5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise

15. SOURCES OF ERRORS. 5.6. Disturbances: interference noise

5.6. Disturbances: interference noise

Measurement errors can occur due to the undesirable

interaction between the measurement system and:

E n v i r o n m e n t

Measurement System

Mat

chin

g

Mat

chin

g

Disturbance

yx

the environment,

the object under test,

observer.

y


To quantify the effect of additive disturbances on the

measurement system, the disturbance sensitivity

(or sensitivity factor) is used:

d y

d dSd

x

Measurement System

Disturbance, d (VCC )

x 0 y

y

dx

.

additive disturbance,

multiplicative disturbance.

There are two types of disturbances (interference noise):

d y Sd d d

(SVCC y/V]supply voltage sensitivity)


Additive disturbances can be written as the equivalent

disturbing input signal

Sd

Sx

xeq d,

where Sx is the sensitivity of the measurement system:

d y

d xSx .

Measurement System

x xeq y y d y Sx xeq

Disturbance, d


Multiplicative disturbances affect the sensitivity Sx of the

measurement system.

xSx

Measurement system

To quantify the effect of multiplicative disturbances, the

disturbance coefficient is used:

d Sx / Sx

ddCd 106[ ppm /dd .]

y Cd d d ) · xy y

Disturbance, d (T )

Sx

dd

(CT ppm/]temperature coefficient)


Example 1: Supply voltage sensitivity SVCC

VIN 0 Vout

VCC

DC-voltagenull detector

VIN Veq VoutDC-voltage

null detector

SVCC

SVINVeq V

Vout SVCC VCC

Vout SVIN Veq

6

G

d T


Example 2: Temperature coefficient CT

VSVout 1

RG 1

Instrumentationamplifier, G

T1

VSVout 2

RG 2

Instrumentationamplifier, G

T2

106 ]ppm/º[ CT

Vout CT T ) ·VS

Vout 2 Vout 1

Vout 1

Vout

75. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances

5.2.1. Reduction of the influence of disturbances

1. Isolate the measurement system. For example, use

electro-magnetic shielding, stabilize the ambient

temperature, etc.

2. Separate the effect of disturbances on the output of

measurement system to correct the measurements. For

example, suppress the input signal and measure the

output signal due to the additive disturbance only. Then

correct the measurements with the input signal applied.

3. Change the input signal in such away to avoid the

disturbance. For example, translate a dc signal into ac

one to avoid dc offset and drift and flicker noise.

4. Split the measurement system (or only its critical part)

into two parallel or series channels and use parallel,

series, or ratio compensation to compensate the

disturbance.


S1 S1

S2 S2

S1 S1

S2 S2

S1 S1 S2

S2

y

y

y

x

x

x

d

d

d d

d

d

ratio

series

parallel

S1 Cd 1 S2 Cd 2

Sd 1 Sd 2

Cd 1 Cd 2

Sd 1 S2 Sd 2

Cd 1 Cd 2

not effectiveAny ratio

measurement system

SensorSensorObjectObject

Example Compensation:


5. Use feedback against multiplicative disturbances.

SOL SOL

yx

T

SOL SOL yx

T


SOL

1 SOL 1. Sf

SOL /SOL

T2. CT OL

Sf /Sf

T3. CT f

1

1 SOL 4. dSfdSOL

SOL )1 SOL )2

1

)1 SOL ) 1

)1 SOL ) SOL

SOL

1

1 SOL 5. dSfSfdSOLSOL

1

1 SOL 6. CT fCT OL


Note that negative feedback reduces additive disturbances by

the same factor as it reduces the sensitivity of the system.

This means that the ratio of the measurement signal and the

disturbances (both referred to the output or the input) will not

change due to the application of feedback.

Reference: [1]

In the same way, the signal-to-noise ratio of the measurement

system will also not be improved by using negative feedback.

(It will be decreased due to the additional noise contribution by

the feedback network.)

SOL SOL

y+yx+xeq

125. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances

5.2.2. Sources of disturbances

A. Thermoelectricity

Reference: [1]

Metal A

Metal A

Metal B

Junction at T1

Junction at T2

V ST )T1T2)

Thermoelectricity is an additive disturbance.


CuAg CuPb/Sn 3 V/º

CuAu 0.3 V/º CuKovar 500

V/º

CuCd /Sn CuCuO 1000

V/º

Reference: [1]

Cu Pb/Sn Kovar

T2T1


B. Leakage currents

Reference: [1]

1 cm )100 M)

Leakage current, IL

IL V2 V1

RL

V2 V1

15

V1

0.5RL


Active guarding

Leakage current, IL

AOL

IL

V1

Vout

V1 Vout

0.5RL

V1 V1 AOL /)1+AOL)

0.5RL

1

1+AOL

16

Measurement system

Zin


C. Capacitive injection of interference

Reference: [1]

ZS

vS

220 V 50 Hz

Cable

Cp

Vin

Vin Vd jCp)ZSIIZin)1/jCp >> ZSIIZin

Vd

)ZSIIZin)Vin

Inductive injection of interference is an additive disturbance.


Reference: [1]

ZS

vS

Measurement system

220 V 50 Hz

Shielded cable

Electrical shielding: grounding at the source

Cp

Zin

ZS < Zin

Vd

Prove that the grounding of the shield at the end of the cable

that is attached to the circuit with the lowest impedance keeps

as small as possible the interference voltage between the

shield and the signal conductors.

Home exercise:


Reference: [1]

ZS

iS

Measurement system

220 V 50 Hz

Shielded cable

Cp

Zin

Vd

Electrical shielding: grounding at the measurement sistem input

ZS > Zin


D. Inductive injection of interference

Reference: [1]

ZS

VS

i(t)

H(t)

Area, A

Zin

Measurement system

Wire loop

Inductive injection of interference is an additive disturbance.

Vd

f)ZS ,Zin)VS

Vd

VdA, d i/d t ;


Reference: [1]

ZS

VS

i(t)

Zin

Measurement system

Wire loop

Vd

AVd

H(t)

Reduction of the wire loop area


Reference: [1]

ZS

VS

i(t)

H(t)

Zin

Measurement system

Twisted pair

Vd

AeqVd

Employment of twisted pair

22

VS


Reference: [1]

ZS i(t)

Zin

Magnetic shielding

Single-shell or multi-shell magnetic shield


E. Injection of interference by imperfect grounding

Reference: [1]

1) Stray currents. Grounding the measurement object and the

measurement system at different points on a ground rail causes

additive voltage disturbances due to stray ground currents.

ZS

vS

Rg

Measurement system

~N

Istray

Istray1 Istray2 vd


Reference: [1]

Single-point grounding helps to reduce the disturbances.

ZS

vSMeasurement

system

~N

Istray

Istray1 Istray2 vd

Rg


Reference: [1]

Differential input and shielded twisted pair further reduce the

disturbances.

ZS

vS

Rg

Measurement system

)CMRR(

~N

Istray

Istray1 Istray2 vd


Reference: [2]

ZS

vS

2) Ground loops. If single-point grounding is impossible, ground

lops can be a significant source of interference noise:

The effect of multiple-point grounding can be minimized by

isolating the two circuits by: (1) transformers,(2) common-mode

chokes, (3) optical couplers, or (4) frequency-selective

grounding (hybrid grounds).

Ground loop)inductive injection of interference)

Measurement system


Reference: [2]

Isolation with:

ZS

vSMeasurement

system

Isolating device

(1) transformers (2) common-mode chokes (3) optical couplers

Common-mode current

Signal current

Balun )balanced, unbalanced signals)


Reference: [2]

Isolation with: (4) frequency-selective grounding (hybrid

grounds) is used when the common-noise voltages are at very

different frequencies from the desired signal:

ZS

vSMeasurement

system

30

Inputtransduction

Inputtransduction

6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.1. General structure of a measurement system

6. MEASUREMENT SYSTEM CHARACTERISTICS

6.1. General structure of a measurement system

Signal processing

Signal processing

ExciterExciter

TransmissionTransmission

MemoryMemory

User interface User interface

Measurement object

Measurement object

ReferenceReference

Measurement system

User

Control

316. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity

6.2. Measurement system characteristics

The sensitivity of a measurement system is the ratio of the

magnitude of the output signal y to that of the input signal x.

1) Static sensitivity.

6.2.1. Sensitivity

yxG

2) Dynamic sensitivity.

g)x0)x x0

y x

Reference: [1]

326. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity

3) Scale factor.

SF1/G

Example: Sensitivity and scale factor

y = 4 divx = 1 mV ppSignal source

G = 4 div/mV; SF = 0.25 mV/div

Reference: [1]

336. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.2. Sensitivity threshold

The sensitivity threshold, ST, of a measurement system is

determined by the smallest signal that can still be detected,

with a given probability of success.

To define a measure for the sensitivity threshold let us first

define the detection criterion D for an average signal S:

6.2.2. Sensitivity threshold

Reference: [1]

t

s

S2

Detection criterion D

t

Detection result

1

0

Average signal, S

346. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.2. Sensitivity threshold

Reference: [1]

A commonly used measure for the sensitivity threshold is the

magnitude of the signal for which the SNR 1.

The detection probability is then approximately 70% for a

Gaussian noise.

f )x)1

1.4

3

4

5

6

8

10

69.15

76.02

93.32

97.72

99.38

99.87

99.9968

99.999971

30.85

23.97

6.68

2.28

0.62

0.13

0.0032

0.000029

SNR *

2 84.13 15.87

DP% , EP% ,

sS2

S

Detection criterion, D

Average signalSN

* SNR S2

,D

N

0

Error probability, EP

Detection probability, DP

Noise

356. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.3. Resolution

The resolution, R, is defined as the smallest interval x of the

measured signal x that will still cause a change in the

measrement result y.

6.2.3. Resolution

Reference: [1]

According to the above: RES ST N.

The resolution can also be defined as the ratio of xmax (or full-

scale value of x, FS) to x:

FSST

RESxmax

x

For example, if xmax 10 V and x 150 V, then

RES 216, which corresponds to a resolution of 16 bit.

366. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Inaccuracy, …

If we define the true magnitude of a signal x as Xtrue, the

average measured magnitude as X, the maximum random

error as A (uncertainty of type A*), the systematic error as B

(uncertainty of type B), and the inaccuracy as A+B, then

6.2.4. Inaccuracy, accuracy, and precision

* International Committee of Measures and Weights, 1986

f ) x )

x0 Xtrue B

3

XA

Inaccuracy,

376. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Inaccuracy, …

the accuracy can be defined as:ACC

and the precision can be defined as: P1AX

the relative inaccuracy can be defined as:

Xtrue

f )x),normalized

x0 Xtrue B

3

XA

Inaccuracy,

More precise and more accurate

More accurate, but same precision

(The ability of a measurement to be consistently reproduced.)

(The ability of a measurement to match the actual value of the quantity being measured.)

38Good luck!

Thank you and good luck in the final exam!

5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise

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