1

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

26. 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]

36. 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]

46. 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

56. 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

66. 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.

76. 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,

86. 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.)

9Good luck!

Thank you and good luck in the final exam!