Budapest, Hungary, 17-19 September 2007
?EDA Publishing/THERMINIC 2007 -page- ISBN: 978-2-35500-002-7
A New Methodology for Extraction of Dynamic
Compact Thermal Models
W. Habra
a, c
, P. Tounsi
a
, F. Madrid
a
, Ph. Dupuy
b
, C.Barbot
a
and J-M. Dorkel
a
a. LAAS-CNRS, University of Toulouse, 7 avenue du Colonel Roche - 31077 Toulouse, France.
b. Freescale Semiconductor, avenue du G?n?ral Eisenhower, 31023 Toulouse, France.
c. University of Aleppo, Faculty of Electronics Engineering. Aleppo - Syria.
Abstract-An innovative and accurate dynamic Compact
Thermal Model extraction method is proposed for multi-chip
power electronics systems. It accounts for thermal coupling
between multiple heat sources. Transient electro-thermal
coupling can easily be taken into account by system designers.
The method is based on a definition of the Optimal Thermal
Coupling Point, which is proven to be valid even for transient
modelling. Compared to the existing methods, the number of
needed 3D thermal simulations or measurements is significantly
reduced.
I. INTRODUCTION
An innovative methodology for power components
manufacturers to generate accurate dynamic Compact
Thermal Models (CTMs) is proposed in this paper. This
allows providing customers (automotive systems suppliers)
with extended datasheets including CTMs, without
publishing any confidential information about technology,
device structures nor materials. The combination of
electrical models with CTMs permits automotive power
electronics systems engineers to optimize electro-thermal
coupling during the design. Embedded electronic system
manufacturers will efficiently improve the working
conditions of their systems while taking into account thermal
phenomena. This leads to increase the reliability of the
electronic systems in the expanding market of electronics for
automotive applications. The figure 1 shows an example of a
power transistor electro-thermal block; a simple coupled
thermal circuit takes account of temperature effects to the
electrical device behaviour. The CTMs produced by the
proposed method are accurate and easy to consider for
electro-thermal coupling prediction.
Fig. 1. Electro-thermal VHDL-AMS model.
The method is specially conceived for multi-chip devices,
i.e., multiple coupled heat sources [1]. The thermal coupling
is based on a definition of an Optimal Thermal Coupling
Point (OTCP). This point helps to realize the thermal
coupling between heat sources in Boundary Condition
Independent (BCI) static CTM [2]. The extension to
transient mode can be easily achieved and the coupling
points are still valid.
II. THERMAL SIMULATION AND CHARACTERIZATION
An example of generating dynamic CTM is presented. The
model of a multichip power module manufactured by
Freescale? is extracted from 3D thermal transient
simulations using COMSOL multiphysics. The characterized
device is a new intelligent power component (figure 2) for
automotive applications, containing four smart MOSFETs.
These switches are controlled by a logical unit integrated in
the same package. The resulting model will provide the
system manufacturer with a model that is capable to show
the thermal effects between transistors in operation
conditions. This CTM will cover customer design needs in a
simple way.
a)
b)
Fig. 2. Modeled device: a) Bottom face schema, b) Mounted on a PCB.
Budapest, Hungary, 17-19 September 2007
?EDA Publishing/THERMINIC 2007 -page- ISBN: 978-2-35500-002-7
The multichip device drawn in figure 3 is simulated in
various dissipation conditions of the MOSFETs providing
transient temperature evolution on every chip composing the
assembly. Example results are shown in figure 4.
Fig. 3. Model of the multi-chip component with active MOSFETs HS0,
HS2, HS3 and HS4.
Fig. 4. Example of 3D resulting temperature mapping after 100s, only HS1
dissipating.
As seen in figure 3, the system is symmetric. This
geometry simplifies the task as only two transient thermal
simulations are necessary for the four heat sources CTM
generation.
A. Extracting the compact thermal model
As said above, the thermal coupling between heat sources
is based on the OTCP. This point is extracted by dissipating
the power in one of the sources and taking the temperature of
active and inactive heat sources. Then, this process is
repeated swapping the heat sources. Knowing the dissipated
power in every case, the steady state CTM can be extracted
from the equilibrium temperature of the junction.
Results of simulations providing the transient temperature
response of the MOSFETs are shown in figure 5 a) and b).
The steady state (equilibrium) temperatures are in table I.
1E-3 0,01 0,1 1 10 100
0
5
10
15
T
e
m
p
er
at
ur
e ?
C
Time s
HS2 or HS3
HS1 or HS0
HS0 or HS1
HS3 or HS2
CTM
a)
1E-3 0,01 0,1 1 10
0
5
10
T
e
m
per
at
ur
e ?
C
Time s
HS0 or HS1
HS3 or HS2
HS1 or HS0
HS2 or HS3
CTM
b)
Fig. 5. Results of transient simulations obtained from COMSOL 3D and
fitting process applied on the CTM: a) HS2 or HS3 dissipating 1W and b)
HS0 or HS1 dissipating 1W.
TABLE I
Equilibrium temperatures corresponding to transient thermal simulations
of figure 5 a) and b).
Power =1W
HS0 HS1 HS2 HS3
HS0 12.2 11.05 10.62 11.41
HS1 11.05 12.2 11.41 10.62
HS2 10.57 11.62 13.06 10.23
Te
m
p
.
(?
C)
HS3 11.62 10.57 10.23 13.06
The thermal model (junction-ambient) is represented as
several thermal resistances in series, one for each junction,
as seen in figure 6. In order to consider the interactive effect
between heat sources the following procedure is applied:
First, for the case that only the device HS0 is dissipating, the
result from figure 5 b) is considered. The element HS0 is the
hottest, followed by devices HS3, HS1 and HS2. This is the
order in which they are represented as nodes in the HS0
branch in figure 6. Each node in this figure is defined as
coupling point between devices.
Budapest, Hungary, 17-19 September 2007
?EDA Publishing/THERMINIC 2007 -page- ISBN: 978-2-35500-002-7
a)
b)
Fig. 6. a) Steady state CTM showing the thermal coupling points. b) Heat
source temperatures resulting from the superposition of heating from every
heat source.
The thermal resistance between the node C
0
and coupling
point C
0-3
is:
P
TT
R
CC 300
)30(0
?
?
?
=
Where: T
C0
is the temperature of node C
0
, T
0-3
is the
temperature of the coupling point (C
0-3
) between HS0 and
HS3 and P is the dissipated power in the HS0 source. The
thermal resistance between coupling points C
0-3
and C
0-1
is:
P
TT
R
CC 1030
)13(0
??
?
?
=
And so for the rest of resistances in the HS0 branch:
P
TT
R
CC 2010
)21(0
??
?
?
=
P
TT
R
aCC
a
??
?
?
=
020
)2(0
Index a is for ambient.
Same procedure is carried out by dissipating power only in
device HS1. Thermal resistance values in the branch
corresponding to this device are extracted. Same method is
applied for devices HS2 and HS3. For the example described
here, the thermal resistance values in table II are obtained.
TABLE II
Thermal resistance values for all branches in fig.5 (?K/W).
HS0 HS1 HS2 HS3
R
0(0-3)
=0.4 R
1(1-2)
=0.4 R
2(2-1)
=1.65 R
3(3-0)
=1.65
R
0(3-1)
=0.57 R
1(2-0)
=0.57 R
2(1-0)
=0.79 R
3(0-1)
=0.79
R
0(1-2)
=0.48 R
1(0-3)
=0.48 R
2(0-3)
=0.39 R
3(1-2)
=0.39
R
0(2-a)
=10.57 R
1(3-a)
=10.57 R
2(3-a)
=10.23 R
3(2-a)
=10.23
As illustrated on the bottom of each branch in figure 6, the
model establishes that the temperature of each heat source is
the sum of the resulting temperature in coupling points of
every branch. For example, actual temperature of HS0
device is due to its self-heating and heating from other heat
sources, i.e., it is the sum of T
C0,
T
C1-0,
T
C2-0
and T
C3-0
.
B. Extension to dynamic models
The thermal resistance values of the static model are kept.
The coupling points are the same for this extension to a
transient model. Thermal capacitances are added at each
node of the model on figure 6 in order to model the transient
behaviour. To increase the precision of the model, each
resistance of the static model is divided into several ones in
series when its value is bigger than 10% of the total
response. The steady state behaviour of the structure, shown
in figure 7, will not be affected at all.
Then, the capacitance values are optimized to fit the
reference curves in figure 5 a) and b) by using optimization
tool that keeps into account the constant value of thermal
resistances. The dynamic model of this electronic device is
presented in figure 7.
Fig. 7. Transient CTM, resulting of the extension of the static model.
After capacitance values have been optimized to fit the
original curves in figure 5, validation of the model has been
carried out using the dissipation conditions in table III. The
model results and simulated behaviour are compared
graphically in figure 8.
TABLE III
Three combinations of different dissipation values applied on the four
MOSFETs.
Power (W)
Case
HS0 HS1 HS2 HS3
a 2 0 1 0.5
b 0 0 1 2
c 6 1 1 0
Budapest, Hungary, 17-19 September 2007
?EDA Publishing/THERMINIC 2007 -page- ISBN: 978-2-35500-002-7
It is found that the deviation of the model results
compared to COMSOL multiphysics thermal simulations
differ at maximum in 2% of its value. Then, it can be
affirmed that model results fit in good approximation the
original system thermal behaviour. These comparisons prove
that the principle of OTCP is valid even for transient
modelling.
1E-3 0,01 0,1 1 10
0
10
20
30
40
Temperatur
e ?
C
Time s
HS2
HS3
HS0
HS1
CTM
a)
1E-3 0,01 0,1 1 10
0
5
10
15
20
25
30
35
40
Tem
pera
t
ure ?
C
Time s
HS2
HS3
HS0
HS1
CTM
b)
1E-3 0,01 0,1 1 10
0
20
40
60
80
100
Temp
erature ?
C
Time s
HS2
HS3
HS1
HS0
CTM
c)
Fig. 8. Comparison between COMSOL 3D simulation and CTM results for:
a) HS0, HS1, HS2 and HS3 dissipate 2W, 0W, 1W and 0.5W respectively.
b) HS0, HS1, HS2 and HS3 dissipate 0W, 0W, 1W and 2W respectively.
c) HS0, HS1, HS2 and HS3 dissipate 6W, 1W, 1W and 0W respectively.
III. CONCLUSION
The proposed example shows that this new method is able
to extract a simple and user friendly compact model through
a repetitive network structure for components or systems
with single and multiple heat sources. One thermal
simulation for each heat source (less in case of symmetry) is
enough to generate the CTM. It is proven that the principle
of using Optimal Thermal Coupling Point (OTCP) is valid
for both steady state and transient modelling. It is possible
also to use results from measurements to extract CTMs even
if internal structure is not perfectly known [3]. In these two
cases, the number of measurements or simulations is
significantly reduced compared to traditional methodologies
to extract CTMs.
The methodology is being improved in order to be able to
model also multiple cooling surfaces being Boundary
Condition Independent (BCI). Also it would be able to deal
with temperature dependent parameters (non-linearity) [4],
while keeping a moderate number of 3D thermal simulations
or experimental curves. This enables us to simply consider
the electro-thermal modeling of complex electronic systems.
This method improves some disadvantages of other known
methods [5,6].
REFERENCES
[1] W. Habra, P. Tounsi, J.M. Dorkel. ?Transient Compact modelling
for multi chips components?. THERMINIC'2005. Belgirate, Italy,
28-30 September 2005.
[2] W. Habra, P. Tounsi, J.M. Dorkel. ?Advanced compact thermal
modelling using VHDL-AMS?. THERMINIC'2006. Nice, C?te
d?Azur, France, 27-29 September 2006
[3] M. Rencz, G. Farkas, A. Poppe, V. Szekely, B. Coutois. ?A
Methodology for the Generation of dynamic Compact Models of
packages and Heat Sinks from Thermal Transient measurements?.
IEEE. CPMT/Semi int. Electronics Manufacturing technology
symposium. 2003, pp. 117 ?123.
[4] W. Habra, P. Tounsi, J.M. Dorkel. ?Improved 3D-nonlinear
compact modeling for power components?. EuroSime'2005. p.390 ?
393.
[5] C.J.M. Lasance, H. Vinke, H. Rosten. ?Thermal characterization of
electronic devices with BCI compact Models?. IEEE Trans. On
Components, Packaging and Manufacturing Tech. Part A Vol. 18 ,
Dec. 1995, pp. 723 ?729.G.
[6] H. Rosten C.J.M. Lasance, J.D. Parry. ?The world of thermal
characterization according to DELPHI- PartI , Part II?. IEEE Trans.
On Components, Packaging and Manufacturing Tech. Part A Vol.
20 , Dec. 1997, pp. 384 ?398.
Budapest, Hungary, 17-19 September 2007
?EDA Publishing/THERMINIC 2007 -page- ISBN: 978-2-35500-002-7