1. 5.3. Noise characteristics
LECTURE 6. Contents
5. Sources of errors
5.1. Impedance matching
Non-energetic matching
Energetic matching
Non-reflective matching
To match or not to match?
5.2. Noise types
Thermal noise
Shot noise
/f noise
5.3. Noise characteristics
Signal-to-noise ratio, SNR
Noise factor, F, and noise figure, NF
Calculating SNR and input noise voltage from NF
Vn-In noise model
5.4. Noise matching
Optimum source resistance Methods for the increasing of SNR
SNR of cascaded noisy amplifiers

2. 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.
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

3. 5. SOURCES OF ERRORS Influencing the measurement object: matching Non-energetic matching
5.1. Impedance matching
Systematic measurement errors can occur due to the undesirable interaction between the measurement system and:
the object under test.
+D x x
Measurement
Object
Measurement
System
Matching
Influence

4. 5.1.2. Non-energetic matching
5. SOURCES OF ERRORS Influencing the measurement object: matching Non-energetic matching
There are three types of impedance matching: non-energetic, energetic, and non-reflective.
Non-energetic matching
Non-energetic 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.
Non-energetic matching is usually used in active measurement systems, which do possess internal power amplification.
Reference: [1]

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

6. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energetic matching
The aim of energetic 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 do not possess internal power amplification.
Reference: [1]

7.  VS2 Rin (RS+Rin)2 + (XS+Xin)2 Pin = Iin2 Rin = . 2
5. SOURCES OF ERRORS Influencing the measurement object: matching Energetic matching
To optimize the energetic 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:
VS2 Rin
(RS+Rin)2 + (XS+Xin)2
Pin = Iin2 Rin =  2
Iin and VS are measured in A rms and V rms.

8. Rin = RS and Xin = - XS or Zin= ZS* . Pin = = . V S2 4 Rin 4 RS
5. SOURCES OF ERRORS Influencing the measurement object: matching Energetic matching
For a fixed non-zero RS, this power is maximal if the following optimal matching is obtained:
Rin = RS and Xin = - XS
or Zin= ZS* .
Therefore, the maximum power that a measurement object with a fixed non-zero RS can deliver to a measurement system is:
Pin = =
V S2
4 Rin
4 RS
Reference: [1]

9. Rin = 0 and Xin = - XS . V S2 Pin = . Rin
5. SOURCES OF ERRORS Influencing the measurement object: matching Energetic matching
If RS = 0, then the optimal matching is obtained when
Rin = 0 and Xin = - XS .
In this case, the maximum power a measurement object can deliver to a measurement system is :
V S2
Pin =
Rin
Reference: [1]

10. 5. SOURCES OF ERRORS. 5.1. Influencing the measurement object: matching. 5.1.2. Energetic matching
Available power (H. T. Friis, 1944) is defined as the maximum power that can be delivered to a load from a source having fixed nonzero resistance
Vin 2
Pa  Pin =
4 RS
RS0
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 are active ones (with built-in power gain).
Reference: [1]

11.  5.1.3. Non-reflective matching L Z0 = R0 = . C
5. SOURCES OF ERRORS Influencing the measurement object: matching Non-reflective matching
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. Illustration: Non-reflective matching: ZS = R0 = Zin
5. SOURCES OF ERRORS Influencing the measurement object: matching Non-reflective matching
Illustration: Non-reflective matching: ZS = R0 = Zin
Measurement object
Measurement system Z0 Z0 ZS vS
Zin
vin = 0.5vS
NB: When ZS = R0 = Zin holds, energetic 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.
Reference: [1]

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

14. 5. SOURCES OF ERRORS Influencing the measurement object: matching When to match and when not?
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:

15. 5. SOURCES OF ERRORS Influencing the measurement object: matching 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:

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