# Temperature coefficient

## Introduction

The models provided for **B(H)** curves, depending on the temperature, with
exponential decay, are defined using:

- the previous models provided for soft materials
- a
**COEF(T)**temperature coefficient, built on the basis of two exponential functions (detailed description is in following blocks)

## Temperature coefficient

The **COEF(T)** temperature coefficient is defined by two exponentials:

- the first, with a negative curvature, is used when this coefficient ranges from 1 to
0.1 (T < T
_{1}) - the second, with a positive curvature, is utilized in the neighborhood of the Curie
point, when this coefficient ranges from 0.1 to 0 (T < T
_{1})

The shape of the **COEF(T)** temperature coefficient is represented in the figure
below.

## Mathematical model

The **COEF(T)** temperature coefficient is defined in the following way:

for T < T_{1}:

where for the temperature T_{1} we have COEF_{1}(T_{1}) =
0.1

The last relationship can be equally written as: T_{1} -Tc =C ln 0.9

for T > T_{1}:

where the quantity T_{2} has the value so that the connection of the two
exponentials could be effected in T_{1}, i.e. COEF_{2}(T_{1}) =
0.1

This last condition can be equally written as: T_{2} -T_{1} =0.1C ln
0.1

where:

- Tc is the Curie temperature °C
- C is the temperature constant °C

## Exact mathematic expression

The expression of COEF(T) used above between 1 and 0,1 is approximate. The accurate expression :

As Tc is elevated, around 1000 K, we use the approximation:

And at T_{d0} = 0°C:

## Example

The shape of the **COEF(T)** function is represented in the figure below.

The decrease of the** COEF(T)** coefficient is more or less rapid following the value
of the **C** temperature constant supplied by the user.