SaM - Inductive Proximity Sensor

Here is a scheme on how we can use a magnetic circuit, to make a proximity sensor, like so:

• We consider to have a ferromagnetic target.
• $I$ is the current flowing here generated by the electric circuit.
• The core has relative permeability ${\mu }_r$, which is large.
• $S_1$: the cross area.
• We expect that the flux line will develop with this geometry here, so:
  • Half circle: $\pi R$
  • Small gap: $l_g$
  • Straith line: $2R$

The inductance value will be:IMPORTANTE $L=\frac{N^2}{{\mathcal{R}}_0\left(1+{\alpha }_T{l}_g\right)}$Here are the calculations:
(NOT IMPORTANT)

• So we have all these surfaces, which have the same magnitude order, but we have these two ${\mu }_1$ and ${\mu }_T$, which really are reallyh larger than ${\mu }_0$.
• so we expect $\frac{2l_g}{{\mu }_0{S}_g}$ to be the most important, even if $\lg \ll R$, the order of magnitude of ${\mu }_0$ and ${\mu }_T$ is bigger.

The sensitivity will be:IMPORTANTE ${\alpha }_T=\frac{l_g}{R{S}_g}\frac{{\mu }_T}{{\mu }_0}$Where:

• $R$ : is fixed due to the sensor.
• $S_T$ and ${\mu }_T$ depend on the material, of the target.
  ⇒ So you see that the sensitivity $\alpha$ this depends on the target, so (${\alpha }_T$)
  ⇒ So you change the material of the target, you change the sensitivity.
  ⇒ The larger is ${\mu }_T$, the larger is the sensitivity.

You can use the same arrangement to sense a variation of the reluctance due to the gap variation, ==even if the target is not ferromagnetic==, but in that case you will have really small sensitivity.

It’s quite similar to what happens for a capacitive sensor, ==but here I have a dependence on the material type==.

Here’s an example of how we can exite and read the sensor:

• I have an electrical circuit for exciting ($V_g$), and another one for sensing, called “sensing coil” ($V_o$).
• Using this setup, usually, the frequency needed to have a sufficiently strong signal are much lower than those used for capacitive sensing.
  In capacitive sensing we have said that we use $10kHz÷MHz$.
  Here, usually since signals are larger, $f_{\text{exc}}$ is less than $20kHz$.
• Here’s a comparison between inductive proximty senors vs. capacitive proximity sensors