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Microelectronics Reliability 47 (2007) 2114–2121

Coupled electro-thermal simulation of a DC/DC converter

Miquel Vellvehi *, Xavier Jorda, Philippe Godignon, Carles Ferrer, Jose Millan

Centre Nacional de Microelectronica (CNM-CSIC), Institut de Microelectronica de Barcelona, Systems Integration Department,

Campus U.A.B. Bellaterra, 08193 Cerdanyola del Valles, Barcelona, Spain

Received 3 April 2006; received in revised form 24 October 2006Available online 19 December 2006

Abstract

Electro-thermal simulation of a DC/DC converter using a two-step methodology and its experimental validation are presented in thispaper. The simulation technique is based on the coupling of a thermal simulator (FLOTHERM) and an electrical one based on VHDL-AMS language. This work is mainly focused on the description of the thermal component with special emphasis in the modelling of theactive power devices (MOSFETs and Schottky diodes) included in the converter. Once these devices have been electro-thermally mod-elled, they are implemented in the DC/DC converter including a 10 layer PCB and some passive components. The modelling results havebeen experimentally checked by means of infrared measurements.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

The performance and characteristics of semiconductordevices in electronic packages can be considerably affectedby temperature variations. For this reason, accurate circuitsimulation requires to take into account the static anddynamic effects induced by the heat dissipation. In thisway, new modelling methodologies are being applied incomplex power systems to study these effects [1–3].

The modelling using electro-thermal interactions in inte-grated circuits has been addressed in a variety of ways. Theexisting methods can be broadly classified into two groups:direct and relaxation methods (Fig. 1) [4]. In both cases,standard electrical models became electro-thermal models,by including an additional thermal electrode in each model.

In the direct or fully coupled method a single electricalsimulation tool is used to model both electrical and ther-mal behaviour [5]. The coupling is possible through theexchange between both models of an electrical parameter(instantaneous dissipated power) and a thermal variable(instantaneous temperature). The problem of this methodis the thermal modelling due to the complex structure of

0026-2714/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.microrel.2006.10.009

* Corresponding author. Tel.: +34 93 594 77 00; fax: +34 93 580 14 96.E-mail address: miquel.vellvehi@cnm.es (M. Vellvehi).

the overall system. Often finite-difference approaches, Fou-rier series, analytical solutions and thermal networks areemployed. Most of them are valid only in the steady-statecases for linear heat equations. Different contributionshave been previously reported using this representationtogether with 1-D heat transfer equations, where voltagesare equivalents to temperatures and currents to thermalpower. As an example, we can mention the electro-thermalmodel of a commercial MOSFET from IR (IRPF254) withSPICE software [6].

In the relaxation method, electrical and thermal equa-tions are solved separately exchanging periodically temper-ature and power parameters until thermal and electricalconvergence is reached [7]. The trade-off of this techniqueis clear: a more accurate representation of the thermalbehaviour of the system is available, at the expense of anincrease of the computation time.

Modelling tasks requires a good knowledge of the geom-etry and physical properties of the different materialsinvolved in the system. In addition, depending on the sys-tem to be modelled, the mesh generation can be complexand time consuming. In our case, the modelling of theDC/DC converter requires more than two million meshpoints. Although these tasks are laborious but not concep-tually complex, the problems can appear in data transfer

Fig. 1. Example of both main electro-thermal coupling methods used for power system modelling.

M. Vellvehi et al. / Microelectronics Reliability 47 (2007) 2114–2121 2115

between both simulators (synchronization, convergenceand mathematical approximation).

This paper shows how the methodology based on therelaxation method can be applied to analyse relatively com-plex industrial systems, such as a DC/DC converter, inorder to predict their thermal behaviour. The wholeapproach has been experimentally validated by means ofan exhaustive thermographic analysis method. In a firststage, we have used and demonstrated the simulationmethod on single power devices (MOSFETs and Schottkydiodes) used in the converter. The methodology used in thiswork will finally allow predicting the chip temperature ofthe power devices used in the DC/DC converter, henceimproving the system design and increasing the reliabilitylevel of the whole system. Other passive components suchas transformers, self-inductances and capacitors have beenalso included in the final model of the converter.

2. Modelling methodology

One of the main objectives of our work is to build amodel for a DC/DC converter usable for electro-thermalsimulation. The block diagram of the relaxation method(usually called two-step method) is shown in Fig. 2. Theelectrical model is defined taking into account the tempera-ture dependence of the more relevant parameters, extractedfrom the characterisation of the components at differentoperating temperatures. On the other hand, the thermal

ElectricalMeasurements

(differentTemperatures)

Package dafrom manufact

ELECTRICALMODELIZATION

USINGVHDL-AMS

THERMALMODELIZATI

(FLOTHERM

P(T)

ElectricalMeasurements

(differentTemperatures)

Package dafrom manufact

ELECTRICALMODELIZATION

USINGVHDL-AMS

THERMALMODELIZATI

(FLOTHERM

Fig. 2. The proposed two step

model is based on the physical and geometrical descriptionof the packages of the components, mainly extracted fromthe datasheets. The coupling between both simulators isachieved in the following way: the results obtained fromthe first iteration of the electrical simulator at a given initialtemperature are exported in a text file containing the valueof the instantaneous power dissipated in the relevant com-ponents (main heat sources). Then, these power values areused as inputs in the thermal simulator. Next, new valuesof the components temperature are obtained, which are alsoexported in a text file and used as a new input for the elec-trical simulator. New values of dissipated power areobtained, being the new inputs for the thermal simulator.This process is iterative and once the convergence criterionis reached (i.e. any significant evolution of powers andtemperatures is observed), we get the final values of instan-taneous dissipated power and temperature in each com-ponent. The used convergence criterion has been that thecomponents’ temperature does not change more than0.05 �C from a coupling loop to the next one.

2.1. The electrical simulator

The electrical simulations have been performed withVHDL-AMS (Analogue Mixed Signal) modelling languageusing ADVanceMS from Mentor Graphics [8]. To representthe power devices (MOSFETS and Schottky diodes), wehave used SPICE models described with VHDL-AMS, as

taurer

ON)

ELECTRICALMODELIZATION

USINGVHDL-AMS

T

P´(T)

taurer

ON)

ELECTRICALMODELIZATION

USINGVHDL-AMS

P´(T)

Δ

s modelling methodology.

Fig. 3. VDMOS forward I–V characteristics at a gate voltage of 7 Vextracted at different temperatures.

20 40 60 80 100 120 140 1600.20

0.25

0.30

0.35

0.40

0.45

0.50

Temperature (°C)

On-

resi

stan

ce (

Ω) VTH

RON

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

4.5

Threshold V

oltage (V)

Fig. 4. Temperature dependence of on-resistance and threshold voltage ofa BUK482-100A MOSFET.

2116 M. Vellvehi et al. / Microelectronics Reliability 47 (2007) 2114–2121

well as the passive components (transformer, self-induc-tance, capacitors. . .). A detailed explanation of the electri-cal modelling of the DC/DC converter has been reportedin [9]. The advantage of using this strategy of modelling isthat it is very convenient to extract the model parametersfrom the characterisation measurements at different tem-peratures. However, some limitations arise: the models areadjusted in specific conditions of measurements and theycan only be used in these conditions. In our case, the modelshave been developed to be compatible with real operatingconditions of the considered converters (input voltage of48 V, an output voltage of 5 V, an output current of 3A, acommutation frequency of 500 kHz and a duty cycle of40%). For example, power MOSFETs are modelled onlyin their lineal region, which is their normal working condi-tion in the DC/DC converter. This modelling approach willbe detailed for the power devices in Section 3.

2.2. The thermal simulator

The thermal models developed for the MOSFET, Scho-ttky diodes and the complete PCB of the DC/DC converterhave been implemented with the FLOTHERMTM packagefrom FLOMERICS [10]. This software uses Computa-tional Fluid Dynamics (CFD) technique and is addressedto solve thermal problems in electronic equipments. It pre-dicts airflow and heat transfer in and around electronicequipments, including the coupled effects of conduction,convection and radiation. In particular, we have used thissoftware to model the thermal behaviour of semiconductorchips and their packages, as a series of layers of materialscharacterised by their thermal conductivities and specificheats. These layers must be properly connected to describethe correct thermal path from chip to environment. Themain heat transfer mechanism from the different devicesto the PCB is the conduction. The convection to the airis considered around the whole DC/DC converter andthe radiation phenomena can be neglected because themaximum temperatures reached in the system are lowenough. Geometrical data, material properties and bound-ary conditions of the full system have to be well known foran efficient modelling.

3. Power devices modelling

As a first step, the two-step electro-thermal modellingmethod using VHDL-AMS and FLOTHERM, has beenapplied to the discrete power devices of the commercialDC/DC converter from ASCOM (SMC CX15C48S5).The active components integrated in this converter arebasically of two types: power MOSFETs (BUK482-100A)and Schottky diodes (EC21QS04).

3.1. MOSFET model

The power MOSFET has been electrically modelledwith a SPICE Level 3 model, using experimentally

extracted parameters of the BUK482-100A. Electricalcharacterizations at several working temperatures and gatevoltages have been performed. Fig. 3 shows the I(V) char-acteristics of the MOSFET at different ambient tempera-tures (from 25 �C to 150 �C) and an applied gate voltageof 7 V. As the MOSFET will work as a switch in its linearregion, the model considers only the parameters relatedwith this working zone (on-state resistance, threshold volt-age, etc.). Apart from the static characterisation, thedynamic electrical behaviour of the MOSFET is describedby its parasitic capacitances. As it has been demonstrated[6], parasitic MOSFET capacitances are practically inde-pendent of temperature, being the main temperaturedependant parameters the on-state resistance (RON) andthe threshold voltage (VTH) as it is shown in Fig. 4.

Electro-thermal iterations have been performed betweenthe electrical model described above with the aid ofVHDL-AMS and the thermal model of the MOSFETpackaged in a SOT-223, developed with FLOTHERM(Fig. 5). As regards the boundary conditions, the MOSFEThas been mounted on a Cu layer with a fixed temperature

Fig. 5. FLOTHERM model of the BUK482-100A MOSFET packaged ina SOT-223.

Table 1Simulation results after successive iterations of the MOSFET coupledelectro-thermal modelling

Vgs (V) Id (A) Tamb (�C) Tj (�C) Pot (W) # Iteration

5 1.25 25 25 0.492 131.45 0.5098 231.69 0.5105 331.7 0.5105 4

Fig. 6. FLOTHERM model of the EC21QS04 Schottky diode packagedin a DO-214AC.

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of 25 �C. As explained in the previous section, the mainheat transfer mechanism is the conduction from the chipto the Cu layer, and the radiation and convection to theair can be neglected.

Under these conditions, we obtain an equilibrium junc-tion temperature under different input powers, consideringa minimum number of iterations. As an example, theresults obtained for the different iterations with Vgs = 5 Vand Ids = 1.25 A biasing, are shown in Table 1. As wecan see from this table, the convergence criterion is reachedafter four iterations between both simulators and we obtaina final chip temperature of 31.7 �C and a dissipated powerof 0.5105 W. From the thermal simulation results, the ther-mal resistance of the device can be deduced as the relation-ship between the silicon temperature increase and thedissipated power. The value obtained in the simulation is13.1 �C/W being the maximum value obtained from themanufacturer’s data sheet of 15 �C/W. Although theseresults represent a first indirect validation of our models,we have performed a direct experimental validation.

In this sense, the power VDMOS BUK482-100A hasbeen mounted on an IMS (Insulated Metal Substrate)applying a uniform temperature on the IMS backside.The measurement conditions are: an applied power of0.51 W, an input gate voltage of 5 V and an output currentof 1.2 A. When the backside temperature is fixed at 25 �C,an equilibrium temperature of 28.6 �C is measured on theMOSFET top surface. This value is in good agreementwith the simulated value (28.8 �C), hence validating ourmodelling approach.

3.2. Schottky diode model

An equivalent model of a Schottky Diode (SPICE Level1) has been developed, adjusting the simulation parameters

of the EC21QS04 Schottky diodes included in the system.As for the MOSFET, an electro-thermal characterizationhas been performed to extract the temperature dependenceof the parameters of the diode (forward voltage drop, leak-age current and junction capacitance). Then, the electricalmodel has been developed considering the temperaturedependence of the electrical parameters. In parallel, thethermal model of the Schottky diode using FLOTHERMTM

(Fig. 6) has also been developed and checked, taking intoaccount the DO-214AC package structure of theEC21QS04.

4. DC/DC converter modelling

The modelled DC/DC converter is mainly composed ofan input filter (two capacitances), power switches stage(including two MOSFETs in parallel), transformer, outputrectifier Schottky diodes and filters (the inductance and thecapacitance) and finally, isolation stage and PWM Control(Fig. 7). The power consumption of the latter is negligiblecompared to other stages and will not be taken intoaccount in the modelling. All these elements are mountedon both faces of a 10-layer PCB board.

The electrical circuit of the converter modelled withADVanceMS is depicted in Fig. 8 [9]. Only the componentsdissipating significant power have been considered. Theelectrical characteristics of the converter are: an input volt-age of 48 V, an output voltage of 5 V, an output current of3 A and a commutation frequency of 500 kHz. A duty cycleof 40% has been chosen taking into account the optimumoperating conditions. Using these parameters as input val-ues, we have calculated the dissipated power mean valuesof the different components (Table 2).

Complete thermal modelling of the DC/DC converterhas been developed using FLOTHERMTM, describing thecomplete PCB. The geometry and components locationhave been obtained from the manufacturer’s datasheet.The active components (MOSFET and Schottky diodes)thermal models previously developed have been includedin the full converter system. The 10-layer board PCB is

INPUTFILTER

POWERSWITCH

INDUCTORTRANSFORMER

OUTPUTRECTIFIERSAND FILTERS

ISOLATIONPWM

CONTROL

VIN VOUTINPUTFILTER

POWERSWITCH

INDUCTORTRANSFORMER

OUTPUTRECTIFIERSAND FILTERS

ISOLATIONPWM

CONTROL

VIN VOUT

Fig. 7. Schematic of the DC/DC converter.

Fig. 8. Schematic corresponding to the simulation of the simplified circuitof the DC/DC converter.

Table 2Calculated dissipated power in the main components of the converter(Tamb = 20 �C)

Component Dissipated power (W)

Transformer 0.834Inductor 0.025MOSFET 0.205Schottky diodes 0.8

Fig. 9. FLOTHERM DC/DC converter model. (a) Face A and (b) FaceB.

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modelled with an orthotropic thermal conductivity. Thepower converter works at an output voltage of 5 V andan output current of 3 A. That brings us to the consider-ation that the most important devices related to power con-sumption will be the switches, the rectifier diodes and thetransformer. It is worth to point out that the passive com-ponents included in the PCB have not been thermally mod-elled. In this sense, such components have been consideredas cuboids placed at the right locations but without anyfunctionality. The active and passive components areplaced in the PCB as shown in Fig. 9:

• Face A includes the half part of the transformer and theinductor, two MOSFETs in SOT-223 package and fourcapacitors.

• Face B includes the second half part of the transformerand the inductor, four Schottky diodes in DO-214ACpackage, a small transformer, a bipolar diode and fivecapacitors.

The values of the power dissipated by each componentextracted from the electrical simulator (see Table 2) areused as input parameters in the thermal simulator. The out-put of the thermal modelling is the internal temperature of

each component. The values of the temperature of theactive devices obtained by modelling at ambient tempera-ture (20 �C) are shown in Table 3. Fig. 10 shows the simu-lated temperature distribution in both faces of the PCB foran output current of 3 A and fixing 20 �C as ambient tem-perature. As it can be observed in Table 3 and in Fig. 10,although the two MOSFETs temperatures are similar,some differences are observed between the four diodes,being the coolest the external ones (CR2 and CR5). Thiswill be corroborated with the infrared measurements.

Fig. 10. Simulated surface temperature distribution of the DC/DCconverter at 20 �C: Face A (a) and Face B (b).

Fig. 11. PCB connections for IR thermography measurements.

Fig. 12. Experimental temperature distribution on Face A (a) and Face B(b) of the converter, using an emissivity equalization technique (outputcurrent of 3 A).

Table 3Simulated surface temperatures of the active components of the DC/DCconverter

Ambient temperature 20 �C

MOSFET Q2 74.23 �CMOSFET Q3 74.29 �CDiode CR2 73.94 �CDiode CR3 76.77 �CDiode CR4 75.66 �CDiode CR5 74.46 �C

M. Vellvehi et al. / Microelectronics Reliability 47 (2007) 2114–2121 2119

5. Experimental validation

To validate the simulation results, temperature distribu-tion has been measured using Infrared (IR) thermographywith AGEMA Thermovision THV900 equipment. Thistechnique allows the monitoring of surface temperaturesand thermal patterns while the converter is operating. Toobtain the IR measurements on both sides of the PCB, atest board has been developed to obtain the temperaturedistribution both on top and back of the PCB (Fig. 11).

Since the various components of the PCB have differentemissivity values, a direct measurement of the surface tem-perature could result in unrealistic temperature values. Forthis reason, the IR measurements methodology includestwo complementary techniques for comparison:

• Emissivity equalization: Initially, an IR image of thePCB is made without biasing the circuit and consideringa fixed external temperature; this gives a reference imagefor the emissivity equalization (i.e. an emissivity map-ping is obtained). After that, we obtain a second IRimage of the system under working conditions. Consid-ering the two images, a surface map of temperature isobtained by software processing (Fig. 12).

• Black paint: the board is painted with black paint (Nex-tel 811-21 Velvet Coating) with a known emissivity(e = 0.97). Then, all components are supposed to pres-ent the same value of emissivity. Consequently, a directtemperature distribution can be measured on the IR pic-ture when the converter is biased (Fig. 13).

Fig. 13. Experimental temperature distribution on Face A (a) and Face B(b) of the converter, using a black paint of known emissivity (outputcurrent of 3 A).

2120 M. Vellvehi et al. / Microelectronics Reliability 47 (2007) 2114–2121

As mentioned before, the converter has been biasedunder the same conditions used for the simulation. Theexperimental results obtained for 1 A and 3 A output cur-rents can be seen in Tables 4 and 5, respectively. Thesetables show the values of the surface temperatures of thedifferent active components in both faces (A and B). Ascan be observed in both tables, the two methods used tomeasure the temperature distribution give similar results,

Table 4Experimental surface temperatures of the active components obtained foran output current of 1 A

Op @ 1A Emissivity equalisation (�C) Black paint (�C)

FACE A TQ2 37.1 37.3FACE A TQ3 37.1 37.3FACE B TCR2 36.8 35.2FACE B TCR3 38.8 36.9FACE B TCR4 38.3 37.0FACE B TCR5 36.5 34.6

Table 5Experimental surface temperatures of the active components obtained foran output current of 3 A

Op @ 3A Emissivity equalisation Black paint

FACE A TQ2 74.2 �C 75.4 �CFACE A TQ3 74 �C 74.4 �CFACE B TCR2 74.0 73.0FACE B TCR3 81.0 78.7 �CFACE B TCR4 80.8 78.0 �CFACE B TCR5 74.3 69.4 �C

with maximum differences of 2 �C. The most important dif-ferences are found for the 3 A output current case and forFace B components.

If we compare the results of the measurements with thesimulated ones (see Table 5) for the 3 A output current(Tamb = 20 �C), we observe a difference on the temperaturedistribution over the transformer. The reason is that pas-sive components have not been thermally modelled in afirst approximation as explained previously. However,regarding the MOSFETs (Q2 and Q3) the temperaturesmeasured in both devices are very similar using both mea-surement techniques and almost equal to the temperaturescalculated by simulation.

In the case of the Schottky diodes, they present slightdifferences between experimental and simulated tempera-tures. For the external diodes (CR2 and CR5) the experi-mental temperature values are similar to those obtainedby simulation. However, for the internal ones (CR3 andCR4), which are the hottest, the temperatures differencescan reach 5 �C, corresponding to an error of 6%. Then,we can conclude that, although the slight discrepancy onthe values of temperatures in two of the active devices,the results obtained from the simulations agree with themeasured results, corroborating the efficient electro-ther-mal modelling of the active devices. Then, using the pro-posed simulation methodology, we can also predict thejunction temperature of the active devices included in theconverter, hence improving its design in order to decreasethe maximum temperature and increasing its reliability.In our case, under the operating conditions describedabove, the obtained chip temperatures of the differentpower devices are around 1 �C above the temperaturesmeasured in the surface of its packages.

6. Conclusions

In this work, the electro-thermal model of a power sys-tem using a modelling methodology based on relaxationmethod is presented and experimentally validated. Thedemonstrator is a DC/DC commercial converter and itsmodelling presents two main characteristics: the first oneis the inclusion of power devices and the second one isthe presence of a large number of active and passive com-ponents mounted in a 10-layer PCB. Electrical modellingperformed with VHDL-AMS (using ADVanceMS) is cou-pled with thermal simulations using FLOTHERMTM. Thiscoupled electro-thermal modelling was applied to singlepower devices (MOSFET and Schottky diode) to validatethe methodology, before considering the complete circuitsimulation. Special emphasis has been done on the thermalsimulations and their experimental validation by means ofan exhaustive infrared thermography analysis. The resultsobtained from the measurements show a good agreementwith those obtained by simulation, hence showing theefficient electro-thermal modelling of the active devices.In addition, using this simulation methodology, we canpredict the junction temperature of the devices. In this

M. Vellvehi et al. / Microelectronics Reliability 47 (2007) 2114–2121 2121

way, we can improve the system design in order to decreasethe maximum junction temperature and to increase the reli-ability of the whole system.

Acknowledgements

The work presented in this paper was supported byEU under SPARTE Euclid contract and by the SpanishMinisterio de Educacion y Ciencia under contractTEC2005-087392 (SPACESIC Project).

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