The temperature coefficient

Introduction

The soft material models provided for B(H) properties, depending on the temperature, with exponential decay, are defined using:
  • their counterpart models non-dependent on the temperature
  • plus a coeff(T) temperature coefficient, built on the basis of two exponential functions (detailed description in the following paragraphs)

Mathematical model

The coeff(T) temperature coefficient describes how materials' magnetic properties degrade when temperature increases up to the Curie temperature TC; this coeff(T) value ranges between 1 and 0 and is defined by two exponential functions:
  • the first, with a negative decay rate, is used when coeff(T) ranges from 1 to 0.1, which means up to a temperature T* equal to TC - 0.10536 C, where C is the inverse of the exponential decay constant of the material
  • the second, with a positive decay rate, is used in the neighborhood of the Curie point, when coeff(T) ranges from 0.1 to 0, which means beyond the temperature T*

From a mathematical point of view, the model for the coeff(T) function can be written as follows:

where the temperature T, the Curie temperature TC, as well as C (the inverse of the exponential decay constant of the material) are expressed in degrees Celsius °C. The coefficients

and

are determined so that the two exponentials can connect at the point where coeff(T*) = 0.1

Being the exponential decay constant of the second function ten times greater than its counterpart of the first exponential, at the temperature T* both exponential functions take the same value, thus ensuring the continuity of the global coeff(T) model, as illustrated in the figure below.

Model parameters

To apply this coeff(T) function to temperature-dependent properties of soft magnetic materials, Flux requires the user to provide:
  • the material Curie temperature TC, which can be found in manufacturer's data-sheets
  • and C, which is the inverse of the exponential decay constant of the material and can be considered a sort of temperature constant to describe how fast the material loses its magnetic properties when the temperature increases.

The figure below plots the coeff(T) function for TC = 727 °C and several values for the parameter C to illustrate its impact on the temperature-dependent material properties. The lower the value of C, the more the material retains its magnetic properties at temperatures close to the Curie point.