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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:

  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=VoutVinD = \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:

    ILpeak=Iout+ΔIL2I_{Lpeak} = I_{out} + \frac{\Delta I_L}{2}

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

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

    and TonT_{on} is the on-time of the MOSFET:

    Ton=DfswT_{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:

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

    Pconduction=IMOSFETRMS2RDS(on)P_{conduction} = I_{MOSFET_{RMS}}^2 \cdot R_{DS(on)}

    Consider the increase in RDS(on)R_{DS(on)} with temperature. Typically, RDS(on)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:

    Pswitching=12VinIout(ton+toff)fswP_{switching} = \frac{1}{2} V_{in} \cdot I_{out} \cdot (t_{on} + t_{off}) \cdot f_{sw}

    where tont_{on} and tofft_{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:

    Ptotal=Pconduction+PswitchingP_{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 (RθJAR_{\theta JA}) and the ambient temperature (TambientT_{ambient}) to calculate the junction temperature (TjunctionT_{junction}):

    Tjunction=Tambient+PtotalRθJAT_{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:

  • Vin=24VV_{in} = 24V
  • Vout=12VV_{out} = 12V
  • Iout=5AI_{out} = 5A
  • fsw=200kHzf_{sw} = 200kHz
  • L=10μHL = 10\mu H
  • RDS(on)=10mΩR_{DS(on)} = 10m\Omega
  • Tambient=25°CT_{ambient} = 25°C
  • RθJA=50°C/WR_{\theta JA} = 50°C/W
  1. Duty Cycle:

    D=12V24V=0.5D = \frac{12V}{24V} = 0.5
  2. Inductor Ripple Current (ΔIL\Delta I_L):

    Ton=Dfsw=0.5200kHz=2.5μsT_{on} = \frac{D}{f_{sw}} = \frac{0.5}{200kHz} = 2.5\mu s ΔIL=24V12V10μH2.5μs=3A\Delta I_L = \frac{24V - 12V}{10\mu H} \cdot 2.5\mu s = 3A
  3. Peak Inductor Current:

    ILpeak=5A+3A2=6.5AI_{Lpeak} = 5A + \frac{3A}{2} = 6.5A
  4. RMS Current Through the MOSFET:

    IMOSFETRMS=5A0.53.54AI_{MOSFET_{RMS}} = 5A \cdot \sqrt{0.5} \approx 3.54A
  5. Conduction Losses:

    Pconduction=(3.54A)210mΩ0.125WP_{conduction} = (3.54A)^2 \cdot 10m\Omega \approx 0.125W
  6. Switching Losses: Assume ton=20nst_{on} = 20ns and toff=20nst_{off} = 20ns:

    Pswitching=1224V5A(20ns+20ns)200kHz0.048WP_{switching} = \frac{1}{2} \cdot 24V \cdot 5A \cdot (20ns + 20ns) \cdot 200kHz \approx 0.048W
  7. Total Power Dissipation:

    Ptotal=0.125W+0.048W0.173WP_{total} = 0.125W + 0.048W \approx 0.173W
  8. Junction Temperature:

    Tjunction=25°C+0.173W50°C/W33.65°CT_{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. 

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