 ### Network # Deriving formulas for calculating the errors that occur in the measurement circuit with a two-wire and three-wire resistance thermometer scheme

May 14, 2023
1
Hello! I need to derive formulas for calculating the errors that occur in the measurement circuit with a two-wire and three-wire resistance thermometer connection scheme. But, unfortunately, I have almost no values except for α (temperature coefficient of the resistance converter), constants A, B and C, the nominal value of resistance R0 at a temperature of 0° C and table values of resistance for certain temperatures. Where can I find some information about it? I will be very grateful for any answer. Thanks in advance.

#### Delta Prime

Jul 29, 2020
1,216
Thermometer scheme??
Thermodynamics of RTD's(Resistance Temperature Detectors).
Thermistors are well known.
Metallurgy! what alloys are using?
Differential equations are involved how good is your math.
The information you seek may be beyond your capabilities.
I will not do the math for you.
Well... maybe I will.

#### Delta Prime

Jul 29, 2020
1,216
mperature of 0° C and table values of resistance for certain temperatures.
Shoot... Sorry, this is homework help.Show me your table values. You have to show an effort ,I will help you.

Last edited:
• Feb 19, 2021
621
Some ref material :

And attached.

Regards, Dana.

#### Attachments

• AN280.pdf
2.1 MB · Views: 3
• #### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
13,337
My guess is that this task is not about the error of the sensor and its parameters but about the error introduced by the measurement method (2-wire vs. 3-wire). To solve this, you model the wires leading to and from the sensor as resistors. Usually all resistors will have the same value since the 2 or 3 wires are the same langth and typically are of the same material and diameter.
For a rather general solution the absolute value of the wire resistance is not important, instead a reference value Rwire can be used in the equations.
Then you can set up the equations for the measurement of the sensor resistance via the 2-wire and the 3-wire circuit using this general Rwire as a variable in the equation. From these equations you can derive the error of the measurement with Rwire being still a variable in the final error equation.
As a last step you could plot the measurement error for the 2-wire and 3-wire circuit on the y-axis versus the value of Rwire on the x-axis.

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