Method of Electro-Thermal Modeling of Electronic Equipment Using the Compensation Theorem

In this work, we propose a method for combining two computer models of simultaneously occurring electrical and thermal processes. These models function as electrical and thermal submodels, collectively forming a unified electro-thermal model. The structural elements of radioelectronic equipment encompass both the supporting components of the structure and the housings of electrical components, which are typically mounted on printed circuit boards. To enhance the accuracy of the modeling, the electro-thermal model also incorporates parasitic electrical resistances, capacitances, and inductances, which become significant at high frequencies. In this study, a voltage divider is presented as a case example of the described electro-thermal modeling. The electro-thermal analogy has proven effective in constructing the thermal model of the divider. The novelty of the proposed method lies in the application of the compensation theorem, known from electrical engineering, to develop a unified electro-thermal model of radioelectronic equipment. The electro-thermal model is represented as a topological graph and is compatible with the Simulation Program with Integrated Circuit Emphasis (SPICE). The increase in resistance of each resistor in the unified electro-thermal model, due to the temperature rise of that resistor, can be treated as an additional resistance. The compensation theorem allows these additional resistances to be replaced by corresponding voltage sources. Ultimately, to obtain a unified electro-thermal model, it is essential that the voltages of these sources in the electrical submodel depend on the nodes of the thermal submodel, with potentials that are numerically equal to the temperatures of these resistors. For this purpose, voltagecontrolled voltage sources are available in software tools such as PSpice, LTSpice, Proteus, NI Multisim, and others. The feedback of power dissipation in the resistor to the node corresponding to the temperature of that resistor is accomplished through a voltage-controlled current source.