Measurement of displacement

Equation for capacitance (in terms of distance and area of parallel plates)

• ε dependent on medium between plates

Equation of Capacitance in terms of Ohms Law

General method of measuring distance through capacitance

changes in distance between plates

→ changes in capacitance

→ obtain measurement of AC current flowing through capacitor

Types of capacitance displacement transducers

1. variable separation

2. variable area

Derivation of voltages in capacitive bridges

Derivation of V₀ for variable separation differential capacitance displacement transducer

General V₀ equation for capacitance displacement transducers

Derivation of V₀ for variable separation differential capacitance displacement transducer

Working principle of linear variable differential transformer(LVDT)

Initial:

• AC in primary coil produces time-varying magnetic field

• magnetic flux produces voltages on both secondary coil in opposite directions → voltage cancels out

Ferromagnetic core moves:

• voltage magnitude becomes greater for one secondary coil, and smaller for the other

• create difference in voltage

Working principle of resistive potential dividers as displacement transducers

• calculation of V0 as it moves along the pot

Method of calculating maximum error of pot

Increasing sensitivity of resistive potential dividers (pot)

1. increasing V_s

• however, may be limited by spec sheet max power dissipation

2. use carbon film, conductive plastic, ceramic metal mix to increase spatial resolution of pot

Range of distance for pots

10mm-1m

Working principle of optimal incremental shaft encoder

2 pairs of light source and sensors out of phase

rotational speed: detect number of pulses per revolution

rotational direction: find which voltage is leading

Working principle of optical absolute shaft encoder

able to create binary counter

Methods of distance measuring system for <1m

• capacitance transducer

• LVDT

• optical shaft encoders

• resisitve potential dividers

Method of distance measuring system for >1m

1. Wave propagation

2. Laser distance measurement

Factors to consider for wave propagation

1. accuracy of measurement hinges on time measurement device accuracy

2. consider what medium, obstacles

3. diffraction

Types of wave propogation method

1. pulse

2. phase difference btw transmitted and reflected wave

Definition of linearity

how much the voltage displacement relationship could go off the linear

Definition of temperature coefficient of sensitivity

change of sensitivity due to the operating temperature

Definition of Zero shift with temperature

how much the null position (location) could be shifted due to the operating temperature

Definition of output ripple

‘Hint’ of AC input in DC output. Does not affect the mean DC output value.

Definition of Resistance range

Range of available (total) pot resistance

Definition of Output smoothness

Maximum resolution error

Tolerance

Uncertainty in manufacturing of the resistance element (but may not be considered depending on the voltage indicator resistance

Meaning of hysteresis

when physical quantity is dependent on input and history states, problem for cyclic loading