What Is Tjmax? Thermal Resistance and Thermal Design

With increasing demand for miniaturization and higher performance in electronic devices, more and more components are being integrated on a single board. Thermal design is becoming ever more important as a result. Failure to pay attention to thermal design not only results in worsened component performance and lower manufacturing efficiency but can also lead to serious problems such as ignition and fires. Therefore, understanding temperature ratings such as T_jmax (maximum junction temperature) is essential to optimize thermal design.

This article details the concept of T_jmax, key points of thermal design, and calculation methods. Use this as a reference for safer and more efficient thermal design.

What are Tjmax and other temperature ratings?

The following temperatures are specified for electronic components:

Junction temperature (Tj)

“Junction” refers to the pn junction of semiconductor devices, and the temperature of the pn junction is called the junction temperature.

T_jmax is the maximum rating of the junction temperature T_j. If electronic equipment components heat up to a temperature exceeding the T_jmax value, it may affect the performance and life of the equipment and in the worst case, it may cause serious failures due to thermal runaway. Therefore, when designing a product it is necessary to take measures such as suppressing heat generation or using cooling means to prevent components from exceeding T_jmax. T_jmax is specified for each product, so check the product specifications on the distributor’s website.

Case temperature (Tc)

Case temperature (T_c or T_case) refers to the temperature of the package surface of an electronic component or device. The maximum case temperature (T_cmax) is specified for each product. In the design process, the T_cmax as well as T_jmax should not be exceeded. Note that T_c values can vary greatly depending on the measurement method, and accurate temperature measurement may be difficult.

Ambient temperature (Ta)

T_a is the temperature of the air around electronic components and equipment during natural air cooling. If T_a exceeds the specified range, devices may malfunction or the device life may be shortened. Therefore, to ensure stable operation, the operating environment must be arranged such that T_a is maintained within the specified range. In particular, note that T_a tends to rise in enclosed spaces.

Thermal resistance and thermal design

Proper thermal design requires an understanding of heat conduction paths and thermal resistance. The following is an explanation of thermal design that includes these factors.

Why is thermal design important?

As high-density mounting becomes more common, it is important to consider heat generation density in thermal design.

If thermal design is not done properly and a thermal design problem is discovered just before mass production of the product, components may need to be replaced or the thermal design may need to be reconsidered, leading to significant amounts of rework. Failure to deliver products on time can also affect related processes, increasing costs and potentially resulting in significant losses.

On the other hand, if products are shipped with thermal design problems, it may cause recalls and human life-threatening problems. It is necessary to be fully aware of the effects of such thermal design errors and incorporate appropriate thermal design from the initial design stage.

Heat conduction and thermal resistance

As basic knowledge of thermal design, it is important to understand heat conduction, thermal resistance, and heat dissipation. There are three modes of heat propagation, which are conduction, convection, and emission, and heat is dissipated through various paths. Thermal resistance is the difficulty of heat propagation, and is expressed using R_th and θ, with the units of °C/W (K/W). Heat propagation and thermal resistance calculations are shown below.

・ Conduction
Heat transfer occurs when the motion of molecules arising due to thermal energy is transmitted to neighboring molecules.
Thermal resistance (R_th) = Length of conducting material/(cross-sectional area x thermal conductivity)

Cross-sectional area: Contact area when the surrounding area is an adiabatic material.
Thermal conductivity: Material-intrinsic value.

・ Convection
Heat transfer occurs due to the flow of materials such as air and water.
Thermal resistance (R_th) = 1/ (convective heat transfer coefficient x object surface area)

Convective heat transfer coefficient: Depends on whether natural or forced convection occurs, and other factors

・Emission (radiation)
Heat transfer is caused by electromagnetic waves.
Thermal resistance (R_th) = 1/ (radiative heat transfer coefficient x object surface area)

Radiative heat transfer coefficient: Depends on the material-intrinsic surface emissivity and the temperature.

From the above equations for thermal resistance, we see that thermal resistance in heat conduction depends on the length, cross-sectional area and thermal conductivity of the conducting material. Thermal resistance in convection is affected by the surface area of the object, and thermal resistance in emission is affected by the surface area, temperature, and emissivity of the object. The basis of thermal design is reducing the thermal resistance of the heat dissipation paths.

In thermal design, one determines the target thermal resistance value and takes measures to achieve it. The thermal resistance is lower for a PCB with more layers, and it also varies depending on the orientation of the PCB (horizontal or vertical) and the PCB mounting position. There are many other factors that affect thermal resistance, and detailed simulations are required to prevent thermal design problems.

How to calculate junction temperature (Tj)

T_j can be calculated using either the ambient temperature, the case temperature, or the transient thermal resistance characteristics. Each calculation method is explained below.

Calculation using ambient temperature

T_j can be calculated using the ambient temperature and power consumption. The calculation equation is as follows.

\( T_j = T_a + R_{th(j-a)} \times P \)

Here T_a is the ambient temperature, R_{th (j-a)} is the thermal resistance between the junction and the atmosphere, and P is the power consumption.

When calculating T_j using the ambient temperature, the thermal resistance of the atmosphere at the junction must be considered in addition to that of the junction. The actual thermal resistance values between the junction and the atmosphere vary for each PCB on which IC chips are mounted.

If the power consumption varies with time, T_j is generally approximated by using the average value of the power consumption. As can be seen from the equation, T_j increases in proportion to power consumption, and T_j can be determined according to power consumption. As a result, the allowable power can be calculated.

Calculation using case temperature

T_j can be calculated using the case temperature as follows.

\( T_j = T_c + R_{th(j-c)} \times P \)

Here T_c is the case temperature, R_{th (j-c)} is the thermal resistance between the junction and the case, and P is the power consumption.

As in the case of calculation using the ambient temperature, if the power consumption varies with time, T_j is approximated by using the average value of the power consumption.

For calculations using the case temperature, it should be noted that the value of R_{th (j-c)} can vary significantly depending on the PCB and heat dissipation conditions, making it difficult to accurately measure the case temperature. Even for boards mounted in-house, the measured values vary from board to board, and if measurements from other companies’ board are used, accurate values may not be obtained. Also, the values will vary depending on the method used to measure the case temperature on the package surface. So if it is difficult to measure R_{th (j-c)} or case temperature, the other calculation methods are preferable.

Calculations using transient thermal resistance characteristics

When calculating T_j using transient thermal resistance, the same equation can be used as in the case of calculation using ambient temperature.

\( T_j = T_a + R_{th(j-a)} \times P \)

While calculation based on ambient temperature assumes continuous application of power, calculation based on transient thermal resistance assumes instantaneous application of power. The increase in T_j when instantaneous power is applied is estimated based on transient thermal data.

T_j rises in proportion to the duration of power application, but after a certain time, thermal saturation occurs, and the temperature stops rising. When power is applied continuously, the average value of power consumption is used in calculation, so the resulting value reflects the occurrence of thermal saturation. Although the equation is the same, there is a difference between instantaneous and continuous application of power.

Incorporate thermal design in an early development stage

Thermal design has become an extremely important process in the development of electronic equipment that grows ever smaller while achieving higher performance. This has led to the introduction of a “front-loading” approach, in which thermal design is introduced early in the design process.

In front-loading, thermal simulations are performed in an early design stage to prevent product defects and avoid the need for rework such as debugging and design changes. Various thermal simulation models are now available to perform highly accurate thermal simulations for front-loading. Although not all manufacturers provide products equivalent to thermal simulation models, it is recommended that you take a look at some of the most common simulation models, in the light of the explanation of this article.

For more information on thermal design, see the following articles.

• ・About Thermal Design
• ・Collection of Important Points Relating to Thermal Design