[sdiy] A little OT, Begging a hand

[ASSI]

On Tuesday 08 February 2011, Veronica Merryfield wrote:
> I have the following resistor network (ascii art follows so you'll need a
> fixed pitch font selected)
> 
>  V1
> 
>  \
>  / R1
>  \
>  /
> 
>  |    R4        R6
>  |
>  |--/\/\/\----/\/\/\----- Vout
> 
>  \          \         \
>  / R2       / R7      / R8
>  \          \         \
>  /          /         /
> 
>  |    R5    |         |
>  |
>  |--/\/\/\--          |
>  |
>  |                    V3
> 
>  \
>  / R3
>  \
>  /
> 
>  V2
> 
> I can set each of V1, V2 and V3 to either +Ve, GND or OC independently,
> although not all combinations are useful, and I can measure Vout.
> R1+R2+R3=K, about 600 ohms. R1=R6 and R2=R7, R4 and R5 vary between
> about 1K and 500K and R8 is fixed at 2K2 although this can be changed.

There's a triangle R2/R4/R2+R5 in the middle of things, making a star out of 
it results in

R'   = R2(R2+R5) / 2R2+R4+R5
R''  = R2R4      / 2R2+R4+R5
R''' = R4(R2+R5) / 2R2+R4+R5

That results in another star 

R1* = R1+R''
R2* = R3+R'
R3* = R8+R1+R'''

that we can transform back into a triangle between the forceable nodes:

Z = (R1+R'')(R3+R') + (R1+R'')(R8+R1+R''') + (R3+R')(R8+R1+R''')
R12 = Z / (R8+R1+R''')
R13 = Z / (R3+R')
R23 = Z / (R1+R'')

(I think... long day)

Nevertheless, we end up with three equations (four if the sum of R1, R2 and 
R3 is exactly known), but we want to know R1, R2, R3, R4 and R5.  At least 
one equation is missing (as has been pointed out already while I was 
doodling away)... unless you know something else, e.g. about the relation 
between R4 and R5 that would allow to formulate this as either a fully 
determined linear system or at least an optimization problem.  If an 
optimization problem, you'd have to be pretty lucky with your constraint to 
be able to separate R4 and R5.


Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

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