# SPICE-Aided Compact Electrothermal Model of Impulse Transformers +
## 5 Conclusions  
This article presents the new electrothermal compact model of the impulse transformer. This model belongs to multi-domain models and it is dedicated for use with SPICE. In this model, magnetic phenomena occurring in the core, electrical phenomena in the winding, and thermal phenomena in the transformer components and between these components are simultaneously taken into account. In particular, the non-linearity of the removal of  
Figure 14: Non-isothermal electrical characteristics of the planar core. Figure 13: Dependences of the transformer energy efficiency on frequency. the heat generated in the transformer components is included in the model by the use of analytic formulae describing dependences of self and transfer thermal resistances on dissipated power. Using the proposed model, it is possible to compute waveforms of voltages and the current of each winding, waveforms of magnetic force and magnetic flux density in the core, and waveforms of power dissipated in each winding and in the core. Taking into account thermal phenomena, waveforms of temperature of the core and of each winding can be also computed. Accuracy and practical usefulness of the new model were verified experimentally for the transformers with ring cores made of different ferromagnetic materials and a planar transformer with the ferrite core. The demonstrated results of computations and measurements proved that the new model correctly describes the influence of frequency and load resistance on the transformer output voltage, its energy efficiency, and temperatures of the core and each winding. The observed differences between the computations and measurements results were smaller than in other models. Of course, many of the simple transformer models described in the literature do not take into account thermal phenomena and such models were not compared with the proposed model. The accuracy of computations obtained using the proposed model was also satisfied from the point of view of scientific investigations and industry applications. Typically, the difference between computations and measurements results did not exceed a few Celsius degrees (for temperature) or a few percent for voltage and energy efficiency. The disadvantage of the proposed model is long computation time indispensable to compute the transformer characteristics shown in this paper. In Table 2, the computation times of the mentioned characteristics are compared for the considered transformers. It is apparent that the computation time depends on the values of the model parameters, which correspond to the type and shape of the ferromagnetic core. The shortest computation times were obtained for the RTF ring core, whereas the longest were for the RTP core. Of course, the computation time will be shorter when fast computers are be used. The presented investigations result also show the strong influence of the selection of the ferromagnetic material used to build the transformer core on the electrical and thermal properties of the transformers. For example, the transformer containing the RTP core is characterized by lower energy efficiency than transformers with other cores. Additionally, the core temperature of such transformers is monotonically increasing function of load resistance. For RTP cores, the transformer output voltage is much smaller (even twice) than for RTN or RTF cores. The described model and presented investigations results can be usable for designers of electronic circuits. The presented findings can be also used in didactics to illustrate the influence of selected factors on the characteristics of impulse transformers. [PERSON]. ([PERSON]) supervised the investigations and took part in elaboration of the article conceptualization, investigation methodology, validation of the model, and writing the article. K.G. ([PERSON]) performed measurements and took part in elaboration of the article conceptualization, validation of the model, and writing the article. Both authors have read and agreed to the published version of the manuscript.