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Sensing Systems and Signal Processing
Dr Richard

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Sensing displacement / motion

Displacement
Why do we need to be able to sense displacement?

Where is this useful?

Displacement
Anywhere we want to move something in a controlled way we need to sense that motion.

This means most forms of automation require sensors for measuring distance or displacement.

We’ll look at a number of different approaches for doing this.

Displacement – resistive
Simple displacement sensor uses a resistive area and a contact on the moving object

Source voltage (Vin) applied across full resistive bar.

Voltage at the object depends on the position on the bar.

Displacement – resistive
If dmin = 0 then the output is just the voltage divider R2/R. Where R is the total resistance of the bar.

Limited resolution depending on form, contacts wear out due to friction during use, and non linear response from loading.

Displacement – capacitive
Capacitance relates the amount of charge (Q) that can be stored for a given voltage across the device (V).

The capacitance has an effect on how a circuit behaves and so if the capacitance varies with our measurand then we have a sensor.

Charge density () across a plate is +/-Q/A coulombs per square meter, then the electric field (E) will be /

The voltage (V) between the plates is then the line integral of the field over the line from one plate to the other. (Gauss’s law)

Displacement – capacitive
The capacitance of a capacitor depends on the plate separation (d), the permittivity of the dielectric filling () and the plate area (A).

All of these effects can be used for displacement sensing depending on what the moving object is attached to.

Operate over a few millimetres of displacement

Can be very temperature / pressure sensitive depending on what dielectric is used.

Displacement – capacitive

Variable area design: linear in capacitance

Variable gap design: nonlinear in capacitance

Displacement – capacitive

Plunger ε2, Space ε1

Variable dielectric: linear in capacitance

Displacement – capacitive
How to measure Capacitance?

Displacement – capacitive
Time to discharge :
Charge C, connect to load and time how long it takes to reach Vref (1V in this example)

Displacement – capacitive

Oscillator :
Output frequency determined by RC of circuit.
Count cycles with microcontroller to measure C

Displacement – inductive

Ferromagnetic core moves in and out ∆x

Similar in concept to capacitive transducers instead of varying the dielectric permittivity use a device sensitive to the magnetic permeability
The simplest device to take advantage of inductive effects is a coil with a movable magnetic core
The most common device is the Linear Variable Differential Transformer (LVDT)

k1,2, represents the coupling from the primary side, which depends on the core position

Displacement – inductive

0.5 = centre position here
Amplitude of final signal proportional to displacement of core.
Direction of displacement obtained from the phase of the signal.

Displacement – inductive
LVDTs usually run at 5V, in the low KHz frequency range

They can measure displacements from mm down to microns.

They have no moving parts so no mechanical wear, giving a long life.

They are electrically isolated so can be used in hazardous environments.

Some limitations:
Temperature affects the performance.
The can be sensitive to stray magnetic fields.

CC BY-SA 3.0 Wikipedia|Wapcaplet

HoneyWell T&M LVDTs

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