1. 1 Input transduction Input transduction 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 Exciter Transmission Memory User interface Measurement object Measurement object Reference Measurement system User Control

2. 2 6. 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 yxyx G  2) Dynamic sensitivity. g(x 0 )   x x0x x0  y x y x Reference: [1]

3. 3 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity 3) Scale factor. SF  1/G  Example: Sensitivity and scale factor y = 4 div x = 1 mV p  p Signal source G = 4 div/mV; SF = 0.25 mV/div Reference: [1]

4. 4 6. 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 S2S2 Detection criterion D  t Detection result 1 0 Average signal, S

5. 5 6. 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)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 * 284.13 15.87 DP, %EP, % s S 2 S Detection criterion, D Average signal SNSN * SNR  S2S2, D  N 0 Error probability, EP Detection probability, DP Noise

6. 6 6. 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 x max (or full- scale value of x, FS ) to   x : FS ST RES  x max   x For example, if x max   10 V and   x   150  V, then RES   2 16, which corresponds to a resolution of 16 bit.

7. 7 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Inaccuracy, … If we define the true magnitude of a signal x as X true, 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 )f ( x )  x 0 X true B 3  X A Inaccuracy, 

8. 8 6. 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: P    1    AXAX the relative inaccuracy can be defined as:     X true f (x), normalized  x 0 X true B 3  X A 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.)

9. 9 Good luck! Thank you and good luck in the final exam!