SaM - RTD Example • Linearized Uncertainty

Remeber:

This is the circuit:

Here’s it the circuit with numerical values (not with real world values tho):

So if we calculate the output of this circuit it will be: $V_{RT D} = (V_{REF} - V_{i o}) \cdot (1 + \frac{R ( t )}{R _{REF}}) - (V_{REF} - V_{i o} + V_{i d})$ Or it can be rewritten as: $V_{RT D} = (V_{REF} - V_{i o}) \cdot \frac{R ( t )}{R _{REF}} - V_{i d}$

==NOTE: The professor found another formula, where it also conisdered the gain of the A.O., so a formula also depending on $G_{0}$ ==.
This is a simpler formula, where I considered $G_{0} = \infty$ and $A_{0} = 1$ , so that it can be remembered more easily.

The complete formula would be: $V_{RT D} = A_{0} [(V_{REF} - V_{i o} - \frac{V _{o u t}}{G _{0}}) \frac{R ( T )}{R _{REF}} - V_{i d}]$ Where $V_{o u t}$ is the output of the A.O.

Rememebr that we can see $R (T) = R_{0} (1 + A T)$ , using the Calendar Van Dusen Equation.

So the complete formula for this RTD circuit depends on:

$V_{REF}$

$V_{i o}$

$V_{i d}$

$V_{o u t}$

$V_{RT D}$

$R_{0}$

$A$

So each of this parameter bring an uncertanty: $u (V_{REF}$ ), $u (V_{i o})$ , $\dots$ , $u (A)$ , we can define the combined unceranty, or uncertanty on the measurament as: $u (T) = \frac{\partial T}{\partial V _{REF}} u (V_{REF}) + \frac{\partial T}{\partial V _{i o}} u (V_{i o}) + \dots + \frac{\partial T}{\partial A} u (A)$

Here are some real world values and names for some of this uncertanties:

$u (V_{REF})$ : “drift of the reference voltage”.

$u (V_{i o})$ : “drift offset” for the PT100 it is about $≃ 10 μ V$ .IMPORTANTE

$u (V_{i d})$ : “drift offset”.

$u (V_{RT D})$ or $V_{L SB}$ : “Voltage at the Least Significant Bit”.

So if we perform some calculations we obtain that: $u (T) \leq \frac{R _{REF}}{R _{0} A _{0} A V _{REF}} \cdot 10 μ V$

Circuit (With 2 A.O.):
In this Circuit the output is capped at $15$ V, that is the source voltage of the amplifier ( $V_{CC}$ ), so it does not depend on the sensor, you need a differential amplifier, with limited gain.
Circuit (With an A.O. and an Ideal Differential Amplifier):
Circuit (With an A.O. and a Non-Ideal Differential Amplifier):