1. 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: E n v i r o n m e n t Measurement System Matching Disturbance y x the environment, the object under test, observer.    y

2. 2 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise To quantify the effect of additive disturbances on the measurement system, the disturbance sensitivity (or sensitivity factor) is used: d yd dd yd d S d   x  Measurement System Disturbance, d (  V CC ) x 0x 0 yy ydyd   x . additive disturbance, multiplicative disturbance. There are two types of disturbances (interference noise): d y   S d d d ( S VCC  y/V] supply voltage sensitivity)

3. 3 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Additive disturbances can be written as the equivalent disturbing input signal SdSxSdSx x eq     d, where S x is the sensitivity of the measurement system: d yd xd yd x S x  . Measurement System x   x eq y yy y d y   S x x eq Disturbance, d

4. 4 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Multiplicative disturbances affect the sensitivity S x of the measurement system. x SxSx Measurement system To quantify the effect of multiplicative disturbances, the disturbance coefficient is used: d S x / S x d  d C d     10 6 [ppm / d  d ].  y    C d d d ) · x y yy y Disturbance, d (  T )  Sxdd Sxdd ( C T  ppm/  ] temperature coefficient)

5. 5 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Example 1: Supply voltage sensitivity S VCC V IN   0  V out  V CC DC-voltage null detector V IN   V eq  V out DC-voltage null detector S VCC S VIN V eq   VV  V out  S VCC  V CC  V out  S VIN V eq

6. 6  Gd T Gd T 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Example 2: Temperature coefficient C T VSVS V out 1 R G 1 Instrumentation amplifier, G T 1 VSVS V out 2 R G 2 Instrumentation amplifier, G T 2  10 6 [ppm/ º ] C T   V out    C T  T ) ·V S V out 2  V out 1 V out 1   V out 

7. 7 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.

8. 8 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances S1 S1 S1 S1 S2 S2 S2 S2 S1 S1 S1 S1 S2 S2 S2 S2 S1 S1 S1 S1 S2 S2 S2 S2 y y y x x x d d dd d d ratio series parallel S 1 C d 1   S 2 C d 2 S d 1   S d 2 C d 1   C d 2 S d 1 S 2   S d 2 C d 1  C d 2 not effective Any ratio measurement system Sensor Object ExampleCompensation:

9. 9 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances 5.Use feedback against multiplicative disturbances. S OL   yx TT yx TT

10. 10 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances S OL 1  S OL   1. S f   S OL /S OL  T  2. C T OL   S f /S f  T  3. C T f  1 1  S OL   4. d  S f  d  S OL    S OL  (1  S OL   ) 2  1 (1  S OL   )  1 (1  S OL   )  S OL  1 1  S OL  5. d  S f  S f   d  S OL  S OL 1 1  S OL  6. C T f   C T OL

11. 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. 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.) S OL   y+  y x+x eq

12. 12 5. 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 B Junction at T 1 Junction at T 2 V  S T (T 1   T 2 ) Thermoelectricity is an additive disturbance.

13. 13 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Cu  AgCu  Pb / Sn 3  V/º Cu  Au 0.3  V/º Cu  Kovar 500  V/º Cu  Cd / SnCu  CuO 1000  V/º Reference: [1] Cu Pb / SnKovar T2T2 T1T1

14. 14 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances B. Leakage currents Reference: [1] 1 cm (100 M  ) Leakage current, I L I L   V2 V1RLV2 V1RL V2V2 V1V1

15. 15 V 1 0.5R L 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Active guarding Leakage current, I L A OL I L       V1V1 V out V 1   V out 0.5R L V 1   V 1 A OL /(1+A OL ) 0.5R L 1 1+A OL

16. 16 Measurement system Z in 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances C. Capacitive injection of interference Reference: [1] ZSZS v S 220 V 50 Hz Cable CpCp V in V in  V d  j  C p (Z S II Z in ) 1/j   C p >> Z S II Z in VdVd (Z S II Z in )  V in  Inductive injection of interference is an additive disturbance.

17. 17 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] ZSZS v S Measurement system 220 V 50 Hz Shielded cable Electrical shielding: grounding at the source CpCp Z in Z S < Z in VdVd 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:

18. 18 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] ZSZS i S Measurement system 220 V 50 Hz Shielded cable CpCp Z in VdVd Electrical shielding: grounding at the measurement sistem input Z S > Z in

19. 19 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances D. Inductive injection of interference Reference: [1] ZSZS V S i(t) H(t) Area, A Z in Measurement system Wire loop Inductive injection of interference is an additive disturbance. VdVd    f(Z S,Z in ) VSVdVSVd V d  A, d i/d t ;

20. 20 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] ZSZS V S i(t) Z in Measurement system Wire loop VdVd A  V d  H(t) Reduction of the wire loop area

21. 21 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] ZSZS V S i(t) H(t) Z in Measurement system Twisted pair VdVd A eq  V d  Employment of twisted pair

22. 22 V S 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] ZSZS i(t) Z in Magnetic shielding Single-shell or multi-shell magnetic shield

23. 23 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances 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. ZSZS v S RgRg Measurement system ~ N I stray I stray1 I stray2 v d

24. 24 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] Single-point grounding helps to reduce the disturbances. ZSZS v S Measurement system ~ N I stray I stray1 I stray2 v d RgRg

25. 25 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [1] Differential input and shielded twisted pair further reduce the disturbances. ZSZS v S RgRg Measurement system (CMRR) ~ N I stray I stray1 I stray2 v d

26. 26 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [2] ZSZS v S 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

27. 27 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [2] Isolation with: ZSZS v S Measurement system Isolating device (1) transformers (2) common-mode chokes (3) optical couplers Common-mode current Signal current Balun (balanced, unbalanced signals)

28. 28 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances 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: ZSZS v S Measurement system

29. 29 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reference: [2] Isolation with: (5) balanced circuitry. ZSZS v S /2 Measurement system ZSZS v S /2 vSvS vSvS vnvn vnvn

30. 30 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

31. 31 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]

32. 32 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]

33. 33 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

34. 34 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

35. 35 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.

36. 36 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, 

37. 37 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.)

38. 38 Good luck! Thank you and good luck in the final exam!