# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 180

168
α
Fig. 4.10
Thermal lateral spread ina flat plate
The thermal resistance of the thermal conductor in which lateral spread occurs can be
moreor less stated for aquadratic heat sourceas:
2
in
out
th
)
tan d2 a(
d
A
d
R
α ⋅ ⋅ + ⋅λ
=
⋅λ
Eq. 4.12
a
in
:
Edge length of theentry surfaceA
in
[m]
α
represents a property of the thermal conductor.
References
and
may be of assistance in calculation. If there are several
layers of different materials, the R
th
of each layer must be determined individually and
then all the values combined to give the total thermal resistance.
hows a
simpleexamplewith two layers.
Fig. 4.11
Thermal lateral spread ina designwith two layers of different materials
2
in
in
a A
=
, for the first
material layer there is thermal resistanceof:
2
1
1
in 1,th
1
1,th
)
tan d2 a(
d
R
α ⋅ ⋅ + ⋅
λ
=
For the second material layer, the lateral spread causes a greater entry surface of
2
1
1
in
1, out
2, in
)
tan d2 a(
A A
α ⋅ ⋅ + = =
, which creates a thermal resistance for the second
layer of
2
2
2
1
1
in 2,th
2
2,th
)
tan d2
tan d2 a(
d
R
α ⋅
⋅ +α ⋅ ⋅ + ⋅
λ
=
1...,170,171,172,173,174,175,176,177,178,179 181,182,183,184,185,186,187,188,189,190,...548