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The method of a fast electrothermal transient analysis of a buck converter Krzysztof Górecki and Janusz Zarębski Department of Marine Electronics Gdynia Maritime University, POLAND

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

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3 Introduction 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

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4 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)

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5 In 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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6 The general conception of the method 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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7 The general conception of the method (cont.) If the values of the considered quantities of the begin (S b ) and the end (S e ) of the period T S are known, the value of these quantities S n 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

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8 The FAST algorithm

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9 The analytical dependences The peak-to-peak value of the inductor current where L – the inductance of the inductor, t p – the time of the diode conducting, V L – the voltage on the inductor at the end of the period of the control signal V out – the converter output voltage, V D – the voltage drop on the diode The average value of the inductor current R 0 – the load resistance In the continuous conducting mode (CCM) I L = I Lsr - I L /2 In the discontinuous conducting mode (DCM) I L = 0

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10 Results of investigations the FAST algorithm clasical transient analysis Two nonphysical thermal time constants are used t th1 = 1 ms and t th2 = 10 ms. The convergence of calculations with FAST algorithm is observed after analysis of 16 -32 x T S. The steady state in the classical algorithm is observed after 6000 x T S. The FAST algorithm is over 200 times faster than the classical algorithm.

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11 Conclusions 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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12 Thank you for your attention

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