**4. Results of Measurements and Computations**

In order to verify usefulness of the proposed electrothermal averaged model of a diode–transistor switch, measurements and computations of characteristics of the boost converter with considered semiconductor devices were performed. A diagram of the tested converter is shown in Figure 5, whereas a photo of the tested converter is presented in Figure 6.

In the considered converter, the input voltage Vin was equal to 12 V, and R0 was load resistance. The inductance of inductor L1 was equal to 560 μH and capacitance of capacitor C1 was equal to 1 mF. Voltage source Vctrl produced a rectangular pulsed train of frequency f equal to 10 kHz and duty cycle d. Ammeters were used to measure the input and output currents of the tested converter. Internal resistance of these ammeters was equal to 0.31 Ω. The prototype was mounted on a PCB; the diode of the type IDP08E65 and IGBT of the type IGP06N60T operated without any heat-sinks. The control signal was given by a signal generator exciting gate driver IR2125 by Infineon Technologies.

Some waveforms of voltages and currents of the tested DC–DC converter were measured using an oscilloscope Rigol MS05104 and current probe Tektronix PCPA 300 for different parameters of the control signal and load resistances. For example, in Figure 7 measured waveforms of vGE(t) voltage (yellow line), vCE(t) voltage (violet line) and iL(t) current (blue line) are shown. The mentioned quantities are marked in Figure 5. Waveform of iL(t) was obtained after conversion of the measured current into voltage in the current probe. The conversion coefficient was equal to 1 A/V. During these measurements load resistance R0 was equal to 47 Ω.

**Figure 5.** Diagram of the tested boost converter.

**Figure 6.** Photo of the tested boost converter.

**Figure 7.** Measured waveforms of vGE(t) voltage, vCE(t) voltages and iL(t) current in the tested boost converter operating at load resistance R0 = 47 Ω.

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As it can be observed, the signal controlling the input of IGBT (vGE voltage) had frequency equal to 10 kHz, duty cycle equal to 0.5, low level voltage equal to zero and high level voltage equal to 15 V. These parameters values of the control signal were adequate for the used transistor. The transistor output voltage vCE(t) had a shape of a rectangular pulsed train. The highest level of this voltage was equal to about 22 V. The current iL(t) had positive values only, which proved that the tested converter operated in CCM.

It is important to notice that the tested DC–DC converter operated without any feedback loop, typically used in switch-mode power supplies including such converters. At the chosen operating condition, the influence of parameters of the control signal and on the load resistance were not compensated by the feedback loop. Therefore, any disadvantages of the proposed model can be clearly illustrated for the tested circuit.

Selected resulted of measurements and computations of the considered DC–DC converter are shown in the successive figures. In these figures points denote the results of measurements, solid lines—the results of computations performed with the use of the proposed electrothermal averaged model of a diode–transistor switch including IGBT and a rapid switching diode (called also the new model), black dashed lines—the results of computations performed with the use of the averaged model of a diode transistor switch with ideal switches described e.g., in [5,8] and blue dotted lines—the results of computations performed with the use of the averaged model of a diode–transistor switch including IGBT described in [21].

Figures 8–11 present computed and measured characteristics of the considered converter operating at the fixed value of duty cycle d = 0.5 and the varied value of load resistance R0. In turn, Figures 12–15 show characteristics of this converter operating at the fixed value of load resistance R0 = 47 Ω and the varied value of duty cycle d. Values of voltages and currents were measured with the used of laboratory voltmeters and ammeters. The diode and transistor temperatures were measured with the use of an infrared method performed with a pyrometer PT-3S by Optex [37]. This instrument made it possible to measure the case temperature of the mentioned semiconductor devices. Due to a very small value of junction–case thermal resistance of the considered semiconductor devices—which was much lower than junction-ambient thermal resistance—a di fference between internal and case temperatures of these devices was not higher than 5 ◦C.

In Figure 8 measured and computed dependences of converter output voltage Vout on load resistance R0 are presented. As is visible, in the considered operating conditions, the boost converter operated in CCM for R0 < 100 Ω and in DCM for R0 > 100 Ω. In both modes of operation, the new model guarantees good accuracy of computations. At small values of load resistance, a decrease was visible in the value of output voltage caused by influence of a voltage drop on the switched on transistor and diode. This voltage drop was an increasing function of converter output current and a decreasing function of load resistance R0. Literature models described in [5,8,21] could be used for the converter operating in CCM only, because di fferences between the results of computations performed with these models and the results of measurements were acceptable only in this mode. Of course, the results performed with the use of the model proposed in [21] were more convergen<sup>t</sup> with the results of measurements in CCM than the results performed with the model given in [5,8].

Figure 9 presents dependences of watt-hour e fficiency of the considered DC–DC converter on load resistance.

The obtained values of watt-hour e fficiency were in the range from 0.8 to 0.9. Values of this parameter computed using the electrothermal model di ffered from the results of measurements by no more than 7%. The resulted obtained using the considered literature models were overstated even by 17%.

In Figure 10 dependence of internal temperature of IGBT on load resistance was shown. Such dependence could be obtained with the use of the electrothermal model only.

 **Figure 8.** Computed and measured dependences of boost converter output voltage on load resistance.

**Figure 9.** Computed and measured dependences of watt-hour efficiency of the boost converter on load resistance.

**Figure 10.** Computed and measured dependence of internal temperature of IGBT on load resistance.

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**Figure 11.** Computed and measured dependence of internal temperature of the diode on load resistance.

**Figure 12.** Computed and measured dependences of boost converter output voltage on duty cycle.

**Figure 13.** Computed and measured dependences of watt-hour efficiency of boost converter on duty cycle.

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**Figure 14.** Computed and measured dependences of internal temperature of IGBT on duty cycle.

**Figure 15.** Computed and measured dependences of internal temperature of the diode on duty cycle.

As can be seen, very good accuracy in modeling this dependence was obtained only was CCM. In DCM differences between the results of measurements and computations increased with an increase in load resistance. They exceeded even 20 ◦C at R0 > 6 kΩ which could be connected with a long switching-off process of IGBT [38], that was not taken into account in the proposed model.

In Figure 11 measured and computed (using the new model) dependence of internal temperature of diode on load resistance is shown.

The considered dependence is a monotonically decreasing function. The result of computations were convergen<sup>t</sup> with the results of measurements. Differences did not exceed 4 ◦C. Of course, the considered literature models did not make it possible to compute such dependence.

Figure 12 shows computed (with the new model) and measured dependences of converter output voltage on duty cycle.

In the whole considered range of changes of duty cycle the tested boost converter operated in CCM. The measured dependence Vout(d) is a monotonically increasing function, but measurements were performed only for d < 0.67. The range of changes of d was limited due to a high increase in internal temperature of IGBT, which attained even 120 ◦C. The considered dependences computed using the electrothermal model and the model given in [21] had maxima at d > 0.9. These maxima were observed due to voltage drops on switched-on semiconductor devices [16]. It was also visible that due to self-heating the value of these maxima decrease even three times. Differences between the results of measurements and computations were small and they do not exceed 5%.

Figure 13 illustrates dependence of watt-hour efficiency of the tested boost converter on duty cycle.

As can be observed, dependences η(d) were monotonically decreasing functions. The results of computations performed with the electrothermal model were convergen<sup>t</sup> with the result of measurements. Differences do not exceed 2%. Values of watt-hour efficiency computed using the other models were overstated even by 15%.

Figure 14 presents measured and computed (with the new model) dependence of internal temperature of IGBT on duty cycle.

The considered dependence was an increasing function. The results of computations differ from the results of measurements not more than 5 ◦C.

Figure 15 shows measured and computed (with the new model) dependence of internal temperature of the diode on duty cycle.

It can be easily observed that temperature TjD increased with an increase in duty cycle. This means that the power dissipated in this diode increased, despite the fact that the time in which this diode was forward-biased decreased. The differences between the results of computations and measurements did not exceed a few degrees Celsius.

Figure 16 illustrates influence of duty-cycle on the output characteristics of the tested DC–DC converter (Figure 16a) and the dependence of diode internal temperature on the converter's output current iout.

**Figure 16.** Computed and measured output characteristics of the tested DC–DC converter (**a**) and dependences of internal temperature of the diode on converter output current (**b**) for selected values of duty cycle.

As it can be observed in Figure 16a, very good agreemen<sup>t</sup> between computed and measured output characteristics of the tested converter was obtained at all the considered values of duty cycle. The considered dependence was a decreasing function. The critical output current at which the mode of DC–DC converter operation change from DCM to CCM decreased with an increase in duty cycle d. In turn, in Figure 16b, it can be observed that the dependence TjD(iout) was an increasing function and values of temperature TjD increase with an increase in duty cycle.

An influence of ambient temperature on characteristics of the tested boost converter is illustrated in Figure 17.

It is clearly visible in Figure 17a that changes in value of ambient temperature practically do not influence value of output voltage of the tested boost converter. Points marking results of measurements performed in both the values of ambient temperature practically overlap as well as lines representing computations performed for these values of Ta. Changes in value of Vout voltage caused by change in ambient temperature did not exceed 0.3 V. Hence, small value of these changes was a result of weak influence of temperature on IGBT output voltage. The same result were obtained during computations and measurements. In contrast, in Figure 17b, it is visible that change in the value of ambient temperature caused practically the same change in the value of internal temperature of the diode. The same influence of ambient temperature the Authors observed also for internal temperature of IGBT.

Some additional computations of the tested boost converter were performed using the worked-out electrothermal averaged model of a diode transistor switch, including the IGBT and a rapid switching diode. For example, Figure 18 illustrated influence of load resistance on dependences of converter output voltage (Figure 18a) and internal temperature of the diode (Figure 18b) on the duty cycle.

**Figure 17.** Computed and measured dependences of converter output voltage (**a**) and internal temperature of the diode (**b**) on duty cycle.

**Figure 18.** Computed dependences of converter output voltage (**a**) and internal temperature of the diode (**b**) on duty cycle for selected values of load resistance.

As it can be observed, an increase of load resistance R0 caused an increase in the maximum value of converter output voltage and an increase in the value of duty cycle, at which the maximum in characteristic Vout(d) was observed. The maximum value of Vout voltage changes in the range from 30 to 94 V. In turn, internal temperature of the diode was an increasing function of duty cycle and a decreasing function of load resistance. It is worth noticing that at the considered cooling conditions of the diode the acceptable value of duty cycle was strongly limited. For the considered values of R0 the maximum value of duty cycle increased from about 0.5 (for R0 = 15 Ω) to about 0.8 (for R0 = 150 Ω).

Figure 19 illustrates the influence of duty cycle on dependences of converter output voltage (Figure 19a) and internal temperature of IGBT (Figure 19b) on load resistance.

In Figure 19a it is visible that dependence Vout(R0) was an increasing function for all considered values of duty cycle d. It could also be observed that the value of load resistance at which the border between the CCM and DCM exists moves right with an increase in the value of d. In CCM influence of energy losses in semiconductor devices on converter output voltage were much more visible for the highest value of duty cycle. In turn, in Figure 19b it can be seen that internal temperature of IGBT is a decreasing function of load resistance and an increasing function of duty cycle. Cooling conditions of IGBT limit the lowest admissible value of load resistance at the adjusted duty cycle. In the considered case for d = 0.8 load resistance should not be smaller than 100 Ω in order to limit the value of internal temperature of IGBT to 150 ◦C.

**Figure 19.** Computed dependences of converter output voltage (**a**) and internal temperature of IGBT (**b**) on load resistance for selected values of duty cycle.
