# How to do worst case calculation of MOSFET in buck converter?

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:

**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

$D = \frac{V_{out}}{V_{in}}$**Calculate Duty Cycle:**

$I_{Lpeak} = I_{out} + \frac{\Delta I_L}{2}$**Determine Peak Inductor Current (I_Lpeak):**The peak inductor current occurs at the highest load current and can be calculated as: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:

$T_{on} = \frac{D}{f_{sw}}$

$I_{MOSFET_{RMS}} = I_{out} \cdot \sqrt{D}$**Calculate RMS Current Through the MOSFET (I_MOSFET_RMS):**The RMS current through the MOSFET can be approximated by:

$P_{conduction} = I_{MOSFET_{RMS}}^2 \cdot R_{DS(on)}$**Calculate Conduction Losses (P_conduction):**Consider the increase in $R_{DS(on)}$ with temperature. Typically, $R_{DS(on)}$ increases by approximately 0.4% per degree Celsius rise in temperature.

$P_{switching} = \frac{1}{2} V_{in} \cdot I_{out} \cdot (t_{on} + t_{off}) \cdot f_{sw}$**Calculate Switching Losses (P_switching):**The switching losses can be estimated as:where $t_{on}$ and $t_{off}$ are the turn-on and turn-off times of the MOSFET.

$P_{total} = P_{conduction} + P_{switching}$**Calculate Total Power Dissipation (P_total):**The total power dissipation in the MOSFET is the sum of the conduction and switching losses:

$T_{junction} = T_{ambient} + P_{total} \cdot R_{\theta JA}$**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 ($T_{junction}$):**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:

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

$D = \frac{12V}{24V} = 0.5$**Duty Cycle:**

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

$I_{Lpeak} = 5A + \frac{3A}{2} = 6.5A$**Peak Inductor Current:**

$I_{MOSFET_{RMS}} = 5A \cdot \sqrt{0.5} \approx 3.54A$**RMS Current Through the MOSFET:**

$P_{conduction} = (3.54A)^2 \cdot 10m\Omega \approx 0.125W$**Conduction Losses:**

$P_{switching} = \frac{1}{2} \cdot 24V \cdot 5A \cdot (20ns + 20ns) \cdot 200kHz \approx 0.048W$**Switching Losses:**Assume $t_{on} = 20ns$ and $t_{off} = 20ns$:

$P_{total} = 0.125W + 0.048W \approx 0.173W$**Total Power Dissipation:**

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

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.

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