The method of a fast The method of a fast electrothermal transient analysis electrothermal transient analysis

of a buck converterof a buck converter

Krzysztof Górecki and Janusz ZarębskiKrzysztof Górecki and Janusz Zarębski

Department of Marine Electronics Department of Marine Electronics

Gdynia Maritime University, POLANDGdynia Maritime University, POLAND

D EP A R T M E N T

F MARINE ELECTRONIC

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OutlineOutline

Introduction The conception of the method The FAST algorithm The analytical dependences Verification of the method Conclusions

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IntroductionIntroduction Dc-dc converters belong to the class of „stiff

circuits” The time of analysis is unacceptable long In literature some methods of shortening

calculations time are proposed These methods needs to use the very

simplified models of semiconductor devices: piecewise-linear dc characteristics Inertialess

44

Introduction (cont.)Introduction (cont.) In semiconductor devices selfheating phenomenon is

strongly observed Selfheating – results from changing the electrical

energy into the heat at non-ideal cooling conditions Due to selfheating

Internal temperatures of semiconductor devices increase Characteristics and parameters values of dc-dc converters

change Electrothermal analysis – analysis with selfheating

taken into account The classical methods of electrothermal analysis

cannot be used for analysis of dc-dc converters (the time of analysis is unacceptable long)

55

In the paperIn the paper

A new method of a fast electrothermal analysis of dc-dc converters is proposed

The verification of correctness of this method was performed for buck converter

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The general conception of the The general conception of the methodmethod

In the network analogue of semiconductor device thermal models and in dc-dc converters the parallely connected RC elements exist

The impulse response of such RC networks has the form of the sum of exponential functions and it can be calculated with the use of the memoryless algorithm [1]

In the steady-state the time dependences of currents, voltages and junction temperatures in dc-dc converters are periodical

If the step of calculations is equal to the period of the control signal, than the values of currents, voltages and temperatures are the sums of the geometrical progression

[1] Zarębski J., Górecki K.: Properties of Some Convolution Algorithms for the

Thermal Analysis of Semiconductor Devices. Applied Mathematical Modelling, Elsevier, Vol. 31, No. 8, 2007, pp.1489 – 1496.

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The general conception of the The general conception of the method (cont.)method (cont.)

If the values of the considered quantities of the begin (Sb) and the end (Se) of the period TS are known, the value of these quantities Sn after n periods can be estimated with the use of the formula

where

Because of the nonlinearity of semiconductor devices, the calculations must be realized iteratively

1

1 n

Xn

bn SSS

beX SSS

STexp

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The FAST algorithmThe FAST algorithm

The electrothermal transient analysis for the final time equals to 2 TS

Determination of the changes of values of the capacitors voltages SC

and junction temperatures of semiconductor devices for one

period TS

Ekstrapolation of the values of the converter output voltage VC and semiconductor devices junction

temperatures Tj in the steady state with the use of the convolution algorithm

START

Calculations of the coil current IL in the steady state using the extrapolated voltage VC, the values of the network components

and parameters of the control signal

Transient analysis for the final time equals to 2 TS with initial conditions

VC, IL, Tj

Determination of the values of capacitors voltages VC1, coil current IL1 semiconductor devices junction temperatures Tj1 on the end of the

second period of analysis

UC – UC1 < U, IL – IL1 < L and Tj –

Tj1 <T?

STOP

YES NO

99

The analytical dependencesThe analytical dependences

• The peak-to-peak value of the inductor current

where L – the inductance of the inductor, tp – the time of the diode conducting, VL – the voltage on the inductor at the end of the period of the control signal

Vout – the converter output voltage, VD – the voltage drop on the diode

• The average value of the inductor current

R0 – the load resistance

• In the continuous conducting mode (CCM) IL = ILsr-IL/2

• In the discontinuous conducting mode (DCM) IL = 0

pL

L tL

VI

DoutL VVV

0RVI outLsr

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Results of Results of investigationsinvestigations

the FAST algorithm clasical transient analysis

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

0 0,2 0,4 0,6 0,8 1

d

Vou

t [V

]

Vin = -20 V

R0 = 5 W

R0 = 10 W

BUCKa)

0

10

20

30

40

50

60

70

80

90

100

0 0,2 0,4 0,6 0,8 1

d

h [%

]

Vin = -20 V

R0 = 5 W

R0 = 10 W

BUCK

b)

0

50

100

150

200

250

300

350

400

0 0,2 0,4 0,6 0,8 1

d

TjT

[K

]

Vin = -20 VR0 = 5 W

R0 = 10 W

BUCKc) •Two nonphysical thermal time constants

are used tth1 = 1 ms and tth2 = 10 ms.• The convergence of calculations with FAST algorithm is observed after analysis of 16 -32 x TS.• The steady state in the classical algorithm is observed after 6000 x TS.• The FAST algorithm is over 200 times faster than the classical algorithm.

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ConclusionsConclusions• The FAST algorithm is universal, that means, it can

be used for each model of semiconductor switch devices implemented in SPICE, such as: diodes, BJTs, MOSFETs or IGBTs.

• The FAST algorithm can be especially profitable in the analyses of switching circuits operating at switching frequencies equal to some hundreds kHz and with semiconductor devices situated on heat-sinks.

• The analysis of such a circuit by the classical method would demand the calculations during the time longer than a lot of millions (or even billions) periods of the control signal. On the other hand, the FAST algorithm allows shortening the time of the analyses up to the time indispensable for the analysis of several periods of the control signal.

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Thank you for your attention