Transfer Function solution

[RY_8246596]

I am trying to find Transfer function for the variables Rc1, Rc2, Rc3 and Rc4 but the tool runs into runtime error . Basically, I need transfer function in terms of Rc1, Rc2,Rc3 and Rc4.

EDIT : attached the worksheet. Now, I am getting out of memory as error.

[mvenich]

Post the full Mathcad worksheet please. Don't expect people to type in the equations for you.

[RY_8246596]

Edited and updated in the original post .Thanks

[ttokoro]

[-MFra-]

As it is written, the system is in 6 equations and eleven unknowns. If you define five of the unknowns and give initial estimates for the remaining six unknowns, you can get a result. The result sought can be obtained by simple inspection of the circuit assuming as output a and b.

[-MFra-]

Using the scheme: "Given .... Find(....)", being known the values of the constants and the initial estimates of the unknowns, you get only numerical results. Since you do not provide numerical values for constants or initial estimates, it is assumed that you are looking for a symbolic solution. The transfer function is defined as the ratio between an output quantity and the system's input quantity. Considering the voltage between a and b as the output quantity, and the current Is as the input quantity, it results that the transfer function is a trans- resistance.
One way to go is by using the network topology as follows (see attached photo -the verses of the currents in the graph are random):

[-MFra-]

Inspection solution:

[RY_8246596]

Basically, the Va and Vb nodes go into InAmp in the real real circuit. The whole thing is differential. It's part of MAX30001 IC  the Va and Vb are BIP and BIN pins of the IC and Is is the current generator across DRVP and DRVN nodes. My intention is to find Transfer function interms of Rc1---Rc4 and later determine the sensitivity of Rc1--Rc4 to Rx and Ry. The, Ra, Rb, Rc and Rd are representing voltage controlled switches which i modelled here as resistances to realize the combinations 0000---1111 for the circuit but now i could see that the Ra-Rd can't be substituted to infinity to represent open switch(0). But, I am getting some sense from your suggestion for the context of my original post.  

[-MFra- · Accepted solution]

We like precise and clear questions. Yours is very cryptic, devoid of data. Questions like that just waste us time.

[RY_8246596]

Excuse me for this. Just too many things were going in my mind. Perhaps I'll try to open a new thread with more clarity.

[LucMeekes]

Your problem is simple, clear from that start (not at all cryptic), and your mistake is obvious.

You have 6 equations, so at best you can solve for 6 variables. I guess they would be the 6 V-terms (Va through Vq). That means adding Rc1 through Rc4 to the Find() statement should result in an error message.

Here is how it can be done:

Note that the expression to the right of the Find() statement is pretty wide, and 6 elements high. I cut it off

You can extract any of the 6 voltages by indexing into the V() function:

(Here the results are also wide, so I cut them off)

You can calculate the voltage difference between a and b like:

Calculate its sensitivity to Ra with:

Of course the result is large, so I cut it off)

And see what happens with Vab if Ra goes to infinity:

Another large result.

Now Mathcad 15 may complain that the (symbolic) results are too large to display, but you should still be able to use them.

Provide any known values for each of the resistors should allow you to get numeric results.

Success!
Luc

[RY_8246596]

Thanks, this solves my issue.