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

2. 2 Reference: [1] 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.1. Anenergetic matching 5.1. Influencing the measurement object: matching 5.1.1. Anenergetic matching Anenergetic matching is used to minimize the transfer of energy between the measurement object and the measurements system. After matching, measurement 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.

3. 3 R msr >> R s  V msr  V in ; the power supplied by the object is small; most part of it is dissipated in R msr. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.1. Anenergetic matching Example: Anenergetic matching RsRs R msr Measurement objectMeasurement system V msr V in RsRs R in Measurement objectMeasurement system I msr I in R msr << R s  I msr  I in ; the power supplied by the object is small; most part of it is dissipated in R msr.

4. 4 Reference: [1] 5.1.2. Energic matching 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: 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. Anenergetic matching is especially important for passive measurement systems, which do not possess internal power amplification.

5. 5 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching Z s = R s + X s Z msr = R msr + X msr Measurement objectMeasurement system V msr V in To optimize the energic matching, let us consider the following equivalent circuits of the measurement object and the measurement system. The average power delivered to the measurement system can be found as: P avg = I 2 R in =. V s 2 R msr  R s + R msr ) 2 +  X s +X msr ) 2

6. 6 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching For a given R o, this power is maximal if the following optimal matching is obtained: R msr = R s and  X msr =  X s or Z msr = Z s *. Therefore, the maximum power a measurement object can deliver to a measurement system is: P avg =  V s2V s2 4 R msr V s2V s2 4 Rs4 Rs Reference: [1]

7. 7 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energic matching If R o can be adjusted, then the optimal matching is obtained when R o = 0 and  X msr =  X o  The maximum power a measurement object can deliver to a measurement system is in this case: P avg =  V s2V s2 2R msr Reference: [1]

8. 8 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 P a  P avg =  Reference: [1] V in 2 4 Ro4 Ro NB: The maximum power matching usually causes greater measurement errors, since the input and output impedances of the chain affect the measurement. For this reason, the measurement systems almost always used are active systems (with built-in power gain). R o 

9. 9 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching Reference: [1] 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, Z 0, of a transmission line equals its input impedance if 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, Z 0 = = R 0  L C 

10. 10 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching Reference: [1] RsRs R msr Measurement objectMeasurement system V msr = 0.5V in V in Z0Z0 Illustration: Non-reflective matching: R o = R 0 = R in NB: When R o = R 0 = R msr holds, energic matching is also achieved simultaneously, since R o = R msr. R 0 is an apparent resistance that does not dissipate energy; half of the energy delivered by V in is dissipated in R o and the other half in R msr. Z0Z0

11. 11 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.3. Non-reflective matching Reference: [1] Example: The characteristic impedances of different connections DEFINITION Characteristic impedance Type of connection Coaxial cable50  75  Printed circuit board traces50  150  Twisted wire pairs100  120  Ribbon cable200  300  Free space376 

12. 12 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.4. When to match and when not? 5.1.5. When to match and when not? 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/

13. 13 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.4. When to match and when not? Do not 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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