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To perform a worst-case calculation of a MOSFET in a buck converter, you need to consider several key parameters and their maximum and minimum values under worst-case conditions. Here are the steps you can follow:

1. Identify Key Parameters:

• Input voltage (V_in)
• Output voltage (V_out)
• Output current (I_out)
• Switching frequency (f_sw)
• Duty cycle (D)
• MOSFET on-resistance (R_DS(on))
• Inductor value (L)
• Capacitor value (C)
• Parasitic elements (inductor ESR, capacitor ESR)
• Temperature effects on the MOSFET parameters
2. Calculate Duty Cycle:

$D = \frac{V_{out}}{V_{in}}$
3. Determine Peak Inductor Current (I_Lpeak): The peak inductor current occurs at the highest load current and can be calculated as:

$I_{Lpeak} = I_{out} + \frac{\Delta I_L}{2}$

where $\Delta I_L$ is the inductor ripple current, given by:

$\Delta I_L = \frac{V_{in} - V_{out}}{L} \cdot D \cdot T_{on}$

and $T_{on}$ is the on-time of the MOSFET:

$T_{on} = \frac{D}{f_{sw}}$
4. Calculate RMS Current Through the MOSFET (I_MOSFET_RMS): The RMS current through the MOSFET can be approximated by:

$I_{MOSFET_{RMS}} = I_{out} \cdot \sqrt{D}$
5. Calculate Conduction Losses (P_conduction):

$P_{conduction} = I_{MOSFET_{RMS}}^2 \cdot R_{DS(on)}$

Consider the increase in $R_{DS(on)}$ with temperature. Typically, $R_{DS(on)}$ increases by approximately 0.4% per degree Celsius rise in temperature.

6. Calculate Switching Losses (P_switching): The switching losses can be estimated as:

$P_{switching} = \frac{1}{2} V_{in} \cdot I_{out} \cdot (t_{on} + t_{off}) \cdot f_{sw}$

where $t_{on}$ and $t_{off}$ are the turn-on and turn-off times of the MOSFET.

7. Calculate Total Power Dissipation (P_total): The total power dissipation in the MOSFET is the sum of the conduction and switching losses:

$P_{total} = P_{conduction} + P_{switching}$
8. Evaluate Thermal Performance: Ensure that the MOSFET can dissipate the total power without exceeding its maximum junction temperature. Use the thermal resistance junction-to-ambient ($R_{\theta JA}$) and the ambient temperature ($T_{ambient}$) to calculate the junction temperature ($T_{junction}$):

$T_{junction} = T_{ambient} + P_{total} \cdot R_{\theta JA}$
9. Verify Voltage Ratings: Ensure the MOSFET's voltage rating (V_DS) is sufficient to handle the maximum input voltage plus any voltage spikes caused by switching and parasitic inductances.

### Example Calculation:

Let's consider a buck converter with the following parameters:

• $V_{in} = 24V$
• $V_{out} = 12V$
• $I_{out} = 5A$
• $f_{sw} = 200kHz$
• $L = 10\mu H$
• $R_{DS(on)} = 10m\Omega$
• $T_{ambient} = 25°C$
• $R_{\theta JA} = 50°C/W$
1. Duty Cycle:

$D = \frac{12V}{24V} = 0.5$
2. Inductor Ripple Current ($\Delta I_L$):

$T_{on} = \frac{D}{f_{sw}} = \frac{0.5}{200kHz} = 2.5\mu s$ $\Delta I_L = \frac{24V - 12V}{10\mu H} \cdot 2.5\mu s = 3A$
3. Peak Inductor Current:

$I_{Lpeak} = 5A + \frac{3A}{2} = 6.5A$
4. RMS Current Through the MOSFET:

$I_{MOSFET_{RMS}} = 5A \cdot \sqrt{0.5} \approx 3.54A$
5. Conduction Losses:

$P_{conduction} = (3.54A)^2 \cdot 10m\Omega \approx 0.125W$
6. Switching Losses: Assume $t_{on} = 20ns$ and $t_{off} = 20ns$:

$P_{switching} = \frac{1}{2} \cdot 24V \cdot 5A \cdot (20ns + 20ns) \cdot 200kHz \approx 0.048W$
7. Total Power Dissipation:

$P_{total} = 0.125W + 0.048W \approx 0.173W$
8. Junction Temperature:

$T_{junction} = 25°C + 0.173W \cdot 50°C/W \approx 33.65°C$

The MOSFET is within its safe operating limits, assuming the maximum junction temperature is much higher than 33.65°C.

By following these steps, you can evaluate the worst-case performance of a MOSFET in a buck converter. Adjust the parameters and recalculate as needed for different scenarios.