Full Thermal Chain

Tj = Ta + P × (Rθjc + Rθcs + Rθsa)

Quick answer

This calculator solves Tj = Ta + P × (Rθjc + Rθcs + Rθsa) for Tj. With Ambient Temp 50 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, Rθsa 94 °C/W, the result is 1630 °C.

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Result
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Formula

Tj = Ta + P × (Rθjc + Rθcs + Rθsa)

Description

The full thermal chain models heat flow from the semiconductor junction through each thermal interface to the ambient air, analogous to series resistors in an electrical circuit. Each thermal resistance represents a barrier to heat flow: Rθjc is junction-to-case (determined by the package and die attach), Rθcs is case-to-sink (determined by thermal interface material like thermal paste or pads), and Rθsa is sink-to-ambient (determined by the heatsink design and airflow). The total thermal resistance is the sum, and the temperature rise is proportional to power dissipated.

Variables

  • Tj — Junction temperature (°C)
  • Ta — Ambient temperature (°C)
  • P — Power dissipation (W)
  • Rθjc — Junction-to-case thermal resistance (°C/W)
  • Rθcs — Case-to-sink thermal resistance (°C/W)
  • Rθsa — Sink-to-ambient thermal resistance (°C/W)

Practical Notes

Typical Rθcs values: thermal grease 0.1-0.5°C/W, silicone pad 0.5-2°C/W, mica insulator 1-3°C/W, bare contact 1-3°C/W. Forced air convection can reduce Rθsa by 3-10x compared to natural convection. Always derate for the maximum expected ambient temperature in the end application.

Symbols and units

Symbol Meaning Default unit Accepted units
Ta Ambient Temp °C °C
P Power W µW, mW, W, kW
Rjc Rθjc °C/W °C/W
Rcs Rθcs °C/W °C/W
Rsa Rθsa °C/W °C/W

Step by step

  1. 1. What you know: Ambient Temp 50 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, Rθsa 94 °C/W
  2. 2. The relation: Tj = Ta + P × (Rθjc + Rθcs + Rθsa)
  3. 3. Substitute: Ta = 50 °C, P = 10 W, Rjc = 20 °C/W, Rcs = 44 °C/W, Rsa = 94 °C/W
  4. 4. Result: Tj = 1630 °C

Worked examples

Minimum range

Given: Ambient Temp 2.5 °C, Power 10 mW, Rθjc 0.1 °C/W, Rθcs 0.22 °C/W, Rθsa 0.47 °C/W

Result: Tj = 2.508 °C

Low range

Given: Ambient Temp 25 °C, Power 100 mW, Rθjc 1 °C/W, Rθcs 2.2 °C/W, Rθsa 4.7 °C/W

Result: Tj = 25.79 °C

Typical

Given: Ambient Temp 50 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, Rθsa 94 °C/W

Result: Tj = 1630 °C

High range

Given: Ambient Temp 85 °C, Power 1 kW, Rθjc 100 °C/W, Rθcs 220 °C/W, Rθsa 470 °C/W

Result: Tj = 790100 °C

Maximum range

Given: Ambient Temp 850 °C, Power 10 kW, Rθjc 1000 °C/W, Rθcs 2200 °C/W, Rθsa 4700 °C/W

Result: Tj = 7.9 × 10⁷ °C

How Tj changes with Ambient Temp

Ambient Temp (input) Tj (result)
5 °C 1585 °C
12.5 °C 1593 °C
25 °C 1605 °C
37.5 °C 1618 °C
50 °C 1630 °C
75 °C 1655 °C
100 °C 1680 °C
200 °C 1780 °C
350 °C 1930 °C
500 °C 2080 °C

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Frequently asked questions

How do you calculate Full Thermal Chain?

Use Tj = Ta + P × (Rθjc + Rθcs + Rθsa). With Ambient Temp 50 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, Rθsa 94 °C/W, Tj works out to 1630 °C.

What is the formula for Full Thermal Chain?

The formula is Tj = Ta + P × (Rθjc + Rθcs + Rθsa). The full thermal chain models heat flow from the semiconductor junction through each thermal interface to the ambient air, analogous to series resistors in an electrical circuit.

Related Concepts

All Thermal formulas →
Junction Temperature Full Thermal Chain Required Heatsink Maximum Power (Junction to Case) Thermal Time Constant Forced Convection Heat Transfer Power Derating (Temperature) Natural Convection Thermal Resistance

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