Calculate PT100 resistance value from attached circuit

[Vindhyachal.takniki]

1. Attached is one analog circuit, whose output I can measure.
2. Its three wire PT100 whose resitance I have to measure. RL1=RL2=RL3 is lead wire resistance.
3. Rs1=Rs2 we can take which is resistance of anlog mux displacyed here as switch for simplicity.
4. Output opamp is conencted with gain of 100. After which I can measure voltage by MCU.
5. I can measure two voltage:
a) when switch is top position
b) when switch is at botton position


6. Now who to caluclate PT100 resistance from this?
I tried using thevnin equivalent diagrams but they become very complex with lots of variables.
Need to implement it in MCU.

[ledtester]

The circuit simplifies a lot when you consider it. For instance, when the switch is in the upper position you can ignore R34. And when it is in the lower position you can ignore R33.

First fix the position of the switch into one specific position. Then the schematic looks like what I've drawn below and you want to find the voltage at X.

Then notice that V7 and V8 are the same so you can draw it as shown in the right hand diagram.

Now compute the voltage at Y using a voltage divider calculation. Next compute the voltage at X using a voltage divider calculation between 2.5V and Y.

When the switch is in the upper position the resistances are:

R1 -> R27
R2 -> R32
R3 -> RL3 + PT100 + RL1
R4 -> R31 + Rs1 + R33 + RL1

When the switch is in the lower position the resistances are:

R1 -> R27 + RL1
R2 -> R32
R3 -> RL3 + PT100
R4 -> R31 + Rs2 + R34 + RL2

The formula you will get for the voltage at X will be a rational function of R3, i.e.:

$$ X = \frac{A + B R_3}{C + D R_3} $$

This can be solved for \$R_3\$:

$$ R_3 = \frac{A-CX}{X D - B} $$

Update: This reminded me of this symbolic circuit analysis project:

https://www.eevblog.com/forum/crowd-funded-projects/symbolic-circuit-analysis-upcoming-kickstarter/msg4022044/#msg4022044

[Vindhyachal.takniki]

1. THis analog part is someone else design, cannot change. I have access of circuit on MCU side & can read output of opamp.



2. So considered R32=open due to high value, R31,R33,R34.Rs1,rs2 as wont happen happen much effect on output, as these goes on high input impedance opamp. (thanks to  @El Tangas for suggestion)



3. Below is equation which comes out, considering R27,Rl1, rl2 & Rl3 in circuit.  Rl1=Rl2=Rl3 is taken. Lets call it reduced circuit.
Rp = (60000V2 - 30000V1) / (6.25 - 2.5V1 - 2V1V2)

where Rp= resistance of PT100
V1 & V2 are voltages measured at the input of opamp when switch is at top & bottom



4. Tried simulating circuit on multisim with reduced circuit & matched values with this formula, seems like ok.



5. Is equation can be solved by also considering R31,R33,R34.Rs1,rs2 . I tried but equation starts very complex. 
Simulating original circuit, with reduced circuit equation does not work actually.