APPLICATION NOTE # B
Thermal resistance
This article introduces a definition of thermal resistance and deals with the ways in which it can be
measured. Furthermore the last part of the article concerns the difference between resistance in parallel
and resistance in series.
How to measure thermal resistance
Heat sinks are devices that enhance heat dissipation from a hot surface, usually the case of a heat
generating component, to a cooler ambient, usually air. The primary purpose of a heat sink is to
maintain the device temperature below the maximum allowable temperature specified by the
device.
The relationship between the reliability and the operating temperature of a generical device
shows that a reduction in the temperature corresponds to an effective increase in the reliability
and life expectancy of the device. Therefore, long life and reliable performance of a component
may be achieved by effectively controlling the device operating temperature within the limits set
by the device design producers.
Heat flows from a high temperature (T1) to a relatively lower one (T2) at a rate determined by the
thermal resistance (R12) between the two points (see Figure B1).
Thermal resistance R 
T T2  T1

Q
Q
C / W 
T : Temp. difference between two points.
Figure B1. Thermal resistance (R12) between the two points.
This thermal resistance is analogous to the electrical resistance Re, given by Ohm’s law:
Ohm’s law :
Re 
V
I
With V being the voltage difference and I the current.
This document is PRIATHERM's intellectual property. It must not be used for any purpose other
than which it is disclosed. Complete or partial reproductions are forbidden without written permission from the owner
-1-
APPLICATION NOTE # B
For the following discussions, air is assumed to be the cooling fluid. The solid-air interface
represents the greatest barrier for heat dissipation. A heat sink lowers this barrier mainly by
increasing the surface area that is in direct contact with the coolant. This allows more heat to be
dissipated and lowers the device operating temperature.
Consider a simple case where a heat sink is mounted on a device package as shown in Figure B2.
Then, we can simplified this configuration system using the concept of thermal resistance as
shown in the figure. In this simplified model, heat flows serially from the junction to the case then
across the interface into the heatsink and is finally dissipated from the heat sink to the air stream.
Figure B2: Thermal resistance chain.
Let's define some terms on the figure and some of the necessary parameters:
Q : Total Power of heat dissipation in W
TJ : Maximum Junction Temperature in °C
TC : Maximum Case Temperature in °C
TS : Maximum Heatsink Temperature in °C
TA*1 : Ambient Temperature in °C
*1
By TA we mean ambient temperature, that is the temperature of the cooling fluid at a certain distance from the
heatsink and in a condition of undisturbed fluid.
This document is PRIATHERM's intellectual property. It must not be used for any purpose other
than which it is disclosed. Complete or partial reproductions are forbidden without written permission from the owner
-2-
APPLICATION NOTE # B
Many definitions of thermal resistance can be given depending on the point where temperature
and consequently T are measured:
Table B1. Definitions of thermal resistance
Parameter
RJA
RJC
RCS
Name
Junction-to-ambient thermal resistance
Junction-to-case thermal resistance
Case-to-heat-sink thermal resistance
Units
o
C/W
o
C/W
o
C/W
RCA
RSA
Case-to-ambient thermal resistance
Heat-sink-to-ambient thermal resistance
o
C/W
C/W
o
Description
Specified in the data sheet
Specified in the data sheet
Thermal interface
material thermal resistance
Specified by the heat sink
manufacturer
If we get the sum of all thermal resistances and called RJA (Junction to Ambient thermal
resistance);
RJA = RJC + RCS + RSA
so;
TJA = TJ - TA
TJA = Q  RJA
We can find :
RJA = (TJ - TA) / Q
RJC = (TJC)/Q = (TJ- TC)/Q
This resistance is specified by the device producer.
Similarly, case-to-sink and sink-to-ambient resistance are defined as:
RCS = (  TCS)/Q = (TC- TS)/Q
RSA = (  TSA)/Q = (TS- TA)/Q
respectively. Rcs represents the thermal resistance across the interface between the case and the
heat sink. This value can be improved substantially depending on the quality of mating surface
finish and/or the choice of interface material.
This document is PRIATHERM's intellectual property. It must not be used for any purpose other
than which it is disclosed. Complete or partial reproductions are forbidden without written permission from the owner
-3-
APPLICATION NOTE # B
The total junction-to-ambient resistance is the sum of all three resistances:
RJA = RJC + RCS + RSA= (TJ – TA)/Q
So that :
(TJ(max) - TA) / Q ≥ RJA
In conclusion:
Table B2.
Device
Without a heat sink
With a heat sink
Equation
RJA = RJC + RCA = (TJ - TA) / P
RJA = RJC +RCS +RSA = (TJ - TA) / P
Thermal Resistance in series and parallel

It is possible to compare heat transfer to current flow in electrical circuits. The analog of Q is
current, and the analog of the temperature difference,  T = (T1 –T 2), is voltage difference. From
this perspective the slab is a pure resistance to heat transfer and we can define:

Q
T1  T2
R
where R is the thermal resistance.
Series thermal resistance: the conduction between two bodies in series takes place as if there
were two resistance in series between the bodies.
Parallel thermal resistance: when two bodies are placed side by side heat transfer by conduction
takes place as if the two bodies were two resistance in parallel.
This document is PRIATHERM's intellectual property. It must not be used for any purpose other
than which it is disclosed. Complete or partial reproductions are forbidden without written permission from the owner
-4-
APPLICATION NOTE # B
Q
T1  T3
R1  R2
Figure B3. Example of series thermal resistance
Q
T1  T2
1
1
1

R1 R2
Figure B4: Example of parallel thermal resistance.
This document is PRIATHERM's intellectual property. It must not be used for any purpose other
than which it is disclosed. Complete or partial reproductions are forbidden without written permission from the owner
-5-