Krzysztof Górecki and Kalina Detka Modelling thermal phenomena in semiconductor devices and magnetic elements of boost converter using averaged models Krzysztof Górecki and Kalina Detka Department of Marine Electronics, Gdynia Maritime University, Poland 11/11/2018

Outline Introduction Averaged electrothermal models of diode transistor switch and inductor Validation of considered models Conslusions 11/11/2018

Introduction The important part of switched-mode power supplies is a single- inductor dc-dc converter, for example the boost converter. Semiconductor devices and an inductor with the ferromagnetic core are the main components of this dc-dc converter. In many papers the properties of this circuit are analysed, but the consideration focused only on semiconductor devices ignoring properties of magnetic elements. As it is commonly known, inductance L of an inductor with ferromagnetic core is not constant, but it depends on current i. In our previous papers it is shown that the nonlinearity of dependence L(i) significantly influences the shape of characteristics of the considered converter. 3 11/11/2018

Introduction In the cited papers, in order to calculate the characteristics of dc- dc converters the classical transient analysis method is used, which is time consuming, and there are often problems to obtain convergence of computations. In some papers of many authors average models of the dc–dc converter are proposed. In these models inertia of semiconductor devices and non- linearity characteristics of these elements and inductors are ignored. During dc-dc converters operation the internal components temperature rises due to a self-heating phenomenon. To take into account this phenomenon in the computer analysis, special electrothermal models are required. 4 11/11/2018

Introduction In this paper a modified version of the average electrothermal models of the diode – transistor switch and the inductor dedicated to the electrothermal analysis of dc-dc converters are proposed. The inductor model takes into account magnetic and thermal phenomena and power losses in the core and in the winding. The parameters of this model can be calculated from the data supplied by the manufacturers. 5 11/11/2018

Averaged electrothermal models of diode transistor switch and inductor The average electrothermal model of the diode-transistor switch is proposed. The model takes into account energy losses for the switch-on semiconductor devices and self-heating phenomenon. Additionally, this model allows determining characteristics of dc-dc converters operating in CCM and DCM mode. This model is dedicated to use with the linear inductor only. The modified form of this model is shown in Figure. 6 11/11/2018

Averaged electrothermal models of diode transistor switch and inductor The controlled voltage sources Et and Er represent the unipolar transistor, The diode is represented by the controlled current source Gd. The independent voltage source V1 of the zero value is used to control the diode average current, The auxiliary circuit is used to determine the mode of dc – dc converter (CCM or DCM) including the considered switch. The voltage on the controlled voltage source Eu depends on the voltage on terminal L, which corresponds to inductance of the inductor included in the considered dc – dc converter. 7 11/11/2018

Averaged electrothermal models of diode transistor switch and inductor The controlled voltage sources Eron, Erd, Eud model the temperature changes of the transistor on state resistance RON, series diode resistance RD and voltage UD on the forward biased p-n junction. Voltage Von on the source Eton is indispensible in the model of the inductor described in the next section. The value of the internal diode and transistor temperatures are calculated using the voltage sources Etd and Ett. The values of these temperatures are equal to the values of the voltages on terminals TT and TD. 8 11/11/2018

Averaged electrothermal models of diode transistor switch and inductor The average electrothermal model of the inductor has the form of a macromodel. Terminals A and B are the terminals of the inductor. The terminal L provides the voltage corresponding to the inductor inductance, Von – the voltage drop on the switched-on transistor terminal TU - the temperature of the winding, terminal TR - the temperature of the core. 9 11/11/2018

Averaged electrothermal models of diode transistor switch and inductor In the main circuit: the voltage source VL with the zero output voltage monitors the current of the inductor, the resistor RS0 represents the winding resistance of the inductor for the direct current at the reference temperature T0 the controlled voltage source ERS describes the influence of temperature and losses of the inductor series resistance. The controlled voltage source ERN models the skin effect The controlled voltage sources ELS model dependences of the inductor inductance L on the current, frequency and temperature. In the auxiliary block the controlled voltage sources are used to calculate the value of the magnetic force H, flux density B, Bsat saturation flux density and the auxiliary value C. 10 11/11/2018

Validation of considered models Inductors containing the toroidal core made of: ferrite RTF (F-867) powdered iron material RTP- T106. For each of these cores the coils of enamel copper wire having the diameter dD = 0.8 mm were wound. Inductance of the inductor with the core RTP in the current range is almost constant, Inductance of the inductor with the core RTF is a strongly decreasing function of the current. 11 11/11/2018

Validation of considered models the electrothermal analysis of the boost converter operating in a wide range of load resistance for the two values of control signal frequencies of 50 and 400 kHz, duty cycle d = 0.5 and input voltage Uwe = 12 V. In the following figures: the points represent the results of measurements the solid lines - the results obtained using the electrothermal averaged model of the diode-transistor switch and the averaged electrothermal model of the inductor, the dashed lines - the results of calculations using the linear model of the inductor having the maximum value of considered inductor inductance the dotted lines - the results obtained using the linear model of the inductor with the minimum value of the considered inductors inductance. 12 11/11/2018

Validation of considered models At f = 50 kHz the test boost converter is operating in DCM and CCM in the considered range of load resistance. An increase in frequency from 50 to 400 kHz causes a rise to 20% in the output voltage. 13 11/11/2018

Validation of considered models The calculations using the proposed models allowed obtaining the good agreement between the calculation and measurement results for both frequencies of the control signal The results obtained using the lossless model of inductor with L = 2 mH caused an even tenfold overestimate of the value of the output voltage. The dependence of watt-hour efficiency of load resistance indicates the maximum at the resistance of about 50 Ω. In the calculations performed using the lossless model of the inductor for f = 400 kHz and L = 10μH, the watt-hour efficiency excess by about 20% the measurement results 14 11/11/2018

Validation of considered models In the range of high values of load resistance R0 the core temperature achieves similar values for both frequencies. The results obtained using the new models have a similar character as the results of measurements. The use of a linear model of the inductor in the analysis does not allow calculating the temperature of the inductor core or winding. 15 11/11/2018

Validation of considered models Changing the mode of converter operation at a lower frequency occurs at the load resistance of about 100 Ω, while for higher control signal frequencies the change was observed at R0 = 1 kΩ. The results obtained using the new models show the good agreement with the results of measurements. Using a linear model of the inductor causes even double increase of the output voltage in the range of load resistance R0 > 100 Ω. 16 11/11/2018

Validation of considered models The dependence of watt-hour efficiency of load resistance have a maximum at the resistance of about 20 Ω. An increase of the control signal frequency causes an even twofold drop in the value of watt-hour efficiency, especially for load resistance R0 > 100 Ω. From the calculations obtained using a lossless model of the inductor for both values of inductance, watt-hour efficiency does not change for R0 > 50 Ω, and the results are inflated by about 30% at the higher value of frequency. 17 11/11/2018

Validation of considered models The inductor core temperature is a decreasing function of load resistance, The higher value of the core temperature for f = 50 kHz is observed. The good agreement between the results of measurements and calculations was obtained. 18 11/11/2018

Validation of considered models The time of calculations using the new models is up to ten thousand times shorter than the time of calculations in the transient analysis. Despite the fact that the shortest duration of calculations was obtained using a linear model of the inductor, it does not provide the good agreement with the results of measurements in a wide range of load resistance. Using the nonlinear average electrothermal model of the inductor extends the duration of calculations by just about 0.2 - 0.3 s, and significantly improves accuracy. 19 11/11/2018

Conclusions The paper presents a new form of the average electrothermal model of the diode – transistor switch and the average electrothermal model of the inductor. The proposed models are verified experimentally in the boost converter. The results show that the proposed model allows obtaining the good agreement between the measurements and calculations for two inductors containing cores made of ferrite or powdered iron. This shows versatility and usefulness of the presented model. 20 11/11/2018

Conclusions The calculation time of the presented model is up to ten thousand times shorter than the time of calculation of the electrothermal transient analysis and comparable to the time of calculations performed with a linear model of inductor. Beside the short time of calculations, the proposed model also allows determining the temperature of the inductor core and the winding. The values of these temperatures are important from the point of view of assessing reliability of the inductor and the circuit containing this element. 21 11/11/2018