Rectifier (neural networks)

The Néel effect appears when a superparamagnetic material placed within a conducting coil is subjected to varying frequencies of magnetic fields. The non-linearity of the superparamagnetic material acts like a frequency mixer. The voltage measured at the coil terminals then comprises several frequential components, not only at initial frequencies, but also at some of certain linear combinations thereof. Therefore, the frequency shift of the field to be measured allows for the detection of a DC field using a standard coil.

Picture 1: magnetizing a superparamagnetic material.

"Neel Effect" is a trademark owned by the company Neelogy.

History

French physicist Louis Néel (1904-2000) discovered in 1949 that materials ferromagnetic finely divided nanoparticle lose their hysteresis below a certain size Louis Néel critical. This phenomenon is called superparamagnetism. The magnetization of these materials is according to the applied field which is highly non-linear as shown in the graph in Picture 1. This curve is well described by the Langevin function but for weak fields we can write more simply as limited development:

$M(H)={\chi }_{0}H+N_e{H}^3+\epsilon (H^3)$

where ${\chi }_0$ is the susceptibility at zero field and $N_e$ is called the Néel coefficient. The Néel coefficient reflects the non-linearity of superparamagnetic materials at low field.

Theory

Picture 2: Demonstration of the Néel effect.

Is a coil of $N$ turns with a surface $S$ through which a current excitation $I_{exc}$ and immersed in a magnetic field $H_{ext}$ 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, $e$, is given by the well known formula:

$e=-d\varphi /dt=-SdB/dt$

where $B$ is the magnetic induction itself given by the equation:

$B={\mu }_0{\mu }_r(H+M)$

In the absence of magnetic material $M=0$ and $B={\mu }_0{\mu }_r(H_{ext}+H_{exc})$. Differentiating this expression, it is obvious that the frequency of the voltage is the same as the excitation current $i_{exc}$ and / or magnetic field $H_{ext}$.

In the presence of superparamagnetic material Neglecting the higher terms of the Taylor expansion, we obtain for B: $B={\mu }_0{\mu }_r((1+{\chi }_0)(H_{ext}+H_{exc})+N_e(H_{ext}+H_{exc}{)}^3)$

New derivation of the first term of the equation ${\mu }_0{\mu }_r(1+{\chi }_0)(H_{ext}+H_{exc})$ provides frequency voltage components of the stream of excitement $i_{exc}$ and/or of the magnetic field $H_{ext}$. On the other hand, the development of the second term $(H_{ext}+H_{exc}{)}^3=H_{ext}^3+3H_{ext}^2{H}_{exc}+3H_{ext}{H}_{exc}^2+H_{exc}^3$ multiplies the different frequency components which intermodule frequencies starting components and generates their linear combinations.

'The non-linearity of the superparamagnetic material acts as a frequency mixer.'

Calling $H(l)$ the total magnetic field within the coil located at the abscissa, by integrating the above induction coil along the abscissa between 0 and $L_p$, and differentiating with respect to $t$, we get:

$u(t)=L\frac{dI(t)}{dt}+F_{Rog}\frac{d}{dt}[{\int }_0^{H}Lp(l)dl]+F_{Neel}[{\int }_0^{H}Lp(l)dl]I(t)\frac{dI(t)}{dt}$

We can find the conventional terms of self-inductance and Rogowski effect 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 harmonic 2, carrying the information flow field:

$u(t)=L{I}_{ex}{w}_{ex}\cos (w_{ex}t)+F_{Rog}\frac{d}{dt}[{\int }_0^{Lp}H(l)dl]+F_{Neel}[{\int }_0^{Lp}H(l)dl]\frac{I_{ex}^2}{2}{w}_{ex}\sin (2w_{ex}t)$

with $I(t)=I_{ex}\sin (w_{ex}t)$

Picture 3: spectral representation of the appearance of the emf due to the Néel effect around a high-frequency carrier.

Applications

The Néel effect current sensor

Picture 4: Design of current sensor Néel effect.

An important application of the Néel effect is the measure of magnetic field radiated by a conductor when a current. This is the principle of Néel effect current sensors, which have been developed and patented by the company Neelogy. The interest of Néel effect is particularly to allow accurate measurement of currents or very low frequency type sensor with a current transformer without contact.

The transducer of a Néel effect current sensor consists of a coil with the core is a filled composite of superparamagnetic nanoparticles. The coil is traversed by a current excitation $i_{exc}(t)$. In presence of an external magnetic field to be measured $H_{ext}(t)$ the transducer transposes by Néel effect the information to be measured, H (f), around a carrier frequency, the harmonic of order 2 excitation current 2$f_{exc}$, which is far easier. The electromotive force generated by the coil is proportional to the magnetic field to measure $H_{ext}(t)$ and to the square of the excitation current:

$fem(t)=F_{Neel}{i}_{exc}^2(t)H(t)$

To improve the performance of the measurement (linearity, temperature sensitivity, sensitivity to vibration, etc.), the sensor also includes a second winding-reaction against permanently to cancel the second harmonic. The relationship between the current reaction against-and the primary current is then purely proportional to the number of turns against reaction ($I_{cr}=I_p/N_{cr}$).

References

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See also

• Superparamagnetism
• Louis Néel

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