*4.2. Parameters Values of a New Model*

Using the measurement set-up (Figure 2), measurements of transient thermal impedances were performed. They were carried out for all the considered inductors at different values of power dissipated in the cores and windings. Based on the obtained measurement results, values of parameters of the nonlinear thermal model were determined for each considered inductor with the use of the method described in Section 2. For example, values of parameters of this model for inductors with the medium cup core and with the toroidal core of the external diameter equal to 16 mm are presented in Table 3.


**Table 3.** Values of parameters of the nonlinear thermal model of inductors with the medium cup core and with the toroidal core.

As can be observed, for both the inductors, the same number of thermal time constants, related to the coefficients *ai*, which describe particular transient thermal impedances, is obtained. Values of thermal capacitances characterising thermal properties of the core are higher than those capacitances characterising the winding properties. Values of parameters *Rth*0 appearing in the description of individual transient thermal impedances are similar for both the considered inductors. In contrast, even ten-fold differences are observed between values of *b* parameter describing the considered transient thermal impedances.

Table 4 compares the values of parameters of transient thermal impedance of the core *ZthC*(*t*) obtained for the inductor with cup cores of different sizes.


**Table 4.** Values of parameters describing *ZthC*(*t*) of inductors with cup cores.

As it is visible, an increase in the dimensions of the cup core causes a decrease in the value of parameters *Rth*0 and *Rth*1, whereas parameter *b* achieves maximum value for medium cup core. Also an increase in thermal capacitances values with core size is observed.

Table 5 compares values of parameters of transient thermal impedance of the winding *ZthW*(*t*) obtained for the inductor with cup cores of di fferent sizes.


**Table 5.** Values of parameters describing *ZthW*(*t*) of inductors with cup cores.

As can be seen, an increase in the dimensions of the cup core causes a decrease in the value of parameters *Rth*0 and *Rth*1, whereas parameter *b* have the same value for both considered cup cores. Additionally, increase in dimensions of the cup core causes a visible increase in the value of thermal capacitance.

Table 6 collects the values of parameters of transient thermal impedance of the core *ZthC*(*t*) obtained for the inductor with toroidal cores of di fferent dimensions.

**Table 6.** Values of parameters describing *ZthC*(*t*) of inductors with toroidal cores of different dimensions.


As shown, an increase in the dimensions of the toroidal core causes an increase in the value of parameters *Rth0* and thermal capacitances.

Table 7 collects values of parameters of transient thermal impedance of the winding *ZthW*(*t*) obtained for the inductor with toroidal core of di fferent dimensions.


**Table 7.** Values of parameters describing *Zthw*(*t*) of inductors with toroidal core.

As can be observed, an increase in the toroidal core dimensions causes an increase in thermal capacitance and a decrease in the parameter *Rth*0. For example, parameter *Rth*0 decreases even triple when the diameter of the core increases 2.5 times.
