# Sensor Systems

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theory:sensor_technology:st18_inductive_sensors

# Sensors based on magnetic effects

## Physical principles

There are several sensor types where the operation is based on magnetic principles. For example:

• Magnetic sensors (Reed contacts)
• Inductive sensors
• Magneto-resistive sensors
• Hall sensors
• LVDT
• Resolvers.

How they differ depends mainly on the physical phenomenon that is behind the operation. To explain this, consider the following phenomena:

1. An electric current results in a magnetic field (as in a coil)
2. A changing magnetic field results in an electric field (as in a dynamo)
3. A static charge results in an electric field
4. A magnetic monopole does not exist
5. A moving charge in a magnetic field experiences a force

These five phenomena may relate to principles you have heard of or with which you are familiar. They are in fact equal to the four Maxwell equations:

\begin{aligned} \nabla\times\mathbf{H} \quad & = \quad \mathbf{J}_{f} + \frac{\partial\mathbf{D}}{\partial t} , & \quad \text{(Ampère's circuital law with Maxwell addition)} \\[5pt] \nabla\times\mathbf{E} \quad & = \quad -\frac{\partial\mathbf{B}}{\partial t}, & \quad \text{(Faraday's law of induction with Maxwell addition)} \\[5pt] \nabla\cdot\mathbf{D} \quad & = \quad \rho_{f}, & \quad \text{(Gauss's law)} \\[5pt] \nabla\cdot\mathbf{B} \quad & = \quad 0 & \quad \text{(Gauss's law for magnetism)} \end{aligned}

or in integral form: \begin{aligned} \oint \mathbf{H}\cdot\mathrm{d}\mathbf{l} \quad & = \quad \int_{S}\left ( \mathbf{J}_{f} + \frac{\partial\mathbf{D}}{\partial t} \right )\cdot\mathrm{d}\mathbf{S} , & \quad \text{(Ampère's circuital law)} \\[5pt] \oint \mathbf{E}\cdot\mathrm{d}\mathbf{l} \quad & = \quad \int_{S}\left ( -\frac{\partial\mathbf{B}}{\partial t} \right )\cdot\mathrm{d}\mathbf{S} , & \quad \text{(Faraday's law of induction)} \\[5pt] \oint_{S} \mathbf{D}\cdot\mathrm{d}\mathbf{S} \quad & = \quad \int_{v}\rho_{f}\mathrm{d}v , & \quad \text{(Gauss's law)} \\[5pt] \oint_{S} \mathbf{B}\cdot\mathrm{d}\mathbf{S} \quad & = \quad 0 & \quad \text{(Gauss's law for magnetism)} \end{aligned}

plus the Lorenz force law

$$\mathbf{F}=q\left ( \mathbf{E}+\mathbf{v}\times\mathbf{B} \right )$$

The first two laws explain the behaviour inductive sensors since they show the mutual interaction between varying magnetic and electric fields. A varying electric field generates a magnetic field, and a varying magnetic field generates an electric field. The fifth law, Lorenz´s law, is the basis of AMR and Hall sensors because it describes the behaviour of moving electrons in an magnetic field.

Fig. 1: Dia05 Fig. 2: Dia06 Fig. 3: Dia07 Fig. 4: Dia08

## Magnetic sensors

Fig. 5: Dia10 Fig. 6: Dia10-03

## Inductive sensors

Fig. 7: Dia12 Fig. 8: Dia12-04 Fig. 9: Dia13 Fig. 10: Dia14 Fig. 11: Dia15

## Magnetoresistive sensors

Fig. 12: Dia17 Fig. 13: Dia18 Fig. 14: Dia19 Fig. 15: Dia19-05 Fig. 16: Dia20 Fig. 17: Dia21 Fig. 18: Dia22 Fig. 19: Dia23 Fig. 20: Dia24 Fig. 21: Dia25 Fig. 22: Dia26 Fig. 23: Dia27 Fig. 24: Dia28 Fig. 25: Dia29 Fig. 26: Dia30 Fig. 27: Dia31 Fig. 28: Dia32

## Hall sensors

Fig. 29: Dia36 Fig. 30: Dia37 Fig. 31: Dia38 Fig. 32: Dia39 Fig. 33: Dia40 Fig. 34: Dia40-06

## The Linear Variable Differential Transformer (LVDT)

Fig. 35: Dia42 Fig. 36: Dia43 Fig. 37: Dia44 Fig. 38: Dia45 Fig. 39: Dia46 Fig. 40: Dia47 Fig. 41: Dia48 Fig. 42: Dia49

## Resolvers

Fig. 43: Dia51 Fig. 44: Dia52 Fig. 45: Dia53 Fig. 46: Dia54 Fig. 47: Dia55-07

## Summary

Fig. 48: Dia55-08

# Sensor Technology TOC

These are the chapters for the Sensor Technology course: