Once the maximum acceptable junction
temperature of the device and the ambient
temperature have been defined, it is
necessary to calculate the maximum thermal
resistance for the Heat Sink which is
acceptable if the required junction
temperature is not to be exceeded.
The basic equation for thermal equilibrium
is:
|
|
Power dissipated =
|
|
Temperature
difference across the system
|
|
-------------------------------------------------------------------------
|
|
Sum of the thermal
resistance in the heat flow path
|
|
|
P =
|
|
Tj - Ta
|
|
--------------------------------------------
|
|
Ø jc
+ Ø cs + Ø sa
|
|
|
|
|
P =
|
Power Dissapation
(W)
|
|
Tj =
|
Max. allowable
junction temp. (°C), specified
by manufacturer
|
|
Ta =
|
Ambient temperature
(°C)
|
|
Ø jc =
|
Thermal resistance,
junction to
case (°C/W), specified by
manufacturer
|
|
Ø cs =
|
Thermal resistance,
case to sink (°C/W)
|
|
Ø sa =
|
Thermal resistance,
sink to
ambient air (°C/W)
|
|
| In practice it is only the
value of Ø Cs which can be improved
(by the use of jointing compound) and of
Ø sa (by the use of a higher performance
sink or a greater air flow rate). ocs can
vary between 0.1 and 1.5°C/W depending
on the use of thermal jointing compound,
and / or insulation washers: a dry mica
washer could give 1 .5°C/ W and a similar
washer using compound 0.5°C/W If the
insulating washer is eliminated and instead
the whole sink assembly is electrically
isolated, the use of compound between device
and sink can reduce the value of Ø
cs to 0.1 / 0.2°C/W
The maximum value for thermal resistance,
sink to air (Ø sa), is determined
by the following equation:
|
Ø sa =
|
Tj - Ta
|
- ( Ø
jc + Ø cs ) |
|
----------------------
|
|
P
|
The result of this calculation provides
a thermal resistance value which must
be equalled or bettered by the Heat Sink
selected for the duty.
Example:
A semi-conductor is to be operated with
its junction temperature not exceeding
135°C whilst dissipating 14.50 watts
to ambient air at a temperature of 45°C.
The thermal resistance, junction to case,
is specified by the manufacturer as 2.25°C/W
and the thermal resistance, case to sink
and using an insulating washer and compound
is calculated as 0.5O°C/W
Thus:
|
Ø sa =
|
135 - 45
|
- ( 2.25
+ 0.50 ) = 3.46°C/W. |
|
----------------------
|
|
14.50
|
The Heat Sink, therefore, must have a
thermal resistance rating which does not
exceed 3.46°C/W. Elimination of the
insulating washer and isolation of the
whole assembly could improve the figure
to approx. 3.8°C/W.
|
