SaM - Accuracy of the Complete Measurement System

Remeber:

This is the scheme of a complete system for measuring temperature:

Where:

• $T_x$ is the real temperature we want to measure, while $T_S$ is the temperature the sensor measures.
• These two temperatures ($T_x$ and $T_S$) are not the same, since there is a Coupling with the Mesurand (drawned as a blank box $1.$), so remember that we cannot actual measure the real temperature, the temperature, specific heat and other properties of the sensor and all the other electronics will alter the measured value.
• Also we also need to note that other errors are due to the non-idealities of the sensor ($2.$), Read-Out Electronics ($3.$), and A/D ($4.$).

We have also seen a simple example using the PT100 sensor:

• $I_{DC}$ is the current source.
• $R(T)$ is the PT100 sensor.
• $V_{io}$ is the bias voltage of the amplifier (read-out electronics).
• We measure $V_A$ and we will convert it using the A/D, however we don’t account for that in this example.
  What we account for is the “complete accuracy” of the complete system, which is:$\alpha \triangleq \frac{d{V}_A}{dT}=I_{DC}\cdot A_0\cdot A\cdot R_0$Where:
  • $R_0$ and $A$ are the resistance value at the reference temperature (usually $0$°C), and the first coefficient specific to the platinum resistance sensor, both defined by the Calendar Van Dusen Relationship.
  • $A_0$ is the open-loop gain of the amplificator.
• So it is important to notice that the sensitivity of the complete system depends on the current source ($I_{DC}$), that means that a higher current improves the SNR (Signal to Noise Ratio), however it can create a self-heating problem.

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