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, DA+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!