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MEASUREMENT THEORY FUNDAMENTALS. Contents

MEASUREMENT THEORY FUNDAMENTALS. Contents. 5. Sources of errors 5.1. Impedance matching 5.4.1. Anenergetic matching 5.4.2. Energic matching 5.4.3. Non-reflective matching 5.4.4. To match or not to match? 5.2. Noise types 5.2.1. Thermal noise 5.2.2. Shot noise

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MEASUREMENT THEORY FUNDAMENTALS. Contents

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  1. MEASUREMENT THEORY FUNDAMENTALS. Contents 5. Sources of errors 5.1. Impedance matching 5.4.1. Anenergetic matching 5.4.2. Energic matching 5.4.3. Non-reflective matching 5.4.4. To match or not to match? 5.2. Noise types 5.2.1. Thermal noise 5.2.2. Shot noise 5.2.3. 1/f noise 5.3. Noise characteristics 5.3.1. Signal-to-noise ratio,SNR 5.3.2. Noise factor, F, and noise figure,NF 5.3.3. Calculating SNR and input noise voltage from NF 5.3.4. Vn-Innoise model 5.4. Noise matching 5.4.1. Optimum source resistance 5.4.2. Methods for the increasing of SNR 5.4.3. SNR of cascaded noisy amplifiers

  2. E n v i r o n m e n t +Dy +Dx Matching Matching Influence 5. SOURCES OF ERRORS 5. SOURCES OF ERRORS • Measurement errors can occur due to the undesirable interaction between the measurement system and: • the object under test, • the environment, • observer. Disturbance x y 1 Measurement Object Measurement System Observer Influence

  3. E n v i r o n m e n t +Dy +Dx Matching Matching Influence 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.1. Anenergetic matching 5.1. Impedance matching • Measurement errors can occur due to the undesirable interaction between the measurement system and: • the object under test. Disturbance x y 1 Measurement Object Measurement System Observer Influence

  4. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.1. Anenergetic matching There are three types of impedance matching: anenergetic, energetic, and non-reflective. 5.1.2. Anenergeticmatching Anenergetic matching is used to minimize the transfer of energy between the measurement object and the measurement system. After matching, measurement system will not supply any appreciable energy to, or receive from the measurement object. Anenergetic matching is usually used in active measurement systems, which do possess internal power amplification. Reference: [1]

  5. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.1. Anenergetic matching Example: Anenergetic matching Measurement object Measurement system Rin>> RS vin vS the power supplied by the object is small most part of it is dissipated inRin RS vS vin Rin Measurement object Measurement system Rin<< RS iin iS the power supplied by the object is small most part of it is dissipated inRin iin RS iS Rin

  6. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching 5.1.2. Energic matching The aim of energic matching is to extract the maximum available power from the measurement object, so that the required power gain in the measurements system can be as small as possible. Energetic matching is especially important for passive measurement systems, which donot possess internal power amplification. Reference: [1]

  7. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching To optimize the energic matching, let us consider the following equivalent circuits of the measurement object and the measurement system. Measurement object Measurement system iin ZS=RS + XS Zin=Rin+ Xin vS vin The average power delivered to the measurement system can be found as: VS2Rin (RS+Rin)2 + (XS+Xin)2 Pin = Iin2Rin = .

  8. Therefore, the maximum power that a measurement object with a fixed non-zeroRS can deliver to a measurement system is: VS2 VS2 Pin = = . 4Rin 4RS 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching For a fixed non-zeroRS, this power is maximal if the following optimal matching is obtained: Rin= RS andXin =- XS or Zin= ZS* . Reference: [1]

  9. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching If RS=0, then the optimal matching is obtained when RS = 0 andXin = - Xo . In this case, the maximum power a measurement object can deliver to a measurement system is : Vs2 Pin = . Rin Reference: [1]

  10. For this reason, the measurement systems almost always are active ones (with built-in power gain). NB: The maximum power matching usually causes greater measurement errors, since the input and output impedances of the chain affect the measurement. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching Available power is defined as the maximum power that can be delivered to a load from a source having fixed nonzero resistance Vin2 Pa Pin = . 4RS RS0 Reference: [1]

  11. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching 5.1.3. Non-reflective matching Non-reflective or characteristic matching is used for transporting high-frequency measurement signals along transmission lines. If a transmission line is not terminated characteristically, reflections off the ends of the line will cause standing waves on the line; the line output signal is no longer a good measure for the line input signal. The characteristic impedance, Z0, of a transmission line equals its input impedance if the transmission line length were infinite. For a lossless transmission line with the series inductance per meter L and the parallel capacitance per meter C,  L Z0= R0=. C Reference: [1]

  12. NB: When ZS = R0 = Zin holds, energic matching is also achieved simultaneously, since ZS = RS and Zin = Rin. R0 is an apparent resistance that does not dissipate energy; half of the energy delivered by vs is dissipated in RS and the other half in Rin. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching Illustration: Non-reflective matching: ZS = R0 = Zin Measurement object Measurement system Z0 Z0 ZS vS vin=0.5vS Zin Reference: [1]

  13. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching Example: The characteristic impedances of different connections Type of connection Characteristic impedance DEFINITION Coaxial cable 50 - 75 W Printed circuit board traces 50 - 150 W Twisted wire pairs 100 - 120 W Ribbon cable 200 - 300 W Free space 376 W Reference: [1]

  14. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.4. When to match and when not? 5.1.5. To match or not to match? • Do match by adjusting impedances, by adding voltage buffers or by adding matching transformers: • To transfer maximum power to the load. The source must be capable. • To minimise reflections from the load. Important in audio, fast (high frequency) systems, to avoid ringing or multiple pulses (e.g. in counting systems). • To transmit fast pulses. Pulse properties can contain important information. • Note that the same physics is encountered in other areas, e.g. optical coatings, gel in ultrasound scans, optical grease, etc. Reference: www.hep.ph.ic.ac.uk/Instrumentation/

  15. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.4. When to match and when not? • Donot match: • High impedance source with small current signals. Typical for many photodiode sensors, or other sensors that must drive high impedance load. Short cables are required to avoid difficulties. • Weak voltage source. Drawing power from source would affect the result, e.g. bridge circuits. • If you need to change properties of a fast pulse, e.g. pulse widening for ease of detection. • Electronics with limited drive capabilities, e.g. logic circuits, many are designed to drive other logic, not long lines, CMOS circuits, even with follower, are an example. Reference: www.hep.ph.ic.ac.uk/Instrumentation/

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