Thermal resistance in electronics
Encyclopedia
Thermal resistance is a heat property - and a measure of a temperature difference, by which an object - or material resist a heat flow (heat per time unit or thermal resistance). Thermal resistance is the reciprocal thermal conductance.
difference across a structure when a unit of heat
energy flows through it in unit time
. It is the reciprocal of thermal conductance. The SI
units of thermal resistance are kelvin
s per watt
, or the equivalent degrees Celsius per watt (the two are the same since as intervals 1 K = 1 °C).
The thermal resistance of materials is of great interest to electronic engineers, because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.
The heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, absolute thermal resistances are represented by resistors and thermal capacitances by capacitors.
The diagram shows an equivalent thermal circuit for a semiconductor device with a heat sink
.
), and the maximum allowable temperature of the semiconductor junction (symbol: 
). The specification for the design should include a maximum temperature at which the circuit should function correctly. Finally, the designer should consider how the heat from the transistor will escape to the environment: this might be by convection into the air, with or without the aid of a heat sink
, or by conduction through the printed circuit board
. For simplicity, let us assume that the designer decides to bolt the transistor to a metal surface (or heat sink
) that is guaranteed to be less than
above the ambient temperature. Note: THS appears to be undefined.
Given all this information, the designer can construct a model of the heat flow from the semiconductor junction, where the heat is generated, to the outside world. In our example, the heat has to flow from the junction to the case of the transistor, then from the case to the metalwork. We do not need to consider where the heat goes after that, because we are told that the metalwork will conduct heat fast enough to keep the temperature less than
above ambient: this is all we need to know.
Suppose the engineer wishes to know how much power he can put into the transistor before it overheats. The calculations are as follows.
where
is the absolute thermal resistance of the bond between the transistor's case and the metalwork. This figure depends on the nature of the bond - for example, a thermal bonding pad or thermal transfer grease might be used to reduce the absolute thermal resistance.
We use the general principle that the temperature drop
across a given absolute thermal resistance 
with a given heat flow 
through it is:
.
Substituting our own symbols into this formula gives:
,
and, rearranging,
The designer now knows
, the maximum power that the transistor can be allowed to dissipate, so he can design the circuit to limit the temperature of the transistor to a safe level.
Let us plug in some sample numbers:
(typical for a silicon transistor)
(a typical specification for commercial equipment)
(for a typical TO-220 package)
(a typical value for an elastomer
heat-transfer pad for a TO-220 package)
(a typical value for a heatsink for a TO-220 package)
The result is then:
This means that the transistor can dissipate about 9 watts before it overheats. A cautious designer would operate the transistor at a lower power level to increase its reliability
.
This method can be generalised to include any number of layers of heat-conducting materials, simply by adding together the absolute thermal resistances of the layers and the temperature drops across the layers.
, the following equation can be derived, and is valid as long as all of the parameters (x, A, and k) are constant throughout the sample.
where:
- Specific thermal resistance or specific thermal resistivity Rλ in (K·m)/W is a material constant.
- Absolute thermal resistance Rth in K/W is a specific property of a component. It is e.g. a characteristic of a heat sinkHeat sinkA heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...
.
Absolute thermal resistance
Absolute thermal resistance is the temperatureTemperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
difference across a structure when a unit of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
energy flows through it in unit time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
. It is the reciprocal of thermal conductance. The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units of thermal resistance are kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
s per watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
, or the equivalent degrees Celsius per watt (the two are the same since as intervals 1 K = 1 °C).
The thermal resistance of materials is of great interest to electronic engineers, because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.
Equivalent thermal circuits
The diagram shows an equivalent thermal circuit for a semiconductor device with a heat sink
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...
.
Example calculation
Consider a component such as a silicon transistor that is bolted to the metal frame of a piece of equipment. The transistor's manufacturer will specify parameters in the datasheet called the absolute thermal resistance from junction to case (symbol:), and the maximum allowable temperature of the semiconductor junction (symbol: ). The specification for the design should include a maximum temperature at which the circuit should function correctly. Finally, the designer should consider how the heat from the transistor will escape to the environment: this might be by convection into the air, with or without the aid of a heat sinkHeat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...
, or by conduction through the printed circuit board
Printed circuit board
A printed circuit board, or PCB, is used to mechanically support and electrically connect electronic components using conductive pathways, tracks or signal traces etched from copper sheets laminated onto a non-conductive substrate. It is also referred to as printed wiring board or etched wiring...
. For simplicity, let us assume that the designer decides to bolt the transistor to a metal surface (or heat sink
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...
) that is guaranteed to be less than
above the ambient temperature. Note: THS appears to be undefined.Given all this information, the designer can construct a model of the heat flow from the semiconductor junction, where the heat is generated, to the outside world. In our example, the heat has to flow from the junction to the case of the transistor, then from the case to the metalwork. We do not need to consider where the heat goes after that, because we are told that the metalwork will conduct heat fast enough to keep the temperature less than
above ambient: this is all we need to know.Suppose the engineer wishes to know how much power he can put into the transistor before it overheats. The calculations are as follows.
- Total absolute thermal resistance from junction to ambient =
where
is the absolute thermal resistance of the bond between the transistor's case and the metalwork. This figure depends on the nature of the bond - for example, a thermal bonding pad or thermal transfer grease might be used to reduce the absolute thermal resistance.- Maximum temperature drop from junction to ambient =
.
We use the general principle that the temperature drop
across a given absolute thermal resistance with a given heat flow through it is:.Substituting our own symbols into this formula gives:
,and, rearranging,
The designer now knows
, the maximum power that the transistor can be allowed to dissipate, so he can design the circuit to limit the temperature of the transistor to a safe level.Let us plug in some sample numbers:
(typical for a silicon transistor) (a typical specification for commercial equipment) (for a typical TO-220 package) (a typical value for an elastomerElastomer
An elastomer is a polymer with the property of viscoelasticity , generally having notably low Young's modulus and high yield strain compared with other materials. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber, although the latter is preferred...
heat-transfer pad for a TO-220 package)
(a typical value for a heatsink for a TO-220 package)The result is then:
This means that the transistor can dissipate about 9 watts before it overheats. A cautious designer would operate the transistor at a lower power level to increase its reliability
Reliability engineering
Reliability engineering is an engineering field, that deals with the study, evaluation, and life-cycle management of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is often measured as a probability of...
.
This method can be generalised to include any number of layers of heat-conducting materials, simply by adding together the absolute thermal resistances of the layers and the temperature drops across the layers.
Derived from Fourier's Law for heat conduction
From Fourier's Law for heat conductionHeat conduction
In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....
, the following equation can be derived, and is valid as long as all of the parameters (x, A, and k) are constant throughout the sample.
where:
-
is the absolute thermal resistance (across the length of the material) (K/W) - x is the length of the material (measured on a path parallel to the heat flow) (m)
- k is the thermal conductivity of the material ( W/(K·m) )
- A is the total cross sectional area of the material (measured perpendicular to the heat flow) (m2)