If a coil of  turns with a surface  through which passes a current of excitation  is immersed in a magnetic field  collinear with the axis of the coil, a superparamagnetic material is deposited inside the coil.
The electromotive force to the terminals of a winding of the coil, , is given by the formula:
where  is the magnetic induction given by the equation:
In the absence of magnetic material,
and
Differentiating this expression, the frequency of the voltage is the same as the excitation current  or the magnetic field .
In the presence of superparamagnetic material, neglecting the higher terms of the Taylor expansion, we obtain for B:
A new derivation of the first term of the equation  provides frequency voltage components of the stream of excitement  or the magnetic field .
The development of the second term  multiplies the frequency components in which intermodular frequencies start components and generate their linear combinations. The non-linearity of the superparamagnetic material acts as a frequency mixer.
Calling  the total magnetic field within the coil at the abscissa, integrating the above induction coil along the abscissa between 0 and  and differentiating with respect to  obtains:
with 
The conventional terms of self-inductance and Rogowski effect are found in both the original frequencies. The third term is due to the Néel effect; it reports the intermodulation between the excitation current and the external field.
When the excitation current is sinusoidal, the effect is Néel characterized by the appearance of a second harmonic carrying the information flow field: