week 5_6

Measurement systems and Sensors

Chapters 3, 5 and 6 form the Principles of

measurements systems Book

The accuracy of measurement systems

Chapter 3 from the book:

principles of measurements

Measurement error of a system of ideal

elements

a=0, Linear , No environmental effects

The system is perfectly accurate

Example

However, None of the elements is ideal: 1. The thermocouple is nonlinear, as the temperature increases the sensitivity is no

longer 40. Also changes in reference junction temperature cause the thermocouple e.m.f. to change

2. The output voltage of the amplifier is also affected by changes in ambient temperature

The error probability density function

of a system of non-ideal elements

review



For a complete system



Example

the platinum resistance temperature detector is characterized by a small amount of non-linearity and a spread of values of R



Example

linear but temperature acts as both a

modifying and an interfering input. The

zero bias and sensitivity are adjustable: we

cannot be certain that the transmitter will be

set up exactly as stated in the table, and this is reected in the non-

zero value ofa



Example

the recorder is linear but again calibration uncertainties are modeled by a non-zero value of a



Summary Example

Modeling using error bands

where element non-linearity, hysteresis and environmental effects are small, their overall effect is quantied using error bands


For the full system

No bias

The mean value of the error

Error reduction

Using the calibration techniques, we can identify which

elements in the system have the most dominant non-ideal

behavior.

We can then devise compensation strategies for these

elements which should produce significant reductions in

the overall system error. compensation methods for non-linear and environmental

effects.

Error Reduction techniques

1. Self study

20 1 2E C C T C T 2 6 20 4.017 10 117 4.66 10 117

4.7637E

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0 1

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22

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Loading Effects and Two-

port Networks

Chapter 5 from the book: principles of measurements

loading

When we insert an instrument into the position to measure a quantity, an error in the measurement may occur due to loading effect.

Also inserting a thermometer at room temperature into a hot water to measure its temperature changes the temperature of the water which leads to error in the temperature measurement.

inserting an ammeter into a circuit to measure the current changes the value of the current due to the ammeters own resistance which changes the total resistance of the circuit.

Examples:

Loading Effects and Two-port Networks

One element of the system may modify the characteristics of the previous one (for example by drawing current).

Electrical loading Thvenin equivalent circuit Norton equivalent circuit

Two-port networks

Electrical Loading

in order to get maximum voltage transfer from the network to the load, the load impedance should be far greater than the Thvenin impedance for the network. In order to get maximum power transfer from network to load, the load impedance should be equal to the network impedance

Therefore, the effect of connecting a load across the network yields a loading error of magnitude

LTh VE Error Loading

LThL

Th ZZZE 1

Example

27

Loading a voltmeter

Assume that a voltmeter of resistance Rm is connected across the shown active circuit to measure the voltage between terminals A and B.

Rm

Active network

Voltmeter

Therefore, the reading indicated by the instrument (voltmeter) is

ThThm

mm ERR

RV

Voltage before the meter was connected

28

This means that the error in the reading is

mTh VE Error

mThm

Th RZRE 1

and the accuracy of the voltmeter is

%100Accuracy Th

m

EV

%100

mThm

RZR

Note that if Rm is very large, the error goes to zero and the accuracy goes to 100%

potentiometric sensor for measuring displacements d

Impedance equivalent, short circuit voltage source

Impedance equivalent, open circuit load

1

1s P th

thP th

P

th s

V iR x EE R x E

R x

E V x

equivalent

Nonlinear

equivalent

equivalent

Note that the system is directly sensitive to the voltage source. At the same time, we have not exceed the maximum power dissipation. How??????

The maximum value of this error occurs when

0Nx

i.e., we can reduce the error by selecting RL to be too much greater than Rp

Ls

dvv

dx

15 % 2%

15 25000

666.6, 250 or 500

p

L

p

p

RN

RR

R either

Ls

dvv

dx 666.6, 250 or 500pR either

2

5

5 250, 5 500

50, 35.335

s

P

s P

s s

s

vpowerR

v power R

v or v

v or

Ls

dvv

dx

max sensitivity=50 35.355

or 25 25

2 or 1.4

sv

x

Norton

Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor.

A current source in parallel with a resistor is called a Norton equivalent circuit.

Finding a Norton equivalent circuit requires essentially the same process as finding a Thevenin equivalent circuit.

indicator cablen

n

nn

n indicator cable

v vi iZ

Zi iZ R R

indicator indicatorv i R 2 2meas indicatorP K v a

1 1n Truei K P a

2 1 1 2nmeas True indicatorn indicator cable

ZP K K P a R aZ R R

Error=-55.8313

Solution

Cross variable (Effort) Through variable (flow) voltage current force velocity torque angular velocity pressure difference volume ow rate temperature difference heat ow rate

The product ( Cross x Through ) represents power in watts. The ratio (Cross /Through) represents impedance.

Generalised effort and flow variables

An effort variable drives a flow variable through an impedance

Equivalent circuit for a mechanical system

Equivalent circuit for a mechanical system

mechanical electrirical mass electrical inductance damping constant electrical resistance 1/stiffness electrical capacitance thermal resistance electrical resistance thermal capacitance electrical capacitance.

Two-port networks

1. The electrical output of a sensing element such as a thermocouple or piezoelectric crystal can be represented by a Thvenin or Norton equivalent circuit. The sensor has therefore two output terminals which allow both voltage and current flow to be specified; this is referred to as an electrical output port.

2. The sensing element will have a mechanical, thermal or fluidic input; these can be represented by equivalent circuits which show the relation between the corresponding effort and flow variables. Thus the input to a mechanical or thermal sensor can be represented by two input terminals which allow both the effort and flow variables to be specified; this is either a mechanical or a thermal input port.

Two-port networks

Under steady-state conditions we have the following force balance equations:

Process loading

Process loading

Bilateral transducers

Self study

Signals and Noise in Measurement Systems

Chapter 6 from the book: principles of measurements

Deterministic signals: a deterministic signal is one whose value at any future time can be exactly predicted. in real measurement applications the input signal to the measurement system is not deterministic but random

Introduction

55

Is unwanted signal that may be picked up by the measurement system and interfere with the signal being measured.

Noise?

Time Si

gnal

with

no

ise Types of noise:

1. Interference noise. This is due to the interaction between external electrical and magnetic fields and the measurement system circuits.

2. Random noise. This noise is due to the random motion of electrons and other charge carriers in components.

This means that with a voltage transmission system all of VSM is across the load; this affects the next element in the system and possibly results in a system measurement error. We dene signal-to-noise or signal to interference ratio S/N in decibels by:

where Eth and VSM are the r.m.s. values of the voltages, and WS and W are the corresponding total signal and noise powers

Effects of noise and interference on

measurement circuits: Thvenin voltage source

Thus a current transmission system has far greater inherent immunity to series mode interference than a voltage transmission system. ( use it for the thermocouple for example)


measurement circuits: Norton current source


measurement circuits: common mode interference

Noise Sources and Coupling mechanisms

The random, temperature-induced motion of electrons and other charge carriers in resistors and semiconductors gives rise to a corresponding random voltage which is called thermal or Johnson noise. This has a power spectral density which is uniform over an infinite range of frequencies (white noise) but proportional to the absolute temperature of the conductor

A similar type of noise is called shot noise; this occurs in transistors and is due to random fluctuations in the rate at which carriers diffuse across a junction. This is again characterised by a uniform power spectral density over a wide range of frequencies.

The mutual inductance M depends on the geometry of the two circuits, namely on the overlapping length and separation. If the circuits are sufciently close together, then there may be a signicant mutual inductance M between them. Inductive coupling will occur even if the measurement circuit is completely isolated from earth.


Types of interference noise

1- Inductive coupling. Is also called electromagnetic coupling or magnetic coupling. A changing current in a nearby circuit produces a changing magnetic field. This induce e.m.f.s in the conductors of measurement system.

series mode interference is zero only if there is perfect balance between the coupling capacitances



2- Capacitive coupling (electrostatic coupling ). Nearby power cables, the earth, and conductors in the measurement system are separated by a dielectric, air. Thus there can be capacitance between the power cable and conductors, and between the conductors and earth. These capacitors couple the measurement system conductors to the other systems and thus signals in those systems pass to the measurement system as interference.

VE is the difference in potential between source earth and receiver earth

leakage paths ZSE and ZRE exist between source/source earth and receiver/receiver earth.

Ideally we require both ZSE and ZRE to be as large as possible in order to minimise IE and VSM ; this, however, is not always possible in an industrial application.



3- Multiple earths. If the measurement system has more than One connection to earth, then there may be problems since there may be some difference in potential between the earth points. If this occurs, the earthing may produce an interference current through the measurement system.

64

Methods of reducing the interference noise

1- Twisted pairs of wires. Used to avoid inductive coupling

Also Physical separation is applicable

Since mutual inductances and coupling capacitances between measurement and power circuits are inversely proportional to the distance between them, this distance should be as large as possible

65


3- Electrostatic screening. Used to avoid capacitance coupling by completely enclosing the transducer and the entire measurement system in an earthed metal screen.

2- Wire shielding. Inclosing the wire in an earthed metal shield

66


4- Single earth point. To avoid multiple earthing problem

5- Differential amplifiers. A differential amplifier can be used to amplify the difference between two signals. Thus if both signals contain the same interference then the output from the amplifier will not have amplified any interference signals.

67


6- Filters. A filter can be selected which transmits the measurement signal but rejects the interference signal.

Filter Raw signal

Filtered signal

Filte

red

sign

al

Time Time

R

aw si

gnal

68


7. Averaging

week 5_6

Documents

Transcript of week 5_6