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Junction temperature of a power semiconductor

Estimate steady-state junction, case, and sink temperatures and a single-pulse junction rise from a four-term Foster model.

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Published 28. October 2026 · version 1

How it is calculated

The steady-state path is $T_j=T_a+P(R_{jc}+R_{cs}+R_{sa})$ , with case and sink temperatures taken at the intermediate nodes. The four-term data-sheet form is $Z_{th(j-c)}(t)=\sum_{k=1}^{4}r_k(1-e^{-t/\tau_k})$ ; a constant-power pulse gives $\Delta T_j=PZ_{th}(t_p)$ .

Assumptions

Constant power during the pulse; case temperature fixed over that pulse; linear, time-invariant thermal behavior; isothermal nodes; the Foster coefficients represent junction-to-case impedance; steady-state interface and heat-sink resistances are independent of temperature and airflow.

Where it applies

Replace the illustrative Foster coefficients with values fitted or published for the selected device and mounting condition. A Foster network is an impedance model, not a literal physical layer stack. The single-pulse result excludes prior heating and repetitive-pulse superposition.

References

Use the selected semiconductor data sheet transient thermal impedance Zth(j-c) curve or fitted Foster coefficients; verify that Σri agrees with the stated steady-state Rθjc.

Inputs

Input	Symbol	Unit	Default
Power loss	`P_loss`	W	20
Ambient temperature	`T_a`	°C	25
Junction-to-case thermal resistance	`R_jc`	K/W	0.5
Case-to-sink thermal resistance	`R_cs`	K/W	0.2
Sink-to-ambient thermal resistance	`R_sa`	K/W	2
Single-pulse length	`pulse_ms`	ms	100

Results

With the default inputs above, the calc gives:

Result	Value
Steady-state junction temperature	79 °C
Steady-state case temperature	69 °C
Steady-state heat-sink temperature	65 °C
Junction-to-ambient thermal resistance	2.7 K/W
Junction-to-case impedance at pulse length	0.3091 K/W
Junction-to-case rise after one pulse	6.182 K

Checked against sources

Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).

20 W with a 2.7 K/W total path

Source: Hand calculation: Tsink = 25 + 20·2 = 65 °C; Tcase = 25 + 20·(0.2 + 2) = 69 °C; Tj = 25 + 20·(0.5 + 0.2 + 2) = 79 °C. At 0.1 s, Zth = 0.08(1−e⁻100)+0.12(1−e⁻10)+0.15(1−e⁻1)+0.15(1−e⁻0.1) = 0.309087 K/W, so ΔTj = 20·0.309087 = 6.18174 K.

Inputs: the default inputs above.

Result	Source	This calc
Steady-state junction temperature	79 °C	79 °C
Steady-state case temperature	69 °C	69 °C
Steady-state heat-sink temperature	65 °C	65 °C
Junction-to-case impedance at pulse length	0.3091 K/W	0.3091 K/W
Junction-to-case rise after one pulse	6.182 K	6.182 K

10 W, a pulse of 1 s

Source: Hand calculation: Tj = 40 + 10·(0.5 + 0.1 + 1.6) = 62 °C; Tcase = 40 + 10·(0.1 + 1.6) = 57 °C. At 1 s, Zth = 0.08(1−e⁻¹⁰⁰⁰) + 0.12(1−e⁻¹⁰⁰) + 0.15(1−e⁻¹⁰) + 0.15(1−e⁻¹) = 0.08 + 0.12 + 0.149993 + 0.094818 = 0.444811 K/W; ΔTj = 10·0.444811 = 4.44811 K.

Inputs: Power loss = 10 W; Ambient temperature = 40 °C; Case-to-sink thermal resistance = 0.1 K/W; Sink-to-ambient thermal resistance = 1.6 K/W; Single-pulse length = 1,000 ms; the others as above.

Result	Source	This calc
Steady-state junction temperature	62 °C	62 °C
Steady-state case temperature	57 °C	57 °C
Junction-to-case impedance at pulse length	0.4448 K/W	0.4448 K/W
Junction-to-case rise after one pulse	4.448 K	4.448 K