Thermal design

Intent

• Estimate a device’s junction temperature from its power and the thermal resistances along the heat’s path.
• Know what a data sheet’s junction-to-ambient resistance does not tell about your board.
• Estimate the junction from a temperature measured on top of the package.

Theory

A series path

A thermal resistance is a temperature difference per watt of the power that flows across it [Texas Instruments 2003]. On a heat sink, a device sheds its power mainly from its junction to its case, through the interface (a pad, grease or an insulator) to the heat sink, and from the heat sink to the air. Taking all of it along that path, each part raises the temperature by its resistance times the power:

$$T_J = T_A + P_D \left(\theta_\mathrm{JC} + \theta_\mathrm{CS} + \theta_\mathrm{SA}\right)$$

$T_J$

junction temperature

$P_D$

dissipated power

$T_A$

ambient temperature

$\theta_\mathrm{CS}$

case-to-sink thermal resistance

$\theta_\mathrm{JC}$

junction-to-case thermal resistance

$\theta_\mathrm{SA}$

sink-to-ambient thermal resistance

Junction temperature through a series thermal path✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• steady state; all of the device's power flows through each part of the path in turn: junction to case, case to heat sink, heat sink to ambient

Notes

each part of the path raises the temperature by its thermal resistance times the power through it, and the rises add; the largest resistance in the chain takes the largest share of the junction's rise, so lowering it helps most

Source

Texas Instruments 2003, thermal resistance as a temperature difference per watt; derived here

Derivation

step-by-step sympy derivation

Equation id

therm.Tj · equations.yaml entry

The largest resistance in the chain takes the largest share of the junction’s rise, so lowering it helps most.

A data sheet’s junction-to-ambient resistance $\theta_\mathrm{JA}$ is the most commonly reported thermal metric, and it is often misused [Texas Instruments 2003]: it describes the whole path from the junction to the air as the device was measured, board and airflow included, not the path on your board.

From the package top

A device without a heat sink sheds its power through its leads, its board and its top, and only part of the power flows through the top. The junction-to-top characterization parameter $\Psi_\mathrm{JT}$ relates the junction to a temperature measured on top of the package, for the device’s whole power; it is not a true thermal resistance, and is not added into a series path [Texas Instruments 2003]:

$$T_J = T_T + \Psi_\mathrm{JT} P_D$$

$T_J$

junction temperature

$P_D$

dissipated power

$\Psi_\mathrm{JT}$

junction-to-top characterization parameter

$T_T$

package-top temperature

Junction temperature from the package-top temperature✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• the device is mounted and cooled as it was characterized (on a board, without a heat sink on the package); the parameter is not a thermal resistance: only part of the power flows through the package top

Notes

only part of the power flows through the package top, so the parameter is not a true thermal resistance and is not added into a series path; it relates the measured top to the junction for the device's whole power, in the conditions it was characterized in: with a heat sink on the package it no longer applies

Source

Texas Instruments 2003, Psi_JT, the junction-to-top characterization parameter

Equation id

therm.psi · equations.yaml entry

A data sheet’s value holds in the conditions it was characterized in; with a heat sink on the package it no longer applies.

Temperature and loss

A silicon MOSFET’s on-resistance rises with its junction temperature: in the cited tutorial it roughly doubles from 25 °C to 125 °C [Advanced Power Technology 2006], and the data sheet’s normalized on-resistance curve gives the factor for the part you use. The conduction loss rises with it (conduction loss). A hotter junction dissipates more, which heats it further: estimate the loss at the junction temperature it causes, not at room temperature.

Worked example

A switch on a heat sink; and, apart from it, a device without a heat sink whose package top is measured:

Thermal example

Symbol	Value	How it is obtained
$P_D$ dissipated power	2 W	given
$T_A$ ambient temperature	40 °C	given
$\theta_\mathrm{JC}$ junction-to-case thermal resistance	1.5 K/W	given
$\theta_\mathrm{CS}$ case-to-sink thermal resistance	0.5 K/W	given
$\theta_\mathrm{SA}$ sink-to-ambient thermal resistance	20 K/W	given
$T_T$ package-top temperature	70 °C	given
$\Psi_\mathrm{JT}$ junction-to-top characterization parameter	2 K/W	given
$T_J$ junction temperature	84 °C	Junction temperature through a series thermal path
${T_J}_{\mathrm{top}}$ junction temperature	74 °C	Junction temperature from the package-top temperature

Through the series path the switch’s junction sits at 84 °C, most of the rise across the heat sink’s 20 K/W. For the device without a heat sink, a package top at 70 °C and the characterization parameter give 74 °C.

Try it

▶ Open in the equation explorer: Junction temperature through a series thermal path
Preset from the example bench-thermal

Sweep the heat sink’s resistance: in the example it is the largest in the chain, and the junction follows it. Lowering the junction-to-case resistance instead moves the junction far less there.

Bench exercise

Run a converter at full load until its temperatures settle, and find each device’s power from the loss model. The measured input less output is the whole converter’s loss, every switch, diode, magnetic part and capacitor and the control circuit together: it checks the loss model’s total, not any one device’s power. For a switch on a heat sink, measure the ambient and estimate the junction through the series path. For a device without a heat sink (a controller, or a surface-mount switch cooled by its board), measure the top of its package and estimate the junction with the data sheet’s characterization parameter: set a thermal camera to the surface’s emissivity, and keep a thermocouple’s wire from drawing heat off a small package. Compare each estimate with what the data sheet’s junction-to-ambient resistance would predict.

Gotchas

• The junction-to-ambient resistance belongs to the board and airflow it was measured with, and is often misused [Texas Instruments 2003].
• A characterization parameter is not a thermal resistance: do not add it into a series path [Texas Instruments 2003].
• Loss estimated at room temperature is too low: the on-resistance rises with the junction’s temperature [Advanced Power Technology 2006].

Go deeper

• Application note Semiconductor and IC Package Thermal Metrics (SPRA953) — Texas Instruments · retrieved 2026-09-24
  What the thermal resistances and characterization parameters on a data sheet mean, how they are measured, and how they are misused.
• Application note Understanding Thermal Dissipation and Design of a Heatsink (SLVA462) — Texas Instruments · retrieved 2026-09-24
  The thermal path from a junction to the air, and sizing a heat sink from it.
• Application note Power MOSFET Tutorial (APT-0403) — Advanced Power Technology (Microchip) · retrieved 2026-09-24
  A power MOSFET's structure, its data sheet's parameters and how they change with temperature.

Quiz

1. A device dissipates 3 W in 25 C air through 2, 1 and 12 K/W in series (junction-case, case-sink, sink-air). What is its junction temperature?

   1. 45 C
   2. 61 C
   3. 100 C
   4. 70 C
   Answer and explanation

   Correct answer: D The rises add: 3 W times 15 K/W is 45 K, so the junction sits 45 K above 25 C.

2. Which change lowers that junction temperature most?

   1. A heat sink of half the resistance
   2. An interface of half the resistance
   3. A device with half the junction-to-case resistance
   4. All three the same
   Answer and explanation

   Correct answer: A The heat sink's is the largest resistance and takes the largest share of the rise: halving it saves 18 K, the others 1.5 K and 3 K.

3. What does a data sheet's junction-to-ambient resistance describe?

   1. The junction-to-ambient path on any board
   2. Only the package itself
   3. The whole path to the air as the device was measured, board and airflow included
   4. The heat sink it needs
   Answer and explanation

   Correct answer: C It is the most commonly reported metric and often misused: it belongs to the conditions it was measured in.

4. A device without a heat sink dissipates 1.5 W, its package top reads 70 C, and the data sheet gives a junction-to-top parameter of 4 K/W. What is the junction temperature?

   1. 70 C
   2. 64 C
   3. 100 C
   4. 76 C
   Answer and explanation

   Correct answer: D The top temperature plus the parameter times the whole power: 70 C plus 6 K.

5. Why is the junction-to-top parameter not added into a series thermal path?

   1. It is not a true thermal resistance: only part of the power flows through the package top
   2. It is always zero
   3. It is measured in another unit
   4. It already includes the heat sink
   Answer and explanation

   Correct answer: A It relates two temperatures to the whole power, most of which leaves by other paths.

6. Why estimate a switch's conduction loss at its hot junction temperature?

   1. The current falls when it is hot
   2. Its on-resistance rises with temperature, by the factor the data sheet's normalized curve gives
   3. Conduction loss does not depend on temperature
   4. The gate charge rises
   Answer and explanation

   Correct answer: B A loss estimated at room temperature is too low, and the extra loss heats the junction further.