Re: [EE] Wonder if anyone can help

Hi Spehro, thank you.

I can arrange to short terminals in as much as I can apply the voltage source to multiple pins at once and can apply ground to multiple pins at once also. Any pin can be independently connected to the voltage source, ground or an ADC.. so that might help. I was hoping that the R1+R2+R3 = a constant would help.

I’ll keep plugging away at it.

And thank you Justin and Jason.  

> On Dec 28, 2025, at 9:56 PM, Spehro Pefhany <[email protected]> wrote:
> 
> 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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