Transfer function calculation Optimization

[RY_8246596]

I have the below circuit for which the switch combinations S1,S2,Sx,Sy[0000...1111] gives me 16 combinations of Va voltages. I have 16 equations for the voltage values. From the equations I am trying to derive the Rc1, Rc2, Rc3 , Rc4 and Rbd transfer function. Please refer attached Mathcad sheet. The issue is, it takes forever to calculate the functions. What I could do to get the symbolic equations?

EDIT : One thing I am thinking is to remove the node R2--Sy and then i'll have 8 combinations of Va.

The Is and Va values are measurable quantities in my case, the switches and R1,R2 is my addition to the circuit with the intention to get individual transfer functions for Rc1..Rc4 and Rbd.

[LucMeekes]

It's essentially the same circuit as presented here (https://community.ptc.com/t5/PTC-Mathcad/Transfer-Function-solution/td-p/736295), So it can be solved as I presented there.

Luc

[LucMeekes]

This is the direction it goes to:

Which results in:

and:

Now all that remains is to find a better way to control the switches, such that I don't get errors, or answers like: Vb.

Luc

[LucMeekes]

Got it:

And with that only three cases don't produce a viable answer:

Which I understand (now) because in those three cases the second and/or third of the five equations read 0+0=Is+0 and/or 0+Is=0+0 respectively. That means I'm trying to solve for more unknowns than I have (independent) equations.

Luc

Hmmm. On closer observation it's not fully correct. Some results contain Ve. That shouldn't be the case.

[RY_8246596]

Hi Luc..I already have the equations for Va..Please refer my attached mathcad sheet. Now, the problem is getting the Transfer function in terms of Rc1...Rc4 and Rbd. As, I stated in my question, I could get rid of R2--Sy node. So, The number of switch combinations be S1,S2,Sx[000...111] essentially leaving all the odd numbered 'Va' in my worksheet. But even with that the tool takes very long time to throw any result.

[LucMeekes]

Your sheet shows 16 equations, and you want to solve for only 5 unknowns, that does not work. Unless it so happens that only 5 of the 16 equations appear to be independent...

Success!
Luc

[RY_8246596]

I get your point..I am thinking I can get 5 equations ignoring R2-Sy node and with following sequence. S1,S2,Sx[000,100,010,101,011].

Note, The Is and Va values are measurable quantities in my case, the switches and R1,R2 has been my addition to the circuit with the intention to get individual transfer functions for Rc1..Rc4 and Rbd.

Refer the updated circuit as below