For the attached circuit attached in LTspice spice, I am trying to find the transfer function interms of Rc1,Rc2,Rc3 and Rc4. For that I have switches which I configure to turn on/off and measure the various values of V(bip) and V(bin). Basically, The for the switches S1 and S2 (00 -- 11),I run a inner loop of Sx and Sy switches (00 -- 11) So, I get 16 combinations of V(bip) and V(bin) readings. Final Aim is to find out the sensitivity of Rc1--R4 w.r.t the Sx and Sy (R8-R11)node resistances, So the resistance at this node would change, the current values are just to solve the transfer function . But, the sheer number of equations are too much for me, solving using pen and paper. Is there simpler way to find the equations and if some approach could be suggested to derive it ?enter image description here -----------------EDIT--------------------->>> Updated the with the equations as per the image, but while doing Find in Mathcad for Rc1-Rc4 the tool runs into runtime errorenter image description hereenter image description here

  • \$\begingroup\$ @seeker In that case use AJN's suggestion. I deleted the answer because I calculated the resistance as seen from I1, not V(A,B) (also had a typo that resulted in 2/Ry, instead of 1/Rx+1/Ry). \$\endgroup\$ Commented Jun 30, 2021 at 20:27
  • \$\begingroup\$ @aconcernedcitizen I have put the equations as per my edit in mathcad but the tool runs into runtime error while trying to calculate Rc1--Rc4. \$\endgroup\$
    – seeker
    Commented Jul 1, 2021 at 6:17
  • \$\begingroup\$ @AJN please refer my edit not sure why but the mathcad tool runs into runtime error while calculating the variables Rc1--Rc4. \$\endgroup\$
    – seeker
    Commented Jul 1, 2021 at 6:18
  • \$\begingroup\$ @AJN sure I could try. The matrix := Find(...), Find() calculates the different variables and the correspond values gets assigned to the matrix variable of size 9x1 in this case, If you want to access Va then use Matrix0,0-> \$\endgroup\$
    – seeker
    Commented Jul 1, 2021 at 13:04
  • \$\begingroup\$ Let us continue this discussion in chat. \$\endgroup\$
    – AJN
    Commented Jul 1, 2021 at 13:19

1 Answer 1


Without a reference node (a node at 0V), you have an indefinite admittance matrix which is singular. There is no unique solution to these equations as, for one solution (v1,v2,..), another solution is (v1+c, v2+c, ..) for any constant c.

Choose a reference node and drop one equation.

  • \$\begingroup\$ Basically, the nodes go into InAmp in the real real circuit..The whole thing is differential..it's part of MAX30001 IC (datasheets.maximintegrated.co…) the Va and Vb are BIP and BIN pins of the IC and Is is the current generator across DRVP and DRVN nodes.So, I am not 100% sure how to go about solving it. My intention is to find Transfer function interms of Rc1---Rc4.please note, I would have the Va and Vb values(Va-Vb) from real world measurement. \$\endgroup\$
    – seeker
    Commented Jul 2, 2021 at 19:50
  • \$\begingroup\$ datasheets.maximintegrated.com/en/ds/MAX30001.pdf \$\endgroup\$
    – seeker
    Commented Jul 2, 2021 at 19:59
  • \$\begingroup\$ It doesn't matter that you don't care what the common mode voltage is, the fact is that the variables you are trying to solve for will give it to you, but the equations you have set up don't define it - hence you can't solve them. You can rewrite you equations in terms of a lot of differential voltages, or simply choose one node and call it 0V. \$\endgroup\$
    – Tesla23
    Commented Jul 2, 2021 at 22:41

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