1 LECTURE 3. Contents 3.Measurement methods 3.1.Deflection, difference, and null methods 3.2.Interchange method and substitution method 3.3.Compensation

1LECTURE 3. Contents

3. Measurement methods

3.1. Deflection, difference, and null methods

3.2. Interchange method and substitution method

3.3. Compensation method and bridge method

3.4. Analogy method

3.5. Repetition method

2

With the deflection method (שיטת ההסחה), the result of the

measurement is entirely determined by the readout of the

measurement device.

3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

3. MEASUREMENT METHODS

3.1. Deflection, difference, and null methods

Reference: [1]

10

0

The linearity of the entire scale is important.

A

3

The difference method (שיטת הפרש), indicates only the

difference between the unknown quantity and the known,

reference quantity. Here, the result of the measurement is

partially determined by the readout of the measurement device

and partially by the reference quantity.


Reference: [1]

10

0

10

0

Reference

The linearity of a part of the scale is important.

RA

A R = ?

R

4

With the null method (שיטת אפס), the result is entirely

determined by a known reference quantity. The readout of the

measurement instrument is used only to adjust the reference

quantity to exactly the same value as the known quantity. The

indication is then zero and the instrument is used as a null

detector.


Reference: [1]

10

0

10

0

Reference

The linearity of the scale is not important.

A =R ?

R AR

5

00

)b(

1 mm ±1 m

Reference

99 mm ±105

00

)c(

0 mm ±1 m

100 mm ±105

Inaccuracy:

Example A: (a) deflection, (b) difference, and (c) null measurements

)a(

Null method: linearity is not important;sensitivity and zero drift are important.


0 ±1 m

100 mm ±0.1 mm

100 mm

Inaccuracy: ±0.1 mm Uncertainty: 1 ±1 mR

efer

ence

Ref

eren

ce

6

Example B: (a) deflection, (b) difference, and (c) null measurements


Let us first define some new terms that describe the interface of

a measurement system:

transducer is any device that converts a physical signal

of one type into a physical signal of another type,

measurement transducer is the transducer that does not

destroy the information to be measured,

input transducer or sensor is the transducer that

converts non-electrical signals into electrical signals,

output transducer or actuator is the transducer that

converts electrical signals into non-electrical signals.

Reference: [1]

7



SensorSensorNon-electrical signal, x Electrical signal, y

Input transducer (sensor)

y

x

8



Electrical signal, z Non-electrical signal, x

Output transducer (actuator)

x

z

ActuatorActuator

9



Measurement system interfaceN

on-e

lect

rical

sig

nals

Non

-ele

ctric

al s

igna

ls

Measurement SystemMeasurement System

SensorSensor

SensorSensor ActuatorActuator

ActuatorActuator

10



Our aim in this example is to eliminate temperature drift in the

sensitivity of a sensor with the help of a linear, temperature-

insensitive reciprocal actuator.

y

x

T1

T2

SensorSensorx y

x

z

ActuatorActuatorxz

T1

T2

11

Example C: Difference measurements


Measurand, Xm Measurement, Zm

Amplifier

Ym

Measurement model:

T1

T2

x

y

Gain, S

Input Transducer

Xm

Xm

Ym

Zm

.

G

S G

12

Example C: Difference measurements



Actuator

G

x

z

Amplifier

Zm

Xcmp

Zm

Ym

Gain, AMeasurement model:

Zm

Xm. .

.

A

T1

T2

x

y

Xcmp

Gain, S

Input Transducer

Xm-Xcmp

S G

1 G S

ZmXm .S G

A. .1 G S

Ym

Ym . .

. 0

A1 G S

Xm S

13

Example B: Null measurements



Actuator

x

z

Amplifier

Zm

Xcmp

Zm

Ym0

Gain, A

Measurement model:

Zm

Xm. .

G A T>>1

1A

.

A . .

Xm = A Zm.

T1

T2

x

y

X cmp Xm

Gain, S

Input Transducer

XmXcmp

Ym . .

. 0

A1 G S

Xm S

S G

1 G S

G

G

14


According to the interchange method, two almost equal

quantities are exchanged in the second measurement.

0 1 2-1-23-3

m2 m1

This method can determine both the difference between the

two quantities and and the offset of the measuring system.

Reference: [1]

3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method

Am m1m2

OFF

= m1m2 OFF

15


m1 m2

0 1 2-13

Reference: [1]

-2-3






= m1m2 OFF

= m2 m1OFFBA

m AB)

OFF AB)

16

m1m2

-23-3


0 1 2-1

Reference: [1]






m 21) 1.5

OFF 21)

0.5

BAm AB)

OFF AB)

17

Vo' AVoff AVaVb)

Example A: Interchange method.

Va Vb

Vo

Voff


A

Vo AVoff AVaVb)Vo

VaVb V

AVoff

Vo' AVoff AVaVb)

Voff = ?

VaVb = ?

18

Vo' AVoff AVaVb)

Voff = ?

VaVb = ?

Vo' AVoff AVaVb)

Vo"AVoff AVaVb)

Voff = ?

VaVb = ?


Va Vb

Vo

VoffA

Vo AVoff AVaVb)Vo

VaVb V

AVoff

Vo"AVoff AVaVb)

Vo' AVoff AVaVb)

Example A: Interchange method.

Vo' Vo"

2A·V off

Vo' Vo"

2A)VaVb)

19

The characteristics of the measurement system should

therefore not influence the measurement. Only the time stability

and the resolution of the system are important.

2 1 0.5 0.2

m

Reference: [1]


m?

According to the substitution method, the unknown quantity is

measured first, and the measurement system reading is

remembered. Then, the unknown quantity is replaced with an

adjustable reference, which is adjusted to obtain the

remembered reading.

20

2m

1 0.5 0.2

Reference: [1]









remembered reading.

m?

21

m

2

1 0.5 0.2

Reference: [1]





m?





remembered reading.

22

1 0.5

1

m

2 0.5

0.2

m=B

12 0.5

Reference: [1]





mR

R





remembered reading.


Calibration of a measurement system is, in fact, an application

of the substitution method. First the system is calibrated with a

know quantity (reference or standard). An unknown quantity

can then be measured accurately if its magnitude coincides with

the calibrating points.

1 0.5

1

m

2 0.5

0.2

m=B

12 0.5

Reference: [1]

Calibration: mR

B


Two next measurement methods, compensation and bridge

methods, are, in fact, applications of the substitution method.

Examples: Substitution method.

253. MEASUREMENT METHODS. 3.3. Compensation method and bridge method

3.3. Compensation method and bridge method

Compensation method removes the effect of unknown quantity

on the measurement system by compensating it with the effect

of known quantity. The degree of compensation can be

determined with a null indicator.

If the unknown effect is compensated completely, no power is

supplied or withdrawn from the unknown quantity.

The compensation method requires an auxiliary power source

that can supply precisely the same power that otherwise would

have been withdrawn from the measured quantity.

Reference: [1]


Example: Measurement of voltage by compensation method.

Vx?

Vref

R

)1) R

Null voltage detector

VxVref

Reference: [1]

Adjustable reference

0


NB: Note that the difference method and the null method make

use of the compensation method. In the difference method,

the compensation is only partial, whereas in the null method

it is complete.

00 00

Ref

eren

ce

Partial compensation Complete compensationNo compensation

Reference: [1]

Ref

eren

ce


Bridge method (Christie, 1833, Wheatstone, 1843)

Vref

Vref

R

)1) R Vref

Null voltage detector

Originally was called ‘the bridge’

It can be shown that the null condition does not depend on the

power delivered by the power supply, on the circuits internal

impedance, or on the internal impedance of the null detector.

Note that the bridge method requires a single power source.

R

RR

Rx

Reference: [1]

VxVref

0 0

R

Rx

293. MEASUREMENT METHODS. 3.4. Analogy method

3.4. Analogy method

Analogy method (simulations) makes use of a model of the

object from which we wish to obtain measurement information.

The following models can be used.

Mathematical models (simulations).

Linear scale models (e.g., acoustics of large halls, etc.).

Non-linear scale models (e.g., wind tunnel models, etc.).

Analogy method also widely uses the analogy existing between

different physical phenomena, for example, equivalent

mechanical models are used to model electrical resonant

circuits, equivalent electrical models are used to model quartz

resonators, equivalent magnetic circuits are used to model

magnetic systems, etc.

303. MEASUREMENT METHODS. 3.5. Repetition method

3.5. Repetition method

Wit this method several measurements of the same unknown

quantity are conducted each according to a different procedure

to prevent the possibility of making the same (systematic)

errors, specific to a certain type of measurements. Different

(correctly applied) methods of measurements will provide

similar results, but the measurement errors in the results will be

independent of each other. This will yield an indication of the

reliability of measurements.

6789

10

9876

6 7 8 9 9 8 7 6

Unreliable Valid

6789

10

9876

6 7 8 9 9 8 7 6

6789

10

9876

6 7 8 9 9 8 7 6

Reliable

Reference: [1]

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1 LECTURE 3. Contents 3.Measurement methods 3.1.Deflection, difference, and null methods 3.2.Interchange method and substitution method 3.3.Compensation