Choose an inductor with a saturation current higher than the maximum load current plus half the ripple current.

2. Capacitor ESR:
   Include the Equivalent Series Resistance (ESR) of the capacitor in the ripple calculation:

   $$\Delta V_{out(ESR)} = \Delta I_L \cdot ESR$$

3. Safety Margins:
   Add safety margins to component ratings to ensure reliable operation under varying conditions.

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Example Calculation:

Suppose:

• $V_{in} = 12V$, $V_{out} = 5V$
• $I_{out(max)}=1A$, $f_{sw}=100kHz$
• Ripple current ($\Delta I_L$) = $0.3\times 1A=0.3$
• Voltage ripple ($\Delta V_{out}$) = $50mV$

Inductor:

$$L = \frac{12V - 5V}{0.3A \cdot 100kHz} = 233 \, \mu H$$

Capacitor:

$$C = \frac{0.3A}{8 \cdot 100kHz \cdot 0.05V} = 75 \, \mu F$$

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By following these formulas and adjusting for your specific application, you can select appropriate L and C values for your buck converter.

There are various ways to design Buck converter such as using 555 Timer IC and Arduino like microcontroller, see the following tutorials on this:

• Buck Converter using 555 Timer
• Buck Converter using Arduino