Microelectronics Reliability 52 (2012) 2391–2396

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Microelectronics Reliability

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Thermal modeling and design of power converters with tight thermal constraints

P. Cova ⇑, N. DelmonteDipartimento di Ingegneria dell’Informazione, University of Parma, viale G.P. Usberti, 181/a, 43124 Parma, ItalyINFN Pavia, via Agostino Bassi, 6, 27100 Pavia, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 31 May 2012Received in revised form 25 June 2012Accepted 25 June 2012Available online 20 July 2012

0026-2714/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.microrel.2012.06.102

⇑ Corresponding author at: Dipartimento di Ingegversity of Parma, viale G.P. Usberti, 181/a, 43124905818; fax: +39 0521 905822.

E-mail address: paolo.cova@unipr.it (P. Cova).

The aim of this paper is to show and discuss results of 3D finite-element simulations for thermal man-agement design with tight constraints taking care of reliability aspects of hybrid power converters. A pro-cedure to obtain simplified but accurate device models has been shown together with experimentalvalidation. The simplified models have been used for converter module modeling. The same procedurehas been applied to analyze the thermo-fluid dynamic problem of a whole converter comprising of threemodules, inner air and enclosure.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Electronic systems operating in hostile environments, such asspace or High Energy Physics Experiments (HEPEs), require thehighest levels of reliability and performance. In these applicationshigh-density power supplies with tight thermal specifications andconstraints are needed and their thermal management design iscritical. Indeed efficient heat removal is crucial for reliability andto ensure, even in case of high dissipated power, negligible heat ex-change between the power converters and surrounding electronics.

In HEPEs applications the main thermal design targets aretwice: (a) for reliability purposes the maximum temperature ofconverter components should be as low as possible; (b) almostall of the generated heat must be extracted by liquid cooledheat-sink, and only a negligible amount of it by air convection[1]. For this reasons the thermal design must consider the 3D con-duction problem, together with air convection in (almost) sealedenclosure.

Accurate numerical studies, e.g. Finite Element (FE) analysis,can be useful to evaluate heat exchange in the environment andthe steady state maximum temperatures reached in the systemcomponents, but detailed geometries representation is needed.This implies very high Degrees Of Freedom (DOF) for the FE modelof the whole system, and consequent big computational effort. Oneway to circumvent this problem is to use simplified geometries orsimplified models of the single components embedded in the sys-tem. It is possible to build a library of component models followingthe procedure described in [2].

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neria dell’Informazione, Uni-Parma, Italy. Tel.: +39 0521

In this paper, as a case study, FE based thermal design of aboxed DC power supply for HEPEs application is shown, referringto the 3 kW, 280–12 V DC/DC, converter for the next generationof ATLAS experiment [3], which is composed by three paralleledpower modules, each cooled by its own water cold plate [4]. Everymodule implements a 100 kHz Switch In Line Converter (SILC) [5]able to supply up to 125 A output current.

Aim of the paper is to show a simplified, but accurate FE mod-eling for thermal design of power converters subjected to tightthermal constraints. In the ATLAS experiment, the converter is nei-ther subjected to power cycling, nor to thermal cycling, except incase of system shut down (seldom), then only steady state thermalanalysis is significant.

In Section 2 the system thermal requirements are given; inSection 3 the accurate and simplified models of the main heatingcomponents are described; Section 4 shows the module thermalsimulation and characterization; in Section 5 the thermal modelof the whole system, including the box and the air inside it, ispresented and discussed.

2. System thermal constraints

The three-modules power converter considered has to be closedin a 402 � 285 � 150 mm ideally adiabatic box to avoid heat flowtowards other electronics of ATLAS experiment. It will work at18 �C ambient temperature. The electronic inside the box can becooled by mean of aluminum cold plate. The cooling liquid is waterwith Tinlet = 18 �C and maximum delivery of 1.9 l/min.

The chosen 2 + 1 modules redundancy leads to two possibleconfigurations, each with different module output power ratingand heat exchange distribution: (i) all modules working, eachdelivering 1 kW; (ii) two modules each delivering 1.5 kW, whena module has failed [3].

Fig. 2. IR thermal map of a TO247 device dissipating 1 W at room temperature of25 �C; labeled by letters, the reference points used to compare experimental withsimulations.

Fig. 3. FEM thermal map of the TO247 MOSFET dissipating 1 W at roomtemperature of 25 �C. Left: detailed model; right: simplified model. Temperaturecolor range in �C. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.).

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Thus, together with the control of the chosen DC/DC convertertopology, the choice of the devices to embed in the module is cru-cial to ensure good heat removal and high electrical powerefficiency.

3. Components thermal library

Each component embedded in the converter was modeled by asimplified geometry, in order to obtain a DOF of the entire model aslow as possible, even though maintaining sufficient accuracy of thesimulation results. The simplified device models can be collectedfrom previous works [2,6,7] or added for the current case study.

In this section, numerical models (and their validation) of thedevices which have to be used in the power module simulation,are presented.

3.1. TO247 thermal modeling and characterization

The designed modules include some TO247 packaged MOSFETs,assembled as SMD to take advantage of Insulated Metal Substrate(IMS) boards (instead of conventional FR4), that can be well con-nected to the cold plate [8]. More expensive ceramic materialscould be possibly tested in next prototypes. A device in TO247package has been analyzed in geometry and materials by usingtechnical sheets and direct inspection. Starting from this, the mod-el for FE analysis was drawn, as in Fig. 1, which refers to an assem-bly on IMS board.

In this geometry only the bonding wires were simplified anddrawn with simpler and larger shapes than the real ones; the ther-mal conductivities in this subdomains were set in order to obtainthe same thermal resistances of the real bonding wires betweensilicon die and pins.

The unavoidable small elements of the mesh (the higher totalnumber of elements, the greater the DOF) derive from the presenceof thin layers (125 lm silicon die, 70 lm copper traces and 75 lmresin insulator underneath) modeled with their actual thickness. Inthe simplified model they can be drawn as 2D geometries. In COM-SOL 4.2, for instance, although modeled as 2D, a thermal conduc-tivity and a thickness can be set for copper traces, in order toapply the Fourier model of heat transmission in this highly conduc-tive layers, neglecting the temperature gradient along thethickness.

To setup a simplified model of a TO247 packaged device, a MOS-FET biased in order to dissipate 1 W was thermally characterizedby Infrared (IR) thermography. It was biased without mounting iton a board and heat-sink. The obtained thermal map is shown inFig. 2.

The detailed FEM simulation of the MOSFET dissipating 1 W,gives the thermal map of Fig. 3 (left). At the boundaries it was im-posed the Newton’s law of cooling q = h (T – Tref), where q is heatflux, h is the heat transfer coefficient and Tref is the temperature

Fig. 1. TO247 detailed 3D model geometry.

suitably far from the boundary (i.e. the ambient temperature).The FEM was tuned with experimental results by using the heattransfer coefficient at boundaries as fitting parameters. This fittingis needed because the actual convection conditions during experi-ments were not well controlled: the transistor was kept in ‘‘quasi’’natural air convection due to air blown by the fans of the near testbench electronic equipment. In this operating condition, to havegood matching of FEM and experimental, h has to be set slightlygreater than the value computed from handbook formula for natu-ral air convection coefficient.

3.1.1. TO247 simplified FE modelTo lower the DOF, the device was modeled with a simplified

geometry. To keep the number of elements as low as possible,the MOSFET geometry was drawn with a 2D silicon die, and with-out holes.

As done for the detailed model, the heat transfer coefficient atthe boundaries was used as fitting parameter. The result after tun-ing is shown in Fig. 3 (right). To compare simulation and experi-mental results some reference points have been taken (see Fig. 2)whose temperature increase over room temperature are given inTable 1. The deviation is always below 10%, so the matching be-tween measurement and simulation of simplified model can beconsidered good.

Table 1Temperature increase in points of Fig. 2 for measurement and simulation (simplifiedmodel). e is the absolute error to DTmeas.

Point DTmeas (�C) DTsim (�C) e (%)

A 34.4 33.7 2.0B 23.5 25.0 6.4C 31.2 33.9 8.7D 19.7 20.2 2.5E 33.9 35.8 5.6F 24.8 26.8 8.1G 25.5 27.5 7.8

Fig. 5. IR picture (top view) of the ISOTOP diodes in horizontal position (flangedown) dissipating 2.58 W at room temperature of 27 �C; all the boundaries are onair, except for the contacts. Excluding the coldest contacts, the maximum andminimum temperatures are 58.6 �C and 48.5 �C, respectively.

Fig. 6. Thermal map by detailed (left) and simplified (right) FEM of the ISOTOPdiodes dissipating 2.58 W at Tamb = 27 �C.

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3.2. ISOTOP thermal modeling and characterization

As done for TO247, a double diode in ISOTOP package has beenanalyzed by inspections and technical sheets [9]. Four of thesecomponents are used as output rectifiers and each of them isloaded by half of the output current. They are mounted with thethermal flange on the circuit baseplate. Fig. 4 shows the ISOTOP3D geometry used for detailed FE thermal analysis.

Fig. 5 shows the IR picture of a couple of ISOTOP diodes pow-ered to dissipate 2.58 W. The diodes were biased in series, usingtwo 1 m long cables from power supply to ISOTOP with 8 mm2 sec-tion area to avoid heating from them (Id � 3.5 A). The short cable(around 5 cm long) used to put in series the diodes can have smal-ler section (1.5 mm2) than the power supply cables. The ISOTOPwas painted black in order to have an emission coefficient equalto 1. The ambient temperature was 27 �C.

The ISOTOP FEM is composed by copper flange and screwedexternal contacts, silicon die, copper electrical contacts betweenanode and cathode on die and resin lid.

The heat generation has been placed in the two silicon die equalto the one of the IR thermal measurement.

As boundary conditions as been considered only the convectivecooling, neglecting the heat-sink behavior of the electrical cablesused to bias the diodes (see in Fig. 5 the lowest temperatures re-corded on the contacts connected to the larger cables). In Fig. 6(left) is shown the result of the FE simulation. It is in good agree-ment with the measurement.

3.2.1. ISOTOP simplified FE modelThe simplified ISOTOP was modeled by drawing (Fig. 7) all sub-

domains as hexahedral, except for the silicon die, modeled as 2Dgeometry. The electrical connections are drawn as vertical hexahe-dral with sections wider than those typical of bonding wires. Inthese subdomains the thermal conductivity was set in order to ob-tain the same thermal resistance as that of the actual internal con-nections. Again, using convective heat transfer coefficients asfitting parameters, it was possible to obtain a FE model whose sim-

Fig. 4. ISOTOP detailed 3D geometry: the inner components, such as dies andelectrical connections, are depicted in green. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Simplified ISOTOP 3D geometry for FE analysis.

ulations are in good agreement with experimental. Fig. 6 (right)shows the simulated thermal map with dissipated power of2.58 W and Ta = 27 �C.

3.3. Planar transformer simplified FE model

This simplified FE model was built as done in [6] assuming thewindings as homogeneous material, with uniform heat sources,and starting from the detailed model described in [7]. The simpli-fied transformer, together with aluminum bars and iron screwsused for clamping it to the heat-sink, is depicted in Fig. 8. Thismodel was used for simulating the whole converter, and it wastuned by the measurements described in Section 4. The tuningwas done by mean of three parameters: thermal conductivity of

Windings

Core

Aluminum bar

Iron screw

Fig. 8. FE thermal map of the simplified planar transformer model dissipating 50 Won core and 70 W on windings. hbottom = 180 W/m2 K, hair = 20 W/m2 K.

Fig. 9. Module prototype.

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the windings domain, heat transfer coefficient of the boundariesexposed to the air, and heat transfer coefficient of the aluminumbar surfaces connected to the heat-sink.

Fig. 8 represents a thermal map obtained from simulations inthe case of a dissipated power of 120 W. It is in good agreementwith experimental results.

4. Power module thermal modeling and measurements

The converter power module taken as case study has a complexgeometry, since it is composed by many devices assembled instacked boards made with different technologies (Fig. 9).

Fig. 10. Module geometry drawn for FE

Four zones compose the module: the primary, the transformer,the secondary and the auxiliary power supply of the control. Thecontrol is placed at the primary top board.

The TO247 power MOSFETs in the primary zone, which need todissipate a lot of power, are placed in the bottom IMS board. TheFR4 boards in the middle layer house both devices with significantand less dissipating power. However, the more dissipating powerdevices (e.g. the ISOTOP diodes in Fig. 10) in middle boards arethermally connected to the aluminum baseplate (by means of theirspecific flange), which acts as module substrate and thermal bridgebetween the devices and the cold plate.

The devices in the FR4 boards at the top (auxiliary circuits) arethose that dissipate less (ideally no) power. The two bigger mag-netic components, the planar transformer and a toroidal inductorare thermally and structurally connected to the baseplate bymetallic screws and aluminum bars and plates. The planar trans-former (Fig. 11) has the core bottom thermally connected to thebaseplate. Starting from the analysis in [7], this transformer waswrapped by aluminum bars and plates, to carry the heat generatedin the upper zones towards the cold plate. Between aluminumthermal bridges and everywhere a part is near the baseplate, athermal conductive gap filler (paste or pad) is placed.

The module was thermal characterized by mean of thermocou-ples and IR thermography at different output power levels. Thethermography at the maximum power rating is shown in Fig. 12.The inlet water temperature and the delivery of the cold plate werefixed in agreement with constraints in Section 2. To achieve a highand uniform emission coefficient the more reflective parts of inter-est were painted by an antireflective coating.

The geometry in Fig. 10 was drawn to simulate the moduleoperating at the same conditions of measurements, by taking intoaccount only the devices where heat generation was significant.The dissipated power in the parts was evaluated by electrical mea-surements or by calculations, for a total amount of 378 W at themaximum output power rating of 1.5 kW. These values are listedin Table 2. The devices are modeled as the simplified ones. To takeinto account the thermal interaction between the devices assem-bled on FR4 boards, the copper traces have also been drawn, butthey were modeled as 2D highly conductive layer, in order to keeplow the DOF. The cold plate has been modeled as 2 mm thick alu-minum plate in contact with the baseplate, setting the external

analysis (partially exploded view).

Fig. 11. Planar transformer: thermal bridging to cold plate.

Fig. 12. IR thermal map of the module prototype delivering 1.5 kW at 24 �C roomtemperature. Primary region to the right.

Table 2Module devices: description and dissipated power at delivered power of 1.5 kW.

No. Device Pd (W)

1 Primary MOSFETs (TO247) 302 Planar transformer–core 1693 Planar transformer–windings 1374 Diodes (ISOTOP) 125 Inductor 126 Copper traces at secondary 107 Auxiliary – MOSFET (TO247) <18 Auxiliary – transformer core <19 Auxiliary – transformer windings <1

10 Auxiliary – MOSFET (D2PAK) <111 Capacitors and other devices 5

Total power dissipation 378

Fig. 13. FE thermal map (in �C) of the module prototype delivering 1.5 kW atTamb = 24 �C. The cold plate temperature is 19.5 �C. Primary section to the right.

Fig. 14. Thermal map of the simplified module delivering 1.5 kW at roomtemperature of 24 �C.

Fig. 15. Thermal map of the middle section of the converter with all modulesoperating at nominal power (1 kW).

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surface temperature (the mean temperature measured in experi-ments between inlet and outlet water) to 19.5 �C. Natural air con-vection was set over all the other boundaries of the module, byusing the heat transfer coefficient as fitting parameter. The result,shown in Fig. 13, is in good agreement with measurements.

5. Thermal modeling of the whole system

A key issue in the present work was to develop a numericalmodel of the whole converter box, able to get accurate indicationsabout the insulation of the box walls, in order to keep the heat re-lease towards surrounding electronics as low as possible. At thesame time the maximum temperatures reached by the internalcomponents of the converter must be kept under control.

Inside the converter box (containing three modules as the onedescribed in the previous section) there is air, which can move be-

cause of buoyancy, resulting in internal heat flow by convection.Therefore, the equations of thermal and fluid dynamic problemsmust be self consistently coupled in the model. The problems re-lated to the needed of high computational capability for fluid dy-namic FE simulations are well known. Typically, to managethermal problems of electronic circuits, the Finite Volume Method(FVM) is used. Although this method is suitable for simulating fluiddynamic problems, when analyzing 3D thermal problems such asthose presented in Section 4 where, for accuracy, the copper ther-mal connections between the devices cannot be modeled as 2D, theDOF turns out to be rather high. Analogue observation can be donefor the die of semiconductor components. Thus, with FVM, espe-cially when using FR4 boards, one tends to neglect or roughlyapproximate the influence of a device on its neighbors, both be-cause of the heat transport through the PCB, and the way to gener-ate heat within the devices. Therefore, even if with modelsgraphically suggestive and accurate fluid dynamic results, alsoapplication of FVM leads to thermal results with errors between5% and 10%. The purpose here promoted is to use the FEM withsimple models, running on standard PC, giving errors comparableto those of FVM models.

Fig. 16. External boundaries thermal map of the converter with all modulesoperating at nominal power.

Fig. 17. Temperatures from simulation of some critical devices of the moduleoperating at the maximum delivering power for different heat transfer coefficient.

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A box with three modules, simplified with respect to the one inFig. 10, was drawn to analyze the thermal problem of the wholeconverter.

Following the same idea of the simplified model device library,a simplified model of the converter was built: the four (primary,planar transformer, secondary, auxiliary) zones were modeled ashexahedral of homogeneous materials, whose dimensions giveapproximately the external shape of the real module. To fit thismodel with experimental results, the thermal conductivities ofthe four zones, and their thermal contact resistances with the base-plate, were used as fitting parameters. The thermal map of Fig. 14was obtained after fitting. Referring to the simulation result of de-tailed module, the absolute error in the mean temperature increasefor every zone is below 5%.

By this model, the stationary state of the converter operating atroom temperature of 18 �C, with the three modules delivering thenominal power, and setting natural air convection condition at theexternal boundaries of the box, was simulated (Figs. 15 and 16).The results showed that more internal insulation will be requiredto increase the amount of heat extracted by the water heat-sinkand reduce the walls temperature.

To evaluate the effect of an additional insulation in the uppersurface of the three modules on their maximum temperatures, asimple approach, which does not require drawing additional lay-ers, consists in lowering the heat transfer coefficient h at the sur-faces which should be covered by insulation. The coefficient hcan be calculated once the thermal conductivity and thickness ofthe insulator material are known. Fig. 17 shows the simulated ef-fect of the thermal insulation on the maximum temperature ofthe most critical components, indicating that further investigationis needed to improve the heat removal from the planartransformer.

6. Conclusions

We developed and experimentally validated a 3D FEM modelfor the thermal analysis of a power converter to use in HEPEs.The model was built using simplified models of the more heatingdevices embedded in the converter.

Thermal measurements and simulations showed good agree-ment both for single devices and the whole module.

Finally, we reported about results of thermo-fluid dynamic sim-ulations of the converter in enclosure, aimed at evaluating maxi-mum temperatures inside, and heat flux from the box walls tothe ambient. The analysis showed that more efficient heat removalat the transformer is needed to satisfy the quasi-adiabatic con-straints on the whole converter.

Acknowledgements

The research presented in this paper was conducted in theframe of the APOLLO experiment and financially supported bythe Italian Istituto Nazionale di Fisica Nucleare (INFN). The authorsare grateful to researchers who contributed to this activity,namely, M. Bernardoni, M. Citterio, A. Lanza, R. Menozzi, and M.Riva.

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