Chapter III – Measurement systems with electrical signals
CHAPTER III
Measurement Systems with Electrical Signals
- Electrical signal measurement system:
Modern measurement systems usually use sensing devices that have an electrical output. Such devices are preferred to mechanical systems because:
1-A higher compatibility with the recording system (an electrical signal is directly sent to the data acquisition card (DAQ)), then to the computer for recording.
2-It is easier to filter or amplify an electrical signal.
Electrical sensing devices are usually called sensors or transducers. They are based on the ability to change their characteristics (resistance, voltage, and capacitance) as a result of the measurand value (the property that you want to record).
Practically speaking, two stages are required to get the value of the measurand:
-In the first stage, the variation in the measurand value causes non-electrical change in the sensor. Exp: Pressure will deform a piezo-electric component.
-In the second stage, the non-electrical response is converted into an electrical signal. Exp: The deformation of the piezo-electric component is converted into an electrical signal that can be amplified, filtered, …
- Signal Conditioners:
The output signal from the sensor is almost never directly recorded, since it is difficult to use such data. Several signal conditioning stages are necessary, therefore, prior to recording the signal:
-Amplification and attenuation (depend on the amplitude of the signal).
-Filtering (remove undesirable frequencies).
-Differentiation.
-Integration.
-Linearization.
-Conversion (V to I, I to V, …).
- General characteristics of signal amplification:
Sensors usually produce very small electrical signals (usually millivolts). These signals are sometimes even smaller than the surrounding electrical noise. It becomes, then, very difficult not only to transport this signal (from the sensor to the recording device), but also to detect the signal. An essential step is then required which consist in amplification of the signal.
Let’s put Vi the low voltage input signal (before amplification) and V0 the higher amplified signal. We call the gain(or degree of amplification) the following ratio:
Usually, G [1 100].
Instead of using this simple ratio, we prefer to use a logarithmic scale and the result is expressed in dB:
It should be noted that sometimes an attenuation of the signal is required (think about measuring the voltage of a high voltage electrical line). In this case, the term gain is also used but it has a value lower than 1 (or Gdb < 0).
In practice, an amplifier does not simply amplify the input signal, it also modifies it (or alters it) in different ways: frequency or phase distortions, common-mode effects and source loading.
- Frequency distortion:
Amplifiers do not respond the same way for all frequencies. They have a certain zone where the answer is flat (constant gain) called: Bandwidth, limited by two upper and lower cutoff frequencies from where the response starts to decrease slowly.
These frequencies are exactly defined as the frequency where the gain is reduced by 3 db.
Figure 3.1. Bandwidth definition.
Note: sometimes, the lower frequency can be equal 0.
Figure 3.2. Frequency attenuation of a square wave due to high frequency attenuation.
- Phase distortion
The amplifier can modify the phase of the output signal leading to a sample shift in time (in the simplest case, linear dependence between phase angle and frequency) to a signal distortion (worse case, non-linear dependence between phase and frequency)
Figure 3.3.Typical phase-angle response of amplifier.
Figure 3.4.Linear and non-linear phase-angle variation with frequency.
Note: the variation of amplification and phase with frequency are called Bode Diagrams.
- Common-mode rejection ratio (CMRR):
The input terminals of an amplifier can be connected to the same source (common-mode voltage) or to two different sources (differential-mode voltage). In the ideal case, the output should be the same. In practice, however, this is not the case.
The measure of the relative response to differential-and-common-mode voltages is described by common rejection ratio:
Gdiff: gain for differential-mode input.
Gcm: gain for common-mode input.
Very high CMRR are usually desirable > 100 db.
- Input loading and output loading
This problem happens when there is a mismatch between the input/output resistance (impedance) of the input source, amplifier and the output load.
We want an amplifier to have a very high input resistance and a very low output resistance.
Figure 3.5. Input source, amplifier and output load.
Then
There is no loading effect if RL > R0 and Ri > Rs. In other terms, the perfect ideal amplifier will have an infinite input resistance (infinite input impedance) and a zero output resistance (zero output impedance).
ExampleA pressure transducer has an output impedance of 120 and is to be connected to an amplifier. What must be the minimum input impedance of the amplifier to keep the loading error less than 0.1%.
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Instrumentation and Measurements \ LK\ 2009