chapter 1

EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement

Dr.LsTeo/Ykleong 1/18

Chapter 1: Instrumentation system and measurement

Objectives of chapter

Introduction to general element of measurement system

Explaining some criteria in defining measurement errors

Describing of limiting error and its derivation/combination

Explaining type of errors that could be involved in a measurement system

Chapter contents and outline

1.0 Introduction to measurement system

1.1 Terms

1.2 Elements of a generalized measurement system

1.3 Functions of instrument

2.0 Measurement errors

2.1 Terms

2.2 Limiting and guarantee errors

2.3 Type of errors

3.0 Measurement Standard

3.1 Terms

3.2 Fundamental and secondary units

3.3 Symbols and notation (refer attachment)

3.4 Equation and numbering

3.5 Dimension analysis



1.0 Instrumentation system

A measurement system converts the unknown quantity of a energy to a numerical unit

using an instrument (result: number + measured unit, e.g.: 6.8 Kg/(ms)2.

1.1 Terms

Measurement comparison between an unknown quality and a predefined standard

Measurand the unknown quality to be measured.

Instrument physical device uses to determined measurand numerically.

1.2 Elements of a generalized measurement system



1. Transducer

a) a device which converts energy from one form to another

b) input transducer (sensor); output transducer (actuator)

2. Sensor

a) a device which senses and detects the physical quantity of measurand

b) mechanical, e.g. Bourdon tube pressure meter, advt: reliable for static & stable

condition, disavdt: not for fast transient measurement

c) electrical, e.g. voltmeter & ammeter, advt: more rapid condition

c) electronic, e.g. digital meter, advt: fast & higher precision

3. Variable conversion element e.g. ADC or DAC

4. Variable manipulation element

a) to manipulate the signal presented to it while preserving the original

information.

b) e.g. : signal amplifier.



5. Signal conditioning

a) operation performed on the signal to bring it to the desired form.

b) includes variable conversion and variable manipulation.

6. Telemetry

a) transmission of data from remote sources to serve specific purposes.

7. data presentation element (also output transducer)

a) to convey the measured quantity for further action: display, recording and

control.

b) E.g. CRT, printer, magnetic tapes, LCD.

1.3 Functions of instrument

a) Indicating function: meter display (in a car or voltmeter), digital display.

b) Recording function: data keeping, e.g. record volume of production

c) Controlling function: temperature, position, speed, liquid level, flow control



2.0 Measurement Error

2.1 Terms

1. True value -- Almost impossible to obtain in practice

2. Measured value value indicated by an instrument

It should follow by its uncertainty in measurement.

Exp:

l = (1.5 0.1) cm

3. Norminal value value of the quality specified by the manufacturer

It normally follows by tolerence

Exp:

R= 10 k 10 %

4. Static error



The difference between the measured value and the true value of the quantity

tm AAAtruevalueluemeasuredvaerror

=

5. Relative static error

tr A

A =

6. Accuracy

Closeness with which an instrument reading approaches the true value

7. Precision

Is a measure of the reproducibility of the measurement

It composed of 2 characteristics : conformity & number of significant figures

E.g.:

At = 1.51 mm

After measured:

System 1 gives; Am1 = 1.478mm (more precise)

System 2 gives; Am2 = 1.5mm (more accurate)

8. Sensitivity



the ratio of the magnitude of the output signal or response to the magnitude of

input signal

9. Hysterisis

A phenomenon which depicts different output effects when loading and unloading

10. Reliability

The period for an instrument which can maintain its accuracy and precision.

11. Resolution or discrimination

The smallest increment in input which can be detected with certainty by an

instrument

12. Response time

Time period for an instrument from sensing till it reached to a steady state



13. Frequency response

A minimum time that an instrument can sense an instantaneous signal changed.

14. Switching time

Normally for all digital circuits (including microprocessor devices)

Minimum time that can perform well in on-off switching

15. Bandwidth

The range of frequency that gives satisfactory output response.

2.2 Limiting or Guarantee Errors

1. What is guarantee error?

a) To ensure the customer the quality of the instrument, the manufacturer guarantees a

certain accuracy of their product.

b) The manufacturers specify the deviations from the nominal value of a particular

quantity.

c) The limits of these deviations from the specified value are defined as limiting errors or

guarantee errors.

d) Actual value Aa= AS A where AS is the nominal value & A is the limiting error.

A a satisfies: AS - A AV AS + A

e) Relative limiting error,

S

r AA

=

f) % Relative accuracy = (1- r )x 100%



g) E.g.: the value of capacitance of a capacitor is specified as 1 F 5% by the

manufacturer.

A = rAS = 0.05 X 1F = 0.05F

0.95F Aa 1.05F

2. Combination of limiting error

a) Sum of quantities

Let y be the final result which is the sum of measured quantities x1, x2,, xn.

y = x1 + x2 + xn

dy= dx1 + dx2 + dxn

If the errors in the component quantities, dxi , are represented by x1, x2, , xn,

limiting error y in y is given by :

y = x1 + x2 + xn

b) Difference of 2 quantities

y = u v

dy = du - dv

If the errors in u and v are u and v respectively, consider worst case, i.e., when the

error in u is +u and error in v is -v and vice versa,

y = ( u + v)

In general,

y = x1 x2 xn

y = (x1 + x2 ++ xn)

c) Product of n components



y=x1x2xn

ln y = lnx1 + lnx2 + +lnxn

differentiating:

n

n

xdx

xdx

xdx

ydy

+++= ...2

2

1

1

Limiting error:

=

=n

i i

i

xx

yy

1

d) Quotient of more then 2 quantities

nxxxy

...1

21

=

ln y = -lnx1 - lnx2 - -lnxn

Than limiting error

=

=n

i i

i

xx

yy

1



e) Power of a factor

y = x1m1x2m2xnmn

ln y = m1 ln x1 + m2 ln x2 ++ mn ln xn

limiting error:

=

=n

i i

ii xxm

yy

1

f) E.g.:

Given 3 resistors with values R1 =37 5% , R2 = 75 10%, R3 =50 5%.

Determine the magnitude and limiting error in ohm and in percent of the resistance of

a) these resistors which are connected in series.

b) These resistor which are connected in parallel

Solution :

In series

R1 = (37 1.85) R2 = (75 7.5) R3 = (50 2.5)

R = R1 + R2 +R3

R= R1 + R2 +R3

R = (1.62 11.85) or 162 7%

In parallel

1/R = 1/R1 + 1/R2 + 1/R3

R/R2 = R1 /R12 + R2/R22 + R3/R32

R= (16.56 1.01) or R= 16.56 6.1%



g) Known error

If error of a quantity is known exactly, the effect of error can be taken into a/c as in

combining limiting error. The only difference is that the sign of the error must be

preserved in all calculations.

2.3 Type of Errors

1. Gross Errors

Refer to errors due to human mistake in reading instruments and recording and

calculating measurement results.

E.g. 1: read the temperature as 31.5C while the actual reading may be 21.5C

E.g. 2: read 25.8C and record as 28.5C

Prevention: read and record carefully, and taking the average of several reading

2. Systematic Errors

a) Instrumental errors

i) due to inherent shortcoming in the instrument

Inherent due to their mechanical structure.

They may be due to construction, calibration or operation of the.

E.g.: If the spring (use for producing controlling torque) of a permanent magnet

instrument has become weak, the device will always read high.

Overcome methods

- re-calibrated carefully

- apply correction factors after determining the instrumental errors

ii) due to misuse of instrument

E.g. 1: failure to adjust the zero of instruments

E.g. 2: using leads of too high resistance (when measure low R value)

iii) due to loading effect of instruments

E.g.:

A voltmeter having a sensitivity of 1000/V reads 100V on its 150V scale



when connected across an unknown resistor in series with a milliammeter.

The milliammeter reads 5mA.

Think of the loading effect introduces by voltmeter or ammeter, and what is the

characteristic of ideal voltmeter and ideal ammeter?

A) calculate apparent resistance of the unknown resistor

Total resistance,

=== kxIE

RT

TT 20105

1003

Neglecting the effect of voltmeter,

unknown resistor, Rx =20k.

B) calculate actual resistance of the unknown resistor

Resistance of voltmeter,

Rx = 150k.

RT= Rx//RV

kkXRRRR

RVX

VXT 65.1720150

15020=

+=

+=

C) calculate % of error due to loading effect of voltmeter

% of error = (17.65-20)/17.65 = -0.133 or 13.3%

Accuracy = 100% - |%loading error| = 100-|-13.33| = 86.67%

i.e. loading effect cause inaccuracy of measurement.

This can be avoided by using appropriate instrument or using them intelligently (use

instrument in proper arrangement).

E.g.: using high voltmeter which have high resistance in relative to the load

resistance



2 (b) Environmental Errors

E.g.: effects of temperature, pressure, humidity, dust, vibrations or external magnetic or

electrostatic fields.

i) Keeping the conditions as nearly as constant as possible.

E.g.: temperature can be kept constant by keeping the equipment in a temperature

controlled enclosure.

ii) use equipment which is immune to these effects

E.g.: variations of resistance with temperature can be minimized by using resistance

materials which have a very low resistance temperature co-efficient

iii) employ techniques which eliminate the effects of disturbances

E.g.: effect of humidity & dust can be entirely eliminated by hermetically sealing the

equipment

iv) apply computed correction

2 (c) Observational Errors

i) Parallax error

ii) Reaction time



3.0 Measurement standard ~ before we can measure something, we must define its dimension and provide some standard, or reference unit, in terms of which the quantity can be expressed numerically. (Lord Kelvin)

3.1 Terms

Dimension- Defines some physical characteristics. Eg. Length, volume, velocity,

heat and etc.

Unit is a standard or reference by which a dimension can be expressed numerically

SI unit The international system of units

3.2 Fundamental and secondary units

There are five fundamental units or base units

a) Meter (m), L

b) Kilogram (Kg), M

c) Second (s), t

d) Ampere (A), I

e) Kelvin (K), T

Secondary units are the product of fundamental units

For eg : Area ( L2)- m2, Newton, Kgms-2 and etc

3.3 Symbols and notation (refer attachment)



3.4 Equation and numbering It is important to have a right concept to write an equation. For an example:

Y=MX + C

Where M and C are the constants. X and Y are the variables.

X is always refers as the input/ changes to the system. (Always put at the right side of

the equation.)

Whereas,

Y is always refers as the result/effect that cause by the changing of the X. (Always

put at the left side of the equation and also always as a single term)

For instant; Instantaneous Force induced that cause by the changing of the current

with a finite length L and constant magnetic flux B is given by

F=BIL

Where B and L are the constant.

I is the cause and F is the result.

But if an instantaneous force is applied to the finite length conductor which cut a

constant magnetic flux. A current is induced.

The equation is rather written as follow

I= F/BL

F is the cause and I is the result.

Although they look exactly the same but in the view for scientists or engineers, it is

totally different.

# The same principles that apply to plot a scientific graph. X axis is always refer as

cause and Y axis is always refer as result.

Question:

How should we write an equation that consists more than one input but just

one output?

And how should we write an equation that only has one input but multiple

output?



3.5 Dimension analysis

It is necessary condition for correctness that every equation be balanced dimensionally.

For example:

Newton, F(N) = mass M(kg) X acceleration LS-2 (ms-2)

Example 1:

The unit of voltage is always expressed as volt (V), try to express this dimension with

only base units expression.

Solution

From definition: electric potential V is expressed either Joules per coulomb or in volts.

Then:

Volts = joules / coulomb

V = FL/Q

= MLS-2 X L / IS

= ML2S-3 I-1

Answer: V= kgm2s-3 A-1

Exercise 1: What is the dimension of electrical resistance? Expressed with base units

only.

Exercise 2: Electrical force expressed as follow:

2

2

rQkF =

What is the dimension of k? Expressed with only base unit only.

chapter 1

Documents

measurement dr

measurement errors

instrumentation system

measurement standard

measurement techniques

terms measurement comparison

b recording function

type of errors