3. Measurement Methods 43

1

With the deflection method, 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.

2

The difference method 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.

3

With the null method, 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.

4

(a)

100 mm ±103

100 mm

Inaccuracy: ±100 m Inaccuracy:

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


5

00

(b)

1 mm ±103

Reference

99 mm ±105

Inaccuracy: ±100 m Inaccuracy:


(a)

100 mm ±103

100 mm


±1 ±1 m

6

00

(b)

1 mm ±103

Reference

99 mm ±105

00

(c)

0 mm ±103

Reference

100 mm ±105

Inaccuracy: ±100 m Inaccuracy: Inaccuracy: ±100 m ±1 ±1 m


(a)

100 mm ±103

100 mm

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


±0 ±1 m

7

Example B: Null measurements, C=0, P0=FA

C1 C2

Oil

Membrane

F = m·g

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

Pressure, P0


8

Example C: Difference measurements, P = P0 P, P C

C1 C2

Oil

Membrane

F = m·gPressure, P0 + P


9


C1 C2

Membrane

Oil

F = m·gPressure, P0


10


C1 C2

Pressure, P0 P

Oil

Membrane

Difference method: linearity is important.

F = m·g


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

Bridge method )Christie, 1833, Wheatstone, 1843(

Vref

Vref

R

(1) R Vref

Null 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, the circuits internal

impedance, or the internal impedance of the null detector.

Note that the bridge method requires a single power source.

R

RR

Rx

Reference: [1]

VxVref

12

Example D: 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]

13



SensorSensorNon-electrical signal Electrical signal

Input transducer )sensor(

ES

N-ES

14



Electrical signal Non-electrical signal

Output transducer )actuator(

N-ES

ES

ActuatorActuator

15



Measurement system interfaceN

on-e

lect

rical

sig

nals

Non

-ele

ctric

al s

igna

ls

Measurement SystemMeasurement System

SensorSensor

SensorSensor ActuatorActuator

ActuatorActuator

16



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

sensitivity of a dc magnetic field sensor with the help of a linear

temperature-insensitive reciprocal actuator.

VS

Ha

T1

T2

SensorSensorHa VS

Hact

Vo

ActuatorActuatorHactVo

T1

T2

17



Any ideas?

SensorSensor

Hact

VS

Ha

AVo

Null detector

Reference (Helmholtz coils)

VS0

Io

Io

T1

T2

Vo

T2

The sensor temperature-drift errors and nonlinearity are not important

Vs HactHaT1

Vo 1Vo 2

Hact 1Hact 2

HHaHact

H1H2 0

18

Example E: Difference measurements


SensorSensor

Hact

VS

Ha

AVo

Reference (Helmholtz coils)

VS 0

Io

HHaHact

T1

T2

Vo

T2

The sensor temperature-drift errors and nonlinearity are important

VS Hact T1

VS

VS

HactHact

Vo 2 Vo 1

H1H2

G AOL

1+AOL HactHa

Io

19

3.2. Interchange method and substitution method

According to the interchange method, two almost equal

quantities are exchanged in the second measurement.

0 1 2-1-23-3

m1 m2

This method can determine both the magnitude of the

difference between the two quantities and and the magnitude

of possible asymmetry in the measuring system.

Reference: [1]

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

20




m2 m1

0 1 2-13




Reference: [1]

-2-3


21

m2m1

-23-3

m =[1)2(]/2

Offset =[1 )2(]/2




0 1 2-1




Reference: [1]


22

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

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 a

known and adjustable quantity, which is adjusted to obtain the

remembered reading.

Reference: [1]


23

2m

1 0.5 0.2





remembered reading.




Reference: [1]


24

m

2

1 0.5 0.2





remembered reading.




Reference: [1]


25

1 0.5





remembered reading.

1

m

2 0.5

0.2

m=3.5

12 0.5




3.5

Calibration

Reference: [1]


26

1 0.5

1

m

2 0.5

0.2

m=3.5

12 0.5

3.5

Calibration

Reference: [1]


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

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

know quantity. An unknown quantity can then be measured

accurately if its magnitude coincides with the calibrating points.

27

Vo' AVoff AVaVb)

Example A: Interchange method.

Va Vb

Vo

Voff


A

Vo AVoff AVaVb)Vo

VaVb V

AVoff

Vo' AVoff AVaVb)

Voff = ?

VaVb = ?

28

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(

29

Voff


Example: Amplifiers with the controllable polarity of the gain.

10k ±1%

10k ±1%

10k ±1%

10k ±1%

5k

5k

5k

Voff

A

A

vin

vin

30

A

A

±?

±?

±?


Example: Amplifiers with the controllable polarity of the gain.

10k ±1%

10k ±1%

10k ±1%

10k ±1%

5k

5k

5k

Voff

Voff

vin

vin


Example B: Interchange method.

1°

? =

Offset?=

msr

true

2

32

1

1°


1°

2

true

msr

Offset = )2°1°= 0.5°

= )2°1° = 1.5°


33

1°


= 1.5°

Offset = 0.5°



Two next measurement methods, compensation and bridge

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

Examples: Substitution 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 with compensation method.

Vx

Vref

R

(1) R

Null detector

VxVref

Reference: [1]


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

Reference

Partial compensation Complete compensationNo compensation

Reference: [1]


Bridge method )Christie, 1833, Wheatstone, 1843(

Vref

Vref

R

(1) R Vref

Null 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, the circuits internal

impedance, or the internal impedance of the null detector.

Note that the bridge method requires a single power source.

R

RR

Rx

Reference: [1]

VxVref

413. MEASUREMENT METHODS. 3.4. Analogy method

3.4. Analogy method

Analogy method 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.

423. 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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