## GENERALIZED THERMAL CIRCUIT MODEL I

Predicting the temperature of a magnetic component is a key step in its design. This can be done using thermal equivalent circuits that contain all different heat transfer mechanisms, enclosed in thermal resistances, and magnetic losses modeled as equivalent current sources.

The aim of this App Note is to present a generalized thermal circuit model for the determination of temperature in magnetic components in different points of the windings and core.

**General equation**

Comparison between Fourier and Ohm’s laws allows us to set up a heat transfer network representing the components of a magnetic. The losses and the temperature of each node are connected by a matrix containing the thermal resistances. For the steady-state, the symbolic equation is presented to the right.

To get the temperature, both losses and thermal resistances of the magnetic element core and winding can be estimated analytically.

The example presented here is based on the paper “General Analytical Model for the Thermal Resistance of Windings Made of Solid or Litz Wire”, where M. Jaritz et al. use a transformer with one primary and one secondary winding. In this study, a generalization for *n* winding layers has been done.

**General thermal circuit**

To build the circuit, the components of a magnetic transformer are separated in the central leg of the core (*cl*), rest of the core (*cr*), bobbin (*b*) and winding layers (*w*) (with or without insulation) as shown in Figure 2.

** **

Besides the component lumping, the key step is splitting the winding into individual layers by:

- Injecting the winding losses per layer in the middle of each layer resistance halves.
- Calculating the thermal resistance* for each type of layer.
- Automating the calculation for
*n*layers.

*An iterative process may be done for the calculation of temperature-dependent resistances.

**Conclusion**

The use of a circuit model has several advantages since it encapsulates the complexity of the different parts of a transformer while being able to estimate the temperature of the magnetic with high speed and low computational effort. The independent calculation of both thermal resistances and losses per layer (which can be done analytically or using AI) allows us to determine each of them according to the wire used in that layer and the type of heat transfer mechanism. Finally, it is important to notice that superficial, hotspot and other temperatures are calculated all at once.