# Using the Thermal Resistance Equation

### Key Takeaways

• An electrical analogy based on thermal resistance is a convenient and appropriate method to analyze heat transfer problems in electronics.

• The thermal resistance of a component indicates how much it can be heated under various loads and how effectively the heat can be removed by using various cooling techniques.

• In semiconductors, thermal resistance is the measure of the ability of the device to transfer heat from the junction to the package and then to the ambient.

Proper electronic cooling mechanisms are required for removing heat from components

In electronics, qualitative estimation of heat flow is helpful for conducting a feasibility analysis of electronic components. The design of a component varies with the heat generation in a circuit. Proper electronics cooling mechanisms are required for removing heat from components. Various engineering approaches can be utilized for estimating the heat generated in each component and to plan the best cooling method.

Thermal resistance-based electrical equivalent circuits are appropriate for determining the heat energy generated. To develop a network, the thermal resistance equation can be used to find out the thermal resistance of each component essential for developing the equivalent network. In this article, we will discuss thermal resistance and its related equations further.

## Electrical Analogies Using Thermal Resistance

An electrical analogy based on thermal resistance is a convenient and appropriate method to analyze heat transfer problems in electronics. Thermal resistance-based electrical equivalent circuits make it easy to visualize heat transfer problems. In these analogies, the temperature and heat is analogous to voltage and current in an electrical circuit. When the thermal resistance of components are known, an electrical equivalent circuit can be developed.

Depending on the internal structure, the thermal resistance of a component can be a combination of various thermal resistances. Before describing the different thermal resistances associated with an electronic component, let’s describe thermal resistance.

## Thermal Resistance

Similar to electrical resistance, which resists the flow of electric current, thermal resistance opposes the flow of heat through electronic components. The thermal resistance of a component  indicates how much it can be heated under various loads and how effectively the heat can be removed by using various cooling techniques.

Thermal resistance is usually expressed as Celsius per Watt or Kelvin per Watt. The thermal resistance is usually denoted by θ or Rth and can be given by equation:

Note that ΔT is the temperature difference driving the heat flow and P is the power dissipated in Watts.

## The Thermal Resistance Equation

Thermal resistance can be conveyed using several expressions. The expression varies with the dependency of the heat flow with temperature and the mode of heat transfer. The thermal resistance of an electronic component is different when the heat is transferred via conduction, convection, radiation, or a combination of them.

Let’s consider a one-dimensional (1-D) steady state heat transfer problem in electronics where heat flow is proportional to the temperature difference. Heat flow can be given by the following equation:

In the above equation, Q is the heat flow, k is the thermal conductivity, A is the area perpendicular to the heat flow, and Δx is the heat flow distance. Applying Ohm’s law on the electrical analogy of the component of interest, the temperature difference analogous to voltage can be expressed as:

From the above equation , thermal resistance can be written as:

Substituting the second equation in the fourth equation, thermal resistance can be expressed as:

Per the last equation, the value of thermal resistance varies with the size, shape, and area of the electronic component under consideration. It is important to design electronic components with  the thermal power dissipation, voltage, and current rating in mind.

### Heat Generation in Semiconductor Electronics

Heat generation is critical for the functioning and lifespan of a component. Implementation of a proper cooling mechanism is mandatory in electronic circuits where the excessive heat generated can damage the circuit when left unattended.

In semiconductor electronics, heat is generated at the source before spreading outside and dissipating to the ambient air. A semiconductor junction can handle heat only upto a temperature called the maximum temperature. Whenever the heat exceeds the maximum temperature, the semiconductor junction becomes thermally unstable and the device is burned off.

## Thermal Resistance in Semiconductor Electronic Components

In semiconductor devices, thermal resistance is the rise in temperature when a power of 1 watt is dissipated in it. In semiconductor devices, heat flows from the junction to the package and from the package to the ambient. In semiconductors, thermal resistance is the measure of the ability of the device to transfer heat from the junction to the package and then to the ambient. The junction, package, and ambient are three points of different temperatures that define three different thermal resistances.

Junction to Ambient Thermal Resistance, ΘJA: The thermal resistance from the junction to ambient is the measure of the semiconductor component’s ability to dissipate heat energy from the surface of the die to the ambient via all paths.

Junction to Case Thermal Resistance, ΘJC: The thermal resistance from the junction to the case (package) represents the resistance to the flow of thermal energy to the semiconductor  package surface through a specific conductive thermal path.

Case to Ambient Thermal Resistance, ΘCA: The thermal resistance from case to ambient takes into account all thermal paths from the external package surface to the ambient. Knowing the values of ΘJC and ΘCA, the thermal resistance from junction to ambient can be determined using the equation:

## ΘJA=ΘJC+ΘCA

It is hard to find electronic circuits without semiconductor components such as integrated circuits, solid-state relays, and power electronic switches. Thermal resistance equations can be utilized for finding out the thermal resistance of these components to model the electrical analogy for thermal performance analysis.

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