1
5. 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:
the object under test,
the environment,
observer.
Environment
Measurement
System
Matching
x
Matching
Disturbance
y + Dy
2
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise
There are two types of disturbances (interference noise):
additive disturbance,
multiplicative disturbance.
To quantify the effect of additive disturbances on the
measurement system, the disturbance sensitivity
(or sensitivity factor) is used:
dy
___
Sd 
dd
x=0
Disturbance, d
x=0
Dy
___

Dd
.
x=0
(DVCC )
Measurement
System
Dy
d y = Sd d d
(SVCC [Dy/V]
supply voltage
sensitivity)
3
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise
Additive disturbances can be written as the equivalent
disturbing input signal
Sd
___
xeq 
Dd ,
Sx
where Sx is the sensitivity of the measurement system:
dy
___
.
Sx =
dx
Disturbance, d
x + xeq
Measurement
System
y + Dy
d y = Sx xeq
4
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise
Multiplicative disturbances affect the sensitivity Sx of the
measurement system.
Disturbance, d
x
(DT )
Sx
y + Dy
dy = (Cd d d ) · x
Measurement system
To quantify the effect of multiplicative disturbances, the
disturbance coefficient is used:
d Sx / Sx
d Sx _______
____
Cd 
=
106 [ppm /d d ].
dd
dd
(CT [ppm/]
temperature
coefficient)
5
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise
Example 1: Supply voltage sensitivity SVCC
DVCC
VIN = 0
SVCC
____
Veq =
DV
SVIN
DC-voltage
null detector
VIN = Veq
DC-voltage
null detector
DVout
DVout = SVCC DVCC
DVout
DVout = SVIN Veq
6
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise
Example 2: Temperature coefficient CT
RG 1
VS
Instrumentation
amplifier, G
T1
Vout 1
dG
CT = ____ 106 [ppm/º]
dT
RG 2
VS
Instrumentation
amplifier, G
T2
Vout 2
dVout
V
-V
out 2
out 1
__________
=
Vout 1
dVout = (CT DT ) ·VS
5. 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.
7
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances
Example
Compensation:
d
parallel
S1
x
y
d
Sd 1 = - Sd 2
S1 Cd 1 = - S2 Cd 2
S2
series
d
Object
Sensor
x
d
S1
S2
y
Sd 1 S2 = - S d 2
Cd 1 = - Cd 2
d
ratio
S1
Any ratio
measurement
system
x
y
d
S2
not effective
Cd 1 = Cd 2
8
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances
5.
Use feedback against multiplicative disturbances.
DT
x
SOL
y
DT
x
SOL
b
y
9
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances
SOL
_______
1. Sf =
1 + SOL b
DS
OL /SOL
________
2. CT OL =
DT
3. CT f
DSf /Sf
______
=
DT
1
SOL
SOL b
1
1
_________
_________
____
_______
_________
4. d Sf /d SOL =
=
1 + SOL b (1 + SOL b )2 (1 + SOL b ) (1 + SOL b ) SOL
1
_______
5. d Sf /Sf =
d SOL /SOL
1 + SOL b
1
_______
6. CT f =
C
1 + SOL b T OL
10
11
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances
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.
x+xeq
SOL
y+Dy
b
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.)
Reference: [1]
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
12
5.2.2. Sources of disturbances
A. Thermoelectricity
Metal A
Junction at T1
V = ST (T1- T2)
Metal B
Metal A
Junction at T2
Thermoelectricity is an additive disturbance.
Reference: [1]
13
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
T1
Cu
Pb/Sn
Kovar
Cu-Ag
Cu-Au
Cu-Cd /Sn
T2
Cu-Pb/Sn
0.3 mV/º
Cu-Kovar
Cu-CuO
3 mV/º
500 mV/º
1000 mV/º
Reference: [1]
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
14
B. Leakage currents
1 cm
V2
(100 MW)
V1
Leakage current, IL
V2 - V1
________
IL =
RL
Reference: [1]
15
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Active guarding
Vout
AOL
V1
Leakage current, IL
V1 - V1 AOL /(1+AOL) ______
V1 - Vout __________________
1 _____
V1
________
IL =
=
=
0.5RL
0.5RL
1+AOL 0.5RL
16
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
C. Capacitive injection of interference
Cp
ZS
vS
Vin
Zin
Cable
Measurement
system
Vin
220 V
50 Hz
Vd
= Vd jw Cp(ZSIIZin)
1/jw Cp >> ZSIIZin
(ZSIIZin)  Vin
Inductive injection of interference is an additive disturbance.
Reference: [1]
17
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Electrical shielding: grounding at the source
Cp
ZS
vS
220 V
50 Hz
Zin
Shielded cable
ZS < Zin
Measurement
system
Vd
Home exercise:
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.
Reference: [1]
18
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Electrical shielding: grounding at the measurement sistem input
Cp
ZS
iS
220 V
50 Hz
Zin
Shielded cable
ZS > Zin
Measurement
system
Vd
Reference: [1]
19
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
D. Inductive injection of interference
ZS
i(t)
VS
Vd
Area, A
H(t)
Zin
Wire loop
Measurement
system
VS
___
 f(ZS ,Zin)
Vd  A, d i/d t ;
Vd
Inductive injection of interference is an additive disturbance.
Reference: [1]
20
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Reduction of the wire loop area
ZS
VS
i(t)
H(t)
Vd
Wire loop
Zin
Measurement
system
A  Vd 
Reference: [1]
21
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Employment of twisted pair
ZS
VS
i(t)
H(t)
Vd
Zin
Twisted pair
Measurement
system
Aeq  Vd 
Reference: [1]
22
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Magnetic shielding
ZS
i(t)
VS
Zin
Single-shell or multi-shell magnetic shield
Reference: [1]
23
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
E. Injection of interference by imperfect grounding
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.
~
N
ZS
Measurement
system
vS
vd
Istray
Istray1
Istray2
Rg
Reference: [1]
24
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Single-point grounding helps to reduce the disturbances.
~
N
ZS
vS
Rg
vd
Measurement
system
Istray1
Istray2
Istray
Reference: [1]
25
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Differential input and shielded twisted pair further reduce the
disturbances.
~
N
ZS
Measurement
system
vS
(CMRR)
vd
Istray
Istray1
Istray2
Rg
Reference: [1]
26
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
2) Ground loops. If single-point grounding is impossible, ground
lops can be a significant source of interference noise:
ZS
vS
Measurement
system
Ground loop
(inductive injection of interference)
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).
Reference: [2]
27
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
Isolation with:
ZS
Measurement
system
vS
Isolating device
(1) transformers
(2) common-mode chokes
(3) optical couplers
Signal current
Balun (balanced, unbalanced signals)
Common-mode current
Reference: [2]
28
5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances
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
vS
Measurement
system
Reference: [2]
30
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.1. General structure of a measurement system
6.
MEASUREMENT SYSTEM CHARACTERISTICS
6.1. General structure of a measurement system
Measurement
system
Measurement
object
Input
transduction
Memory
Transmission
Signal
processing
Control
Exciter
User interface
Reference
User
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity
31
6.2. Measurement system characteristics
6.2.1. Sensitivity
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.
y
G= x .
2) Dynamic sensitivity.
g(x0) =
y
x
.
x = x0
Reference: [1]
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity
32
3) Scale factor.
SF =1/G .
Example: Sensitivity and scale factor
Signal source
y = 4 div
x = 1 mV p-p
G = 4 div/mV; SF = 0.25 mV/div
Reference: [1]
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.2. Sensitivity threshold
33
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:
s
Average signal, S
Detection criterion D 
S
2
t
Detection result
1
0
t
Reference: [1]
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.2. Sensitivity threshold
34
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.
SNR * DP, %
f (x)
Detection probability, DP
Noise
N
s
Error probability, EP
0 S S
2
1
69.15
30.85
1.4
76.02
23.97
2
84.13
15.87
3
93.32
6.68
4
97.72
2.28
5
99.38
0.62
6
99.87
0.13
8
99.9968
0.0032
99.999971
0.000029
10
Average signal
*
Detection criterion, D
EP, %
SNR = S , D = S
N
2
Reference: [1]
35
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.3. Resolution
6.2.3. Resolution
The resolution, R, is defined as the smallest interval D x of the
measured signal x that will still cause a change in the
measrement result y.
According to the above: RES  ST  s  N.
The resolution can also be defined as the ratio of xmax (or fullscale value of x, FS) to D x:
RES 
xmax FS

Dx
ST
For example, if xmax = 10 V and D x = 150 mV, then
RES  216, which corresponds to a resolution of 16 bit.
Reference: [1]
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Inaccuracy, …
36
6.2.4. Inaccuracy, accuracy, and precision
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 D  A+B, then
f(x)
s
3s
X
0
Xtrue
B
A
x
Inaccuracy, DA+B
*
International Committee of Measures and Weights, 1986
6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Inaccuracy, …
the relative inaccuracy can be defined as:
the accuracy can be defined as:
(The ability of a measurement to match the actual value of
the quantity being measured.)
and the precision can be defined as:
(The ability of a measurement to be consistently reproduced.)
d
D
100%
Xtrue
ACC  100% - d
P  (1- A ) 100%
X
More accurate, but same precision
f (x),
normalized
More precise and more accurate
s
3s
X
0
Xtrue
B
Inaccuracy, D
A
x
37
38
Good luck!
Thank you and good luck in the final exam!