# Output Voltage Formula verification of Operational Amplifier circuit

I'm trying to built an op-amp circuit for a PT100 temperature sensor. I've found the following circuit diagram online (from a polish website): And I'm trying to find the formula for the output voltage as a function of the input voltage. I came up with the following formula (sorry, it's an image, no Latex here): Can someone please help me verify that the last formula expressing Vout as a function of Vin is correct? Thanks in advance

EDIT1: at the beginning of the demonstration, R1 and R2's values have been switched.

EDIT2: Please, this question IS NOT a duplicate of a previous question I've posted. In this question, I'm trying to verify that my computations are OK. In the other question I was trying to ask if it was common for Proteus to present results that slightly differ from the electric model.

• Possible duplicate of Difference between Proteus results and KCL-deduced formula May 1 '19 at 19:43
• I think there is an error in the OpAmp law: $V_1 = V_2 = v$ should be $V_4 = V_2 = v$ May 1 '19 at 19:59
• Rest of equations (including last steps) seem correct. Next step, expanding A and B. Good luck :) May 1 '19 at 20:08
• @Huisman, you're right! but doesn't change the result! Thank you!! May 1 '19 at 20:25
• – JRE
May 1 '19 at 20:56

The above design is an amalgamation of a Wheatstone bridge and a differential amp. It is hard to analyze and IMO an improper way to design a temperature sensor circuit. A better way is to have a wheatstone bridge followed by a diffamp as shown below:

The equations for that bridge are as follows:

• The TS circuit is using positive feedback to linearization the temp pt100 sensor. ti.com/lit/an/slyt442/slyt442.pdf
– G36
May 1 '19 at 19:58
• @laptop2d, great answer, but sorry doesn't solve my problem. My circuit works pretty well on Proteus, although with slight different results. However, how do I find out the output voltage in your diagram? May 1 '19 at 20:29
• @G36, thanks for the PDF link. Do you how I can get rid of VRTD in the formula presented in the document? Thanks. May 1 '19 at 20:33
• @N.Wells As you can see the Author is using superposition principle to find the voltage at the noninverting input (V"+"). So, you need to do the same and find the expression for the inverting input (V"-") next set V"+" = V"-". ti.com/lit/zip/SLYT442
– G36
May 1 '19 at 20:45
• @G36, I read the attached files and I don't understand anything in it; yet, I'll give a try in a proteus Simulation and let you know ASAP. May 2 '19 at 9:59