This paper presents dynamic thermal analyses of a power amplifier. All the
investigations are based on the transient junction temperature measurements
performed during the circuit cooling process. The presented results include the
cooling curves, the structure functions, the thermal time constant distribution
and the Nyquist plot of the thermal impedance. The experiments carried out
demonstrated the influence of the contact resistance and the position of the
entire cooling assembly on the obtained results.Comment: Submitted on behalf of TIMA Editions
  (http://irevues.inist.fr/tima-editions

Banaszczyk, J.

De Mey, G.

Janicki, M.

Kawka, P.

Napieralski, A.

Vermeersch, B.

English

arXiv

This paper presents dynamic thermal analyses of a power amplifier. All the investigations are based on the transient junction temperature measurements performed during the circuit cooling process. The presented results include the cooling curves, the structure functions, the thermal time constant distribution and the Nyquist plot of the thermal impedance. The experiments carried out demonstrated the influence of the contact resistance and the position of the entire cooling assembly on the obtained results

I-Revues

 Nice, Côte d’Azur, France, 27-29 September 2006 
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9   
 
DYNAMIC THERMAL ANALYSIS OF A POWER AMPLIFIER 
 
Jedrzej Banaszczyk * #, Gilbert De Mey #, Marcin Janicki *, Andrzej Napieralski *,  
Bjorn Vermeersch #, Piotr Kawka # † 
 
* Department of Microelectronics and Computer Science, Technical University of Lodz,  
Al. Politechniki 11, 90-924 Lodz, Poland 
# Department of Electronics and Information Systems, University of Ghent,  
Sint Pietersnieuwstraat 41, 9000 Ghent, Belgium 
† Agilent Technologies, Pegasus Park, De Kleetlaan 12A bus 12, 1831 Diegem, Belgium 
 
 
ABSTRACT 
 
This paper presents dynamic thermal analyses of a power 
amplifier. All the investigations are based on the transient 
junction temperature measurements performed during the 
circuit cooling process. The presented results include the 
cooling curves, the structure functions, the thermal time 
constant distribution and the Nyquist plot of the thermal 
impedance. The experiments carried out demonstrated the 
influence of the contact resistance and the position of the 
entire cooling assembly on the obtained results. 
 
1. INTRODUCTION 
 
The increased density of power dissipated in the state-of-
the-art electronic devices and circuits has forced engineers 
to seek for new and innovative ways of thermal analysis  
of electronic structures. Since power circuits often operate 
in a pulsed mode, their steady state thermal conditions are 
practically never reached. Therefore, in the case of power 
amplifier analyzed here it is important to determine not 
only the steady state temperature distribution, but also its 
dynamic thermal behaviour. Then, knowing the transient 
characteristics it is possible to obtain a useful dynamic 
thermal model. 
The next section provides a brief overview of various 
methods of dynamic thermal analysis of electronic circuits 
such as: cooling curve, thermal time constant distribution, 
differential and cumulative structure function and finally 
the Nyquist plot of thermal impedance. Next, the theory  
is used in the experimental part of the paper to investigate, 
based on the example of a power amplifier, the effects  
of varying the contact resistance between the amplifier 
package and the cooling fin. This was done by loosing the 
screw or applying thermal grease. Moreover, the influence 
of the cooling fin position has been also investigated. 
2. DYNAMIC THERMAL ANALYSIS 
 
There exist several methods of representing the dynamic 
thermal behaviour of electronic structures. One of such 
methods is the structure function approach. This approach 
had been originally developed by Szekely and his research 
team. For thermal analyses in electronics, the differential 
structure functions are of a particular interest because they 
provide the incremental thermal capacitance as a function 
of the distance from the junction (heat source). The main 
advantage of this representation is that, as it will be shown 
later on, it allows the direct identification of particular 
sections of the heat path of an electronic structure, such  
as chip, package, solder or radiator. More theory on this 
subject can be found in [1]-[3]. 
Another possible method of describing the dynamic 
behaviour is to use Nyquist plots of the complex thermal 
impedance. The thermal impedance as a function of the 
angular frequency ω can be found performing the Laplace 
transform of the structure transient thermal response [4]. 
Owing to this, in most cases it is possible to determine the 
time constant distribution analytically because the Nyquist 
plots resemble a combination of circular arcs. As it was 
proved in [5], for simple geometrical shapes the Nyquist 
plot can be fitted to a circular arc with a high precision. 
For all the above described thermal analysis methods, 
it is required to take adequate temperature measurements. 
The measurements can be taken using a forward biased  
p-n junction. If the bias current is constant, the voltage 
drop across the junction is the measure of temperature. 
Usually, temperature is measured as the response to the 
power step excitation. However, this requires using the 
same junction for heating and measurement, which might 
cause some technical problems. An alternative method, 
used also in this paper, is to heat the junction till steady 
state is reached and to switch the power off. In this way  
a cooling curve is obtained, which is just the complement 
of the heating curve and contains the same information. 
J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka 
Title. Dynamic Thermal Analysis of a Power Amplifier 
 
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9   
 
Fig. 1: Simplified schematics of the amplifier. 
 
3. MEASUREMENTS 
 
This section presents in detail the thermal analyses of the 
power amplifier. First the circuit and the entire 
measurement setup is introduced. Then, the measurement 
results are presented and discussed. 
 
3.1. Measurement setup 
 
For the experiments the APEX PA60 power amplifier was 
used. The circuit, whose simplified schematics is shown in 
Fig. 1, was chosen expressly to simplify the measurement 
procedure. This was possible owing to the fact that the 
package contains twin operational amplifiers with their 
outputs protected by diodes connected between the output 
and the positive power supply as shown in Fig. 2. Then, 
one of the amplifiers was powered in order to provide the 
heat dissipation and the protection diode and the other one 
was used as the temperature sensor. Consequently the 
temperature measurement point does not coincide exactly 
with the heat source. Hence, there was an inevitable delay 
between the sensed temperature and the temperature of the 
heated operational amplifier. However, because both 
amplifiers are integrated on one single chip, the delay 
might be assumed to be very small. Experimentally it was 
found that the delay time did not exceed 100 µs. Finally, 
as shown in Fig. 2, the power amplifier has been screwed 
to a cooling fin, which in turn was placed on a thermally 
insulating material. All the dimensions in the figure are 
given in mm. 
The measurements were performed using the thermal 
tester T3Ster provided by the MicRed company. The 
heating amplifier was operated in the saturation mode 
with the constant power dissipation of 10 W till steady 
state temperature was reached. After switching the power 
off, the protection diode of the other amplifier was used  
to measure the temperature cooling curve. The forward 
current forced through the diode during the measurement 
was 1mA. The photograph of the entire equipment used 
for the measurements is shown in Fig. 3. 
 
Fig. 2:  View of the amplifier with the radiator.  
 
3.2. Interface thermal resistance influence 
 
Initially, the measurements were taken for the radiator 
placed horizontally in three different configurations. First 
the radiator was firmly attached to the circuit. Then, the 
screw fixing the package to the cooling fin was loosed 
slightly, thus introducing some additional thermal contact 
resistance. Finally, thermal grease was applied and the 
screw was tightened again to improve the thermal contact. 
The captured cooling curves are presented in Figure 4. 
The logarithmic time scale was used so as to visualize 
better the very beginning of the cooling process, because 
after some 90 s the cooling curves are indistinguishable. 
As can be seen in the figure, tightening the screw and the 
use of thermal grease lowered the total thermal resistance 
by more than 1 K/W (the power dissipated was 10 W). 
 
 
Fig. 3: Photograph of the equipment. 
J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka 
Title. Dynamic Thermal Analysis of a Power Amplifier 
 
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9   
 
Fig. 4: Cooling curves - influence of interface resistance. 
 
Fig. 5: Cumulative structure functions  
- influence of interface resistance. 
 
Fig. 6: Differential structure functions  
- influence of interface resistance 
 
Fig. 7: Time constant distribution  
- influence of interface resistance. 
 
The measured cooling curves were processed further 
using the software provided by MicRed company together 
with the measurement equipment. The results of various 
thermal analyses performed by the authors are presented 
in Figures 5-8, which show respectively: the cumulative 
structure function, the differential structure function, the 
thermal time constant distribution and the Nyquist plot  
of thermal impedance. The cumulative structure functions 
are useful in the steady state thermal analysis, whereas the 
other quantities are important in the dynamic analysis. 
Examining the cumulative structure function pictured 
in Figure 5, it can be observed that the change of contact 
resistance does not affect the total value of the thermal 
capacitance (the large plateau is located at the same value 
of the thermal capacitance) but it influences the thermal 
resistance (see the shift of the vertical lines at the ends  
of the curves). Namely, tightening the screw lowered the 
total thermal resistance by 0.8 K/W and the application  
of the thermal grease reduced its value further by 0.6 K/W 
down to 6.2 K/W. 
 
 
Fig. 8: Thermal impedance  
- influence of interface resistance. 
J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka 
Title. Dynamic Thermal Analysis of a Power Amplifier 
 
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9   
Investigating the differential structure function, shown 
in Figure 6, further interesting observations can be made. 
In this figure there are three peaks visible. These peaks 
can be attributed to the chip, the package, and the cooling 
fin. The shift of the third peak caused by the change of the 
interface resistance is evident. The distance between the 
second and the third peak can serve as the measure of the 
thermal resistance of the contact between the package and 
the radiator. As indicated in the figure, the value of this 
resistance for tightly screwed radiator with thermal grease 
slightly exceeds 1 K/W, whereas in the case of loosely 
attached cooling fin it amounts to almost 2.6 K/W.  
Furthermore, the time constant distribution presented 
in Figure 7 clearly shows that there are four peaks located 
near the values of 60µs, 9ms, 8s and 800s. These peaks 
correspond to the four aforementioned sections of the heat 
flow path, i.e. the chip, the package, the interface and the 
radiator. The variation of the interface thermal resistance 
affects only the peak corresponding to the time constant  
of a few seconds. This peak has almost disappeared when 
the thermal grease was used, so it has to be related to the 
contact thermal resistance. 
The Nyquist plot of the thermal impedance, presented 
in Figure 8, shows three circular arcs centered around the 
same time constant values as the last three peaks in the 
time constant distribution. The high frequency peak is not 
visible on the Nyquist plot. For the well-attached radiator, 
the middle arc in the Nyquist plot practically disappears 
similarly to the peak in the time constant distribution, thus 
proving that this circle can be attributed to the interface 
thermal resistance. 
Moreover, it is worth noticing that the change of the 
interface resistance does not affect the overall shape of the 
analyzed curves in all the regions reflecting the heat flow 
through the inner parts of the package and the radiator. 
 
3.2. Cooling condition influence 
 
The second part of the experiments presented here was 
devoted to the investigation of the effects of the radiator 
position on the previously analyzed curves. The position 
of the radiator was changed by varying its tilt angle. 
Except for the horizontal position, the tilt angles of 45° 
and 90° (vertical position) were considered. Finally, in the 
last experiment the radiator was lifted by some 5 mm, thus 
creating an air gap between the radiator and the insulating 
material, but still maintaining the horizontal position. All 
the measurements were performed for the tightly screwed 
radiator without the thermal grease. The obtained results 
of thermal analyses are shown in Figures 9-13. Similarly 
to the previous cases, the charts represent: the cooling 
curves, the cumulative structure function, the differential 
structure function, the time constant distribution and the 
Nyquist plot of the thermal impedance. 
The examination of the curves shown in Figures 9-11 
provides some important conclusions. Namely, when the 
radiator was slightly tilted, the hot air from beneath could 
be evacuated more efficiently by the gravitational forces 
through the natural convection thus reducing the thermal 
resistance. The change of the position from the horizontal 
one to 45° caused the reduction of the thermal resistance 
by 0.6 K/W, which constitutes almost 10% of the total 
junction-to-ambient resistance. Further tilting the radiator 
to the vertical position did not influence the value of the 
thermal resistance significantly. On the other hand, lifting 
of the radiator produces the decrease of 0.4 K/W owing  
to the improved cooling from the bottom. 
Analysing Figures 12-13, it can be observed that the 
cooling conditions have no impact on the high frequency 
time constants. Thus, when the time constant distribution 
is concerned, only the large peak around 800 s is changed. 
Hence this peak can be attributed to the heat transfer from 
the radiator to the ambient by convection. It is also worth 
noticing that the third peak corresponding to the thermal 
interface between the package and the cooling fin was not 
influenced by these experiments at all. Similarly, in the 
Nyquist plot, only the largest low frequency circular arc 
was influenced. Concluding, compared to the previous 
experiment, the cooling conditions changed the analyzed 
curves only in the regions representing the heat transfer 
between the radiator and the ambient without affecting 
their shape in all the regions reflecting the heat flow from 
the heating junction to the radiator. 
 
4. CONCLUSIONS 
 
In this paper, the thermal dynamic behaviour of a power 
amplifier was discussed thoroughly employing different 
analysis methods. Specifically, the effects of the interface 
thermal resistance and the radiator position on the circuit 
temperature were investigated. The influence of both 
phenomena was illustrated in various diagrams. Analysing 
the results it was possible to characterize thermally the 
entire structure. Each part of the resulting curves was 
attributed to different sections of the heat path between 
the junction and the ambient. The presented methodology 
can be applied for various practical investigations such  
as compact model creation or fault identification, e.g. for 
die attach delamination detection. 
 
ACKNOWLEDGEMENTS 
 
Bjorn Vermeersch, a Research Assistant for the Scientific 
Research Foundation - Flanders (Fonds Wetenschappelijk 
Onderzoek - Vlaanderen), would like to thank for their 
financial support. This research was supported also by the 
internal grant of the Technical University of Lodz Dz.St. 
K-25/1/2006. 
J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka 
Title. Dynamic Thermal Analysis of a Power Amplifier 
 
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9   
 
Fig. 9: Cooling curves - position influence. 
 
Fig. 10: Cumulative structure function  
- position influence. 
 
 Fig. 11: Differential structure function  
- position influence. 
 
Fig. 12: Time constant distribution - position influence. 
 
REFERENCES 
 
[1] V. Szekely, T. Van Bien, "Fine Structure of Heat Flow Path 
in Semiconductor Devices: A Measurement and Identification 
Method", Solid-State Electronics, Elsevier, Vol. 31, pp. 1363-
1368, 1998. 
 
[2] V. Szekely, "On The Representation of Infinite-Length 
Distributed RC One-Ports", IEEE Transactions on Circuits and 
Systems, Vol. 38, pp. 711-719, 1991. 
 
[3] M. Rencz, V.Szekely, A. Poppe, G. Farkas, B. Courtois, 
"New Methods and Supporting Tools for The Thermal Transient 
Testing of Packages", Proceedings of International Conference 
on Advances in Packaging APACK, Singapore, pp 407-411, 5-7 
December 2001. 
 
[4] Kawka, P., Thermal Impedance Measurements and Dynamic 
Modelling of Electronic Packages, PhD Thesis, Universiteit 
Gent, 2005. 
 
[5] B. Vermeersch, and G. De Mey, "Thermal Impedance Plot  
of Microscaled Devices", Microelectronics Reliability, Elsevier, 
Vol. 46, pp. 174-177, 2006. 
 
 
 
Fig. 13: Thermal impedance – position influence. 


Dynamic Thermal Analysis of a Power Amplifier

Banaszczyk, Jedrzej

De Mey, Gilbert

JANICKI, M

NAPIERALSKI, A

Vermeersch, Bjorn

KAWKA, P

Ghent University Academic Bibliography

 Nice, Côte d’Azur, France, 27-29 September 2006  DYNAMIC THERMAL ANALYSIS OF A POWER AMPLIFIER  Jedrzej Banaszczyk * #, Gilbert De Mey #, Marcin Janicki *, Andrzej Napieralski *,  Bjorn Vermeersch #, Piotr Kawka # †  * Department of Microelectronics and Computer Science, Technical University of Lodz,  Al. Politechniki 11, 90-924 Lodz, Poland # Department of Electronics and Information Systems, University of Ghent,  Sint Pietersnieuwstraat 41, 9000 Ghent, Belgium † Agilent Technologies, Pegasus Park, De Kleetlaan 12A bus 12, 1831 Diegem, Belgium   ABSTRACT  This paper presents dynamic thermal analyses of a power amplifier. All the investigations are based on the transient junction temperature measurements performed during the circuit cooling process. The presented results include the cooling curves, the structure functions, the thermal time constant distribution and the Nyquist plot of the thermal impedance. The experiments carried out demonstrated the influence of the contact resistance and the position of the entire cooling assembly on the obtained results.  1. INTRODUCTION  The increased density of power dissipated in the state-of-the-art electronic devices and circuits has forced engineers to seek for new and innovative ways of thermal analysis  of electronic structures. Since power circuits often operate in a pulsed mode, their steady state thermal conditions are practically never reached. Therefore, in the case of power amplifier analyzed here it is important to determine not only the steady state temperature distribution, but also its dynamic thermal behaviour. Then, knowing the transient characteristics it is possible to obtain a useful dynamic thermal model. The next section provides a brief overview of various methods of dynamic thermal analysis of electronic circuits such as: cooling curve, thermal time constant distribution, differential and cumulative structure function and finally the Nyquist plot of thermal impedance. Next, the theory  is used in the experimental part of the paper to investigate, based on the example of a power amplifier, the effects  of varying the contact resistance between the amplifier package and the cooling fin. This was done by loosing the screw or applying thermal grease. Moreover, the influence of the cooling fin position has been also investigated. 2. DYNAMIC THERMAL ANALYSIS  There exist several methods of representing the dynamic thermal behaviour of electronic structures. One of such methods is the structure function approach. This approach had been originally developed by Szekely and his research team. For thermal analyses in electronics, the differential structure functions are of a particular interest because they provide the incremental thermal capacitance as a function of the distance from the junction (heat source). The main advantage of this representation is that, as it will be shown later on, it allows the direct identification of particular sections of the heat path of an electronic structure, such  as chip, package, solder or radiator. More theory on this subject can be found in [1]-[3]. Another possible method of describing the dynamic behaviour is to use Nyquist plots of the complex thermal impedance. The thermal impedance as a function of the angular frequency ω can be found performing the Laplace transform of the structure transient thermal response [4]. Owing to this, in most cases it is possible to determine the time constant distribution analytically because the Nyquist plots resemble a combination of circular arcs. As it was proved in [5], for simple geometrical shapes the Nyquist plot can be fitted to a circular arc with a high precision. For all the above described thermal analysis methods, it is required to take adequate temperature measurements. The measurements can be taken using a forward biased  p-n junction. If the bias current is constant, the voltage drop across the junction is the measure of temperature. Usually, temperature is measured as the response to the power step excitation. However, this requires using the same junction for heating and measurement, which might cause some technical problems. An alternative method, used also in this paper, is to heat the junction till steady state is reached and to switch the power off. In this way  a cooling curve is obtained, which is just the complement of the heating curve and contains the same information. ©TIMA Editions/THERMINIC 2006 ISBN: 2-916187-04-9   128  J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka Title. Dynamic Thermal Analysis of a Power Amplifier   Fig. 1: Simplified schematics of the amplifier.  3. MEASUREMENTS  This section presents in detail the thermal analyses of the power amplifier. First the circuit and the entire measurement setup is introduced. Then, the measurement results are presented and discussed.  3.1. Measurement setup  For the experiments the APEX PA60 power amplifier was used. The circuit, whose simplified schematics is shown in Fig. 1, was chosen expressly to simplify the measurement procedure. This was possible owing to the fact that the package contains twin operational amplifiers with their outputs protected by diodes connected between the output and the positive power supply as shown in Fig. 2. Then, one of the amplifiers was powered in order to provide the heat dissipation and the protection diode and the other one was used as the temperature sensor. Consequently the temperature measurement point does not coincide exactly with the heat source. Hence, there was an inevitable delay between the sensed temperature and the temperature of the heated operational amplifier. However, because both amplifiers are integrated on one single chip, the delay might be assumed to be very small. Experimentally it was found that the delay time did not exceed 100 µs. Finally, as shown in Fig. 2, the power amplifier has been screwed to a cooling fin, which in turn was placed on a thermally insulating material. All the dimensions in the figure are given in mm. The measurements were performed using the thermal tester T3Ster provided by the MicRed company. The heating amplifier was operated in the saturation mode with the constant power dissipation of 10 W till steady state temperature was reached. After switching the power off, the protection diode of the other amplifier was used  to measure the temperature cooling curve. The forward current forced through the diode during the measurement was 1mA. The photograph of the entire equipment used for the measurements is shown in Fig. 3.  Fig. 2:  View of the amplifier with the radiator.   3.2. Interface thermal resistance influence  Initially, the measurements were taken for the radiator placed horizontally in three different configurations. First the radiator was firmly attached to the circuit. Then, the screw fixing the package to the cooling fin was loosed slightly, thus introducing some additional thermal contact resistance. Finally, thermal grease was applied and the screw was tightened again to improve the thermal contact. The captured cooling curves are presented in Figure 4. The logarithmic time scale was used so as to visualize better the very beginning of the cooling process, because after some 90 s the cooling curves are indistinguishable. As can be seen in the figure, tightening the screw and the use of thermal grease lowered the total thermal resistance by more than 1 K/W (the power dissipated was 10 W).   Fig. 3: Photograph of the equipment. ©TIMA Editions/THERMINIC 2006 ISBN: 2-916187-04-9   129  J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka Title. Dynamic Thermal Analysis of a Power Amplifier   Fig. 4: Cooling curves - influence of interface resistance.  Fig. 5: Cumulative structure functions  - influence of interface resistance.  Fig. 6: Differential structure functions  - influence of interface resistance  Fig. 7: Time constant distribution  - influence of interface resistance.  The measured cooling curves were processed further using the software provided by MicRed company together with the measurement equipment. The results of various thermal analyses performed by the authors are presented in Figures 5-8, which show respectively: the cumulative structure function, the differential structure function, the thermal time constant distribution and the Nyquist plot  of thermal impedance. The cumulative structure functions are useful in the steady state thermal analysis, whereas the other quantities are important in the dynamic analysis. Examining the cumulative structure function pictured in Figure 5, it can be observed that the change of contact resistance does not affect the total value of the thermal capacitance (the large plateau is located at the same value of the thermal capacitance) but it influences the thermal resistance (see the shift of the vertical lines at the ends  of the curves). Namely, tightening the screw lowered the total thermal resistance by 0.8 K/W and the application  of the thermal grease reduced its value further by 0.6 K/W down to 6.2 K/W.   Fig. 8: Thermal impedance  - influence of interface resistance. ©TIMA Editions/THERMINIC 2006 ISBN: 2-916187-04-9   13  0  J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka Title. Dynamic Thermal Analysis of a Power Amplifier  Investigating the differential structure function, shown in Figure 6, further interesting observations can be made. In this figure there are three peaks visible. These peaks can be attributed to the chip, the package, and the cooling fin. The shift of the third peak caused by the change of the interface resistance is evident. The distance between the second and the third peak can serve as the measure of the thermal resistance of the contact between the package and the radiator. As indicated in the figure, the value of this resistance for tightly screwed radiator with thermal grease slightly exceeds 1 K/W, whereas in the case of loosely attached cooling fin it amounts to almost 2.6 K/W.  Furthermore, the time constant distribution presented in Figure 7 clearly shows that there are four peaks located near the values of 60µs, 9ms, 8s and 800s. These peaks correspond to the four aforementioned sections of the heat flow path, i.e. the chip, the package, the interface and the radiator. The variation of the interface thermal resistance affects only the peak corresponding to the time constant  of a few seconds. This peak has almost disappeared when the thermal grease was used, so it has to be related to the contact thermal resistance. The Nyquist plot of the thermal impedance, presented in Figure 8, shows three circular arcs centered around the same time constant values as the last three peaks in the time constant distribution. The high frequency peak is not visible on the Nyquist plot. For the well-attached radiator, the middle arc in the Nyquist plot practically disappears similarly to the peak in the time constant distribution, thus proving that this circle can be attributed to the interface thermal resistance. Moreover, it is worth noticing that the change of the interface resistance does not affect the overall shape of the analyzed curves in all the regions reflecting the heat flow through the inner parts of the package and the radiator.  3.2. Cooling condition influence  The second part of the experiments presented here was devoted to the investigation of the effects of the radiator position on the previously analyzed curves. The position of the radiator was changed by varying its tilt angle. Except for the horizontal position, the tilt angles of 45° and 90° (vertical position) were considered. Finally, in the last experiment the radiator was lifted by some 5 mm, thus creating an air gap between the radiator and the insulating material, but still maintaining the horizontal position. All the measurements were performed for the tightly screwed radiator without the thermal grease. The obtained results of thermal analyses are shown in Figures 9-13. Similarly to the previous cases, the charts represent: the cooling curves, the cumulative structure function, the differential structure function, the time constant distribution and the Nyquist plot of the thermal impedance. The examination of the curves shown in Figures 9-11 provides some important conclusions. Namely, when the radiator was slightly tilted, the hot air from beneath could be evacuated more efficiently by the gravitational forces through the natural convection thus reducing the thermal resistance. The change of the position from the horizontal one to 45° caused the reduction of the thermal resistance by 0.6 K/W, which constitutes almost 10% of the total junction-to-ambient resistance. Further tilting the radiator to the vertical position did not influence the value of the thermal resistance significantly. On the other hand, lifting of the radiator produces the decrease of 0.4 K/W owing  to the improved cooling from the bottom. Analysing Figures 12-13, it can be observed that the cooling conditions have no impact on the high frequency time constants. Thus, when the time constant distribution is concerned, only the large peak around 800 s is changed. Hence this peak can be attributed to the heat transfer from the radiator to the ambient by convection. It is also worth noticing that the third peak corresponding to the thermal interface between the package and the cooling fin was not influenced by these experiments at all. Similarly, in the Nyquist plot, only the largest low frequency circular arc was influenced. Concluding, compared to the previous experiment, the cooling conditions changed the analyzed curves only in the regions representing the heat transfer between the radiator and the ambient without affecting their shape in all the regions reflecting the heat flow from the heating junction to the radiator.  4. CONCLUSIONS  In this paper, the thermal dynamic behaviour of a power amplifier was discussed thoroughly employing different analysis methods. Specifically, the effects of the interface thermal resistance and the radiator position on the circuit temperature were investigated. The influence of both phenomena was illustrated in various diagrams. Analysing the results it was possible to characterize thermally the entire structure. Each part of the resulting curves was attributed to different sections of the heat path between the junction and the ambient. The presented methodology can be applied for various practical investigations such  as compact model creation or fault identification, e.g. for die attach delamination detection.  ACKNOWLEDGEMENTS  Bjorn Vermeersch, a Research Assistant for the Scientific Research Foundation - Flanders (Fonds Wetenschappelijk Onderzoek - Vlaanderen), would like to thank for their financial support. This research was supported also by the internal grant of the Technical University of Lodz Dz.St. K-25/1/2006. ©TIMA Editions/THERMINIC 2006 ISBN: 2-916187-04-9   13  1  J. Banaszczyk, G. De Mey, M. Janicki, A. Napieralski, B. Vermeersch, P. Kawka Title. Dynamic Thermal Analysis of a Power Amplifier   Fig. 9: Cooling curves - position influence.  Fig. 10: Cumulative structure function  - position influence.   Fig. 11: Differential structure function  - position influence.  Fig. 12: Time constant distribution - position influence.  REFERENCES  [1] V. Szekely, T. Van Bien, "Fine Structure of Heat Flow Path in Semiconductor Devices: A Measurement and Identification Method", Solid-State Electronics, Elsevier, Vol. 31, pp. 1363-1368, 1998.  [2] V. Szekely, "On The Representation of Infinite-Length Distributed RC One-Ports", IEEE Transactions on Circuits and Systems, Vol. 38, pp. 711-719, 1991.  [3] M. Rencz, V.Szekely, A. Poppe, G. Farkas, B. Courtois, "New Methods and Supporting Tools for The Thermal Transient Testing of Packages", Proceedings of International Conference on Advances in Packaging APACK, Singapore, pp 407-411, 5-7 December 2001.  [4] Kawka, P., Thermal Impedance Measurements and Dynamic Modelling of Electronic Packages, PhD Thesis, Universiteit Gent, 2005.  [5] B. Vermeersch, and G. De Mey, "Thermal Impedance Plot  of Microscaled Devices", Microelectronics Reliability, Elsevier, Vol. 46, pp. 174-177, 2006.    Fig. 13: Thermal impedance – position influence. ©TIMA Editions/THERMINIC 2006 ISBN: 2-916187-04-9   13  2  

Dynamic thermal analysis of a power amplifier

This paper presents dynamic thermal analyses of a power amplifier. All the investigations are based on the transient junction temperature measurements performed during the circuit cooling process. The presented results include the cooling curves, the structure functions, the thermal time constant distribution and the Nyquist plot of the thermal impedance. The experiments carried out demonstrated the influence of the contact resistance and the position of the entire cooling assembly on the obtained results. 1

Dynamic Thermal Analysis of a Power Amplifier

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