**3. Estimation of Model Parameters**

Practical applications of the proposed model require estimation of parameter values existing in this model. For example, an estimate is performed for the IGBT of the type IGP06N60T [29] by Infineon Technologies and for the diode of the type IDP08E65 [30] by Infineon Technologies. Input data are characteristics of such devices measured by the authors with the use of the impulse method [31] and a source-meter Keithley 2612a [32] at di fferent fixed values of ambient temperature. When these measurements are performed, the tested semiconductor devices are situated in a thermal chamber, in which the adjustable value of temperature can be obtained.

Values of the model parameters obtained by matching piecewise linear models of characteristics of the considered devices are given in Table 1.

**Table 1.** Values of parameters of the piecewise linear model of the used insulated gate bipolar transistor (IGBT) and diode.


In Figures 3 and 4 measured (points) and computed (lines) characteristics of the diode (Figure 3) and IGBT (Figure 4) are shown. These characteristics are measured and computed at selected values of ambient temperature Ta.

**Figure 3.** Characteristics of a forward-biased diode computed with the use of a piecewise linear model (lines) and measured (points) at selected values of temperature Ta.

**Figure 4.** Output characteristics of insulated gate bipolar transistor (IGBT) computed with the use of a piecewise linear model (lines) and measured (points) at selected values of temperature Ta.

As is visible, the results of measurements and computations are convergen<sup>t</sup> for both considered semiconductor devices in a wide range of changes of ambient temperature Ta. As can be observed, all characteristics are described using 4 line segments. A slope of the considered characteristics increases with an increase of the main current of the tested device. This means that series resistances of the diode and IGBT decrease with an increase of this current. It is also observed that the diode forward-voltage and on-voltage of IGBT at zero current decreases with an increase in ambient temperature.

With the diode, an increase in temperature causes a decrease in diode forward-voltage. In turn, for IGBT with a range of low collector current values, an increase in ambient temperature causes a decrease in on–voltage of IGBT. In contrast, for high collector current values, an increase in temperature Ta causes an increase in on–voltage of IGBT.

The presented characteristics correspond to isothermal operating conditions of tested devices, at which self-heating phenomena can be omitted. In the real case, device internal temperature is higher than ambient temperature as a result of the mentioned phenomena [26,27,33]. The cooling conditions of this device are characterized by thermal resistance. This parameter is measured using impulse electrical methods described in [34–36].

Both considered semiconductor devices are situated in the TO-220 case. The measured values of IGBT and the diode are nearly the same and they are equal to about 44 K/W. Reference temperature *T*0 is equal to 20 ◦C.
