SaM - VRS (Variable Reluctance Sensors)

Memory Card

---

We have seen how inductive proximity sensors works. Now we can go instead to the other possibility: I take into account the fact that there is no excitation.

Here’s a VRS (variable reluctance sensors):

• When speaking about this usually we think to a structure where there is no external excitation.
  ⇒ So an active sensor.
• For semplicity (and also because it’s a good approximation) I consider $I=0$.7

In this case we have to forget the part which depends on the current, so we will get an output voltage equal to:$v=-N\frac{d}{dt}\left(\frac{{\text{MMF}}_{eq}}{{\mathcal{R}}_{TOT}}\right)=N\frac{{\text{MMF}}_{eq}}{{\mathcal{R}}_{TOT}^2}\frac{d{\mathcal{R}}_{TOT}}{dt}$Where:

• $v$ is the electro-motive force (this is actual voltage measured in Volts, but has sign inverted with rispect to the actual voltage drop).
• ${\text{MMF}}_{eq}$ : equivalent magneto motive force.
• ${\mathcal{R}}_{TOT}$ : total reluctance

And if I use a very large resistance $R_L\to \infty$, for example tanks to an amplifier, then actually I will have a very small current, and the assumption $I=0$, is true in general. So not only because I don’t force a current, but also there is no current induced in the circuit due to the very large impedance at the sensing coil.

---

IMPORTANTE So in this case to generate a voltage I need a varying reluctance, so the drawing doesn’t show it but I need the gap length to change.

---

We have also seen a variable reluctance sensor used to measure speed, or anglular speed:

This is its lumped parameter model:

So while the thoothed wheel rotates this will be the plot of $v=\frac{dx}{dt}$:

• The period $T$ is given by the angular rotation between two theeth, the more theet the wheel has, the lower will be the period:$T=\frac{1}{\omega \cdot \#\text{theeths}}$Where: - $\omega$ (previously called ${\omega }_M$) is the angular velocity. - $\#\text{theeths}$ : number of theets.
  • We need to mention that also the amplitude of the graph will scale with $\omega$, not just the period.
    This can be a problem, because we will have a good signal to noise ratio (SNR) when the machine is rotating fast, and a lower one when it rotates slow.
    If the machine is still the only thing I will measure will be the noise.