5.6. Disturbances: interference noise 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 environment. E n v i r o n m e n t Disturbance +Dy +D x x y 1 Measurement Object Matching Measurement System Matching Observer Influence Influence

Sd = ___  ___ . x=0 x=0 d y = Sd d d 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise There are two types of disturbances: additive disturbance, multiplicative disturbance. To quantify the effect of additive disturbances on the measurement system, the disturbance sensitivity (or sensitivity factor) is used: d y d d Dy Dd Sd = ___  ___ . x=0 x=0 Disturbance, d x=0 Measurement System Dy d y = Sd d d

Sd Sx xeq = ___ Sx = ___ . d y = Sx xeq 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Additive disturbances can be written as the equivalent disturbing input signal Sd Sx xeq = ___ Dd , where Sx is the sensitivity of the measurement system: d y d x Sx = ___ . Disturbance, d x + xeq Measurement System Dy d y = Sx xeq

Sx dy = (Cd d d )·x Cd = ______ 106 [ppm/ d ]. 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Multiplicative disturbances affect the sensitivity Sx of the measurement system. Disturbance, d Dy x Sx dy = (Cd d d )·x Measurement system To quantify the effect of multiplicative disturbances, the disturbance coefficient (or influence function) is used:  Sx / Sx  d Cd = ______ 106 [ppm/ d ].

the supply voltage sensitivity SV [Dy/V], 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Nomenclature: When dealing with a specific disturbances, their names are used in the just described characteristics of measurement systems. For example, we speak of the supply voltage sensitivity SV [Dy/V], and the temperature coefficient CT [ppm/º], of a measurement system.

Example 1: Supply voltage sensitivity SV 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Example 1: Supply voltage sensitivity SV DVCC VS =0 DC-voltage null detector DVout DVout = Sd DV Sd Sx VS +Veq DC-voltage null detector DVout Veq = ___ DV DVout = Sx Veq

______ 106 [ppm/º] __________ Example 2: Temperature coefficient CT 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise Example 2: Temperature coefficient CT T1 RG 1 VS Instrumentation amplifier Vout 1  G/G  T CT = ______ 106 [ppm/º] T2 RG 2 Vout 2 - Vout 1 Vout 1 __________ dVout = VS Instrumentation amplifier Vout 2 dVout = (CT DT )·VS

5.2.1. Reduction of the influence of disturbances 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. 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.

d Sd 1 = - Sd 2 x y d S1 Cd 1 = - S2 Cd 2 d d Sd 1 S2 = - Sd 2 x y 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances Example Compensation d parallel S1 Sd 1 = - Sd 2 x y d S1 Cd 1 = - S2 Cd 2 S2 series d d Sd 1 S2 = - Sd 2 x y Object Sensor S1 S2 Cd 1 = - Cd 2 d ratio S1 Any ratio measurement system not effective x y d Cd 1 = Cd 2 S2

DT x y DT x y 5. Use feedback against multiplicative disturbances. SOL 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 y SOL DT x y SOL b

_______ ________ ______ _______ _________ _________ _________ ____ SOL 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.1. Reduction of the influence of disturbances SOL 1 + SOL b _______ 1. Sf = DSOL /SOL DT ________ 2. CT OL = DSf /Sf DT ______ 3. CT f = 1 1 + SOL b SOL b (1 + SOL b )2 1 (1 + SOL b ) 1 (1 + SOL b ) SOL _______ _________ _________ _________ ____ 4. d Sf /d SOL = - = 1 1 + SOL b 5. d Sf /Sf = _______ d SOL /SOL 1 1 + SOL b 6. CT f = _______ CT OL

5. SOURCES OF ERRORS. 5. 6. Disturbances: interference noise. 5. 6. 1 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. 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]

5.2.2. Sources of disturbances 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances 5.2.2. Sources of disturbances A. Thermoelectricity Metal A Junction at T1 V = ST (T1- T2 ) Metal B Metal A Junction at T2 Reference: [1]

Cu-Au 0.3 mV/º Cu-Kovar 500 mV/º Cu-Cd/Sn Cu-CuO 1000 mV/º 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances T1 T2 Cu Pb/Sn Kovar Cu-Ag Cu-Pb/Sn 3 mV/º Cu-Au 0.3 mV/º Cu-Kovar 500 mV/º Cu-Cd/Sn Cu-CuO 1000 mV/º Thermoelectricity is an additive disturbance. Reference: [1]

B. Leakage currents V2 - V1 RL IL = ________ V2 V1 1 cm (100 MW) 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances B. Leakage currents 1 cm (100 MW) V2 V1 Leakage current, IL V2 - V1 RL IL = ________ Reference: [1]

IL = ________ = __________________ = ______ ____ 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Active guarding Vout AOL V1 Leakage current, IL V1 - Vout R’L V1 - V1 AOL /(1+AOL) R’L 1 1+AOL V1 R’L IL = ________ = __________________ = ______ ____ “Leakage currents cause multiplicative errors as they give rise to an extra equivalent loading impedance.” (?) Reference: [1]

C. Capacitive injection of interference 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances C. Capacitive injection of interference Cp ZS vS 220 V 50 Hz Vin Zin Vd Cable Measurement system Vin = vd jw Cp(ZSIIZin) 1/jw Cp >> ZSIIZin (ZSIIZin)  Vin Inductive injection of interference is an additive disturbance. Reference: [1]

Vd Electrical shielding Cp ZS vS Zin ZS < Rin Shielded cable 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Electrical shielding Cp ZS vS 220 V 50 Hz Zin Shielded cable Vd Measurement system ZS < Rin Reference: [1]

Vd Electrical shielding Cp ZS iS Zin Zin < ZS Shielded cable 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Electrical shielding Cp ZS iS 220 V 50 Hz Zin Shielded cable Vd Measurement system Zin < ZS Reference: [1]

D. Inductive injection of interference 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 Vd Vd  A, d i/d t; ___  f(ZS ,Zin) Inductive injection of interference is an additive disturbance. Reference: [1]

Reduction of the wire loop area 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Reduction of the wire loop area ZS i(t) VS H(t) Vd Zin Wire loop Measurement system A  Vd  Reference: [1]

Employment of twisted pair 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances Employment of twisted pair ZS i(t) VS H(t) Vd Zin Twisted pair Measurement system Aeq  Vd  Reference: [1]

Magnetic shielding i(t) ZS VS Zin 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]

E. Injection of interference by imperfect grounding 5. SOURCES OF ERRORS. 5.6. Disturbances: interference noise. 5.6.2. Sources of disturbances E. Injection of interference by imperfect grounding 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 vS Measurement system vd Istray1 Istray2 Rg Istray Reference: [1]

Single-point grounding helps to reduce the disturbances. 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 Measurement system vd Istray1 Istray2 A B Istray Reference: [1]

5. SOURCES OF ERRORS. 5. 6. Disturbances: interference noise. 5. 6. 2 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 vS Measurement system (CMRR) vd Istray1 Istray2 Rg Istray Reference: [1]

6. MEASUREMENT SYSTEM CHARACTERISTICS 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.1. General structure of a measurement system 6. MEASUREMENT SYSTEM CHARACTERISTICS 6.1. General structure of a measurement system -.

6.2. Measurement system characteristics 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.1. Sensitivity threshold 6.2. Measurement system characteristics 6.2.1. Sensitivity threshold -.

6.2.2. Signal shape sensitivity 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.2. Signal shape sensitivity 6.2.2. Signal shape sensitivity -.

6. MEASUREMENT SYSTEM CHARACTERISTICS. 6. 2 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.3. Resolution 6.2.3. Resolution -.

6. MEASUREMENT SYSTEM CHARACTERISTICS. 6. 2 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.4. Non-linearity 6.2.4. Non-linearity -.

6. MEASUREMENT SYSTEM CHARACTERISTICS. 6. 2 6. MEASUREMENT SYSTEM CHARACTERISTICS. 6.2. Measurement system characteristics. 6.2.5. System response 6.2.5. System response -.

Thank you and good luck in the final exam!