Re: [EE] Wonder if anyone can help

At 05:00 PM 2025-12-28, you wrote:

Hi, V. -

Unless I'm missing something this sounds a bit difficult.

I see 5 independent variables and I think you can get 5 independent
measurements (the symmetry you've described
means that not all the measurements made are actually independent- for
example with a voltage between T1 (V) and T3 (GND) we know VT2+VT4 = V).

You can write the equations for the voltages in terms of resistances
with the usual circuit analysis tools such as wye-delta transformations
and Ohm's law.

But they're nonlinear in terms of the resistances. Which probably
means they have to be solved numerically with Newton-Raphson iteration
or something along those lines.

GNU Octave has a nonlinear solver called fsolve.
https://docs.octave.org/v4.0.0/Solvers.html

Note:

"This is an iterative technique so a starting point must be provided. This
also has the consequence that convergence is not guaranteed even if a 
solution exists"

Since this is something real a reasonable starting point will probably lead to
convergence, at least that's _my_ guess. ;-)

A more complex problem is the sensitivity of the results to the measurement
accuracy. That can be explored in simulation- change each measurement by a
small amount, maybe 10uV and see how much the results of the solver for
each resistance change. There might be better measurements that will 
yield less
sensitivity- for example measuring the resistance from T1&T3 shorted to
T2&T4 shorted will give you (R1+R2+R3)/2 eliminating R4 and R5 (by
symmetry no current flows through them). But that's not as easy.. and may not
be necessary.

Best regards,
Spehro Pefhany


>All
>
>I have a sensor in development that has the following resistor network
>
>T1 - - - - R1 - - - - - R2 - - - - - R3 - - - - T2
>                   |            |
>                   R4           R5
>                   |            |
>T3 - - - - R6 - - - - - R7 - - - - - R8 - - - - T4
>
>
>R1+R2+R3 = always constant (known)
>R1 = R6; R2 = R7; R3 = R8
>Therefore R6+R7+R8 = also always constant
>
>During sensing the value of R1, R2, R3, R4 and R5 change.
>
>So R1, R2 and R3 vary but always sum to a constant (they sense one 
>thing), R4 and R5 vary independently (they sense separate things).
>
>I can apply a voltage source to any terminal, a ground to any 
>terminal and monitor the voltages at all.
>
>I figure I can apply gnd to T1, V to T2 and measure T3 and T4, then 
>move the V and Gnd around until I have 6 unique V and Gnd 
>combinations and sets of measurements.
>
>I think I can assume the current draw to make the measurement is for 
>these purposes negligibly, thus resistor at each measurement 
>terminal is out of the equation for that setup.
>
>I need a bit of help figuring out how to get the equations I need to 
>determine the resistances from each of the setups and measurements. 
>Any help would be deeply appreciated.
>
>Thank you
>--
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