502 - Junction Temperature¶

Thermal network modeling and transient analysis.

Overview¶

Junction temperature directly affects: - Semiconductor reliability (Arrhenius law) - Conduction losses (RDS(on) increases) - Switching characteristics - Safe Operating Area (SOA)

Thermal Equivalent Circuit¶

Electrical-Thermal Analogy¶

Thermal	Electrical	Unit
Temperature T	Voltage V	°C / V
Heat Flow P	Current I	W / A
Thermal Resistance Rth	Resistance R	K/W / Ω
Thermal Capacitance Cth	Capacitance C	J/K / F

Basic Thermal Network¶

  Ploss      Rth,jc     Rth,ch     Rth,ha
   (I)   ●───/\/\/───●───/\/\/───●───/\/\/───●
         │           │           │           │
        Tj          Tc          Th          Ta
                   (Cth)       (Cth)        ⏚

Thermal Network Models¶

Foster Network¶

Parameters from datasheet curve fitting
Cannot be cascaded (nodes have no physical meaning)
Faster simulation

        R1         R2         R3
   ●───/\/\/───●───/\/\/───●───/\/\/───●
       │           │           │
      C1          C2          C3
       │           │           │
       ⏚           ⏚           ⏚

Cauer Network¶

Physically meaningful nodes (material layers)
Can be cascaded (junction→case→heatsink→ambient)
Derived from Foster via mathematical transformation

        R1         R2         R3
   ●───/\/\/───●───/\/\/───●───/\/\/───●
               │           │           │
              C1          C2          C3
               │           │           │
               ⏚           ⏚           ⏚

Setting Up Thermal Models¶

Datasheet Parameters¶

From semiconductor datasheet: - Rth,j-c (junction to case) - Rth,c-h (case to heatsink) - depends on mounting - Transient thermal impedance curve Zth(t)

Extracting Foster Parameters¶

From Zth curve fitting: $$Z_{th}(t) = \sum_{i=1}^{n} R_i \cdot (1 - e^{-t/\tau_i})$$

Where τᵢ = Rᵢ × Cᵢ

Temperature Calculations¶

Steady-State¶

\[T_j = T_a + P_{loss} \cdot (R_{th,jc} + R_{th,ch} + R_{th,ha})\]

Transient Response¶

For step power change: $$T_j(t) = T_a + P \cdot Z_{th}(t)$$

Periodic Power¶

Average temperature + ripple: $$T_{j,avg} = T_a + P_{avg} \cdot R_{th,total}$$ $$\Delta T_{j,ripple} = P_{peak} \cdot Z_{th}(t_{on})$$

Design Guidelines¶

Maximum Junction Temperature¶

Device	Tj,max	Recommended Max
Si MOSFET	150-175°C	125°C
Si IGBT	150-175°C	125°C
SiC MOSFET	175-200°C	150°C
GaN HEMT	150°C	125°C

Derating¶

Temperature margin for reliability: $$T_{j,design} = T_{j,max} - \Delta T_{margin}$$

Typical margin: 25-50°C

Simulation Exercises¶

Build Cauer thermal network from datasheet
Simulate startup thermal transient
Compare Foster vs Cauer response
Analyze temperature at different switching frequencies