[sdiy] A little OT, Begging a hand

[David G. Dixon]

> But in the end R1+R2+R3 = K  *must* be satisfied. So all three are not
> independent.

Yes.  Actually, that constraint adds the fifth equation we need to solve the
system.  It's not linear, but it doesn't need to be.

The problem is soluble.  We know that G8 = 1/2k2, and we have six equations
for six conductances:

G1 - G6 = 0

G1*(VA - V1) + G2*(VA - VB) + G4*(VA - VC) = 0

G2*(VB - VA) + G3*(VB - V2) + G57*(VB - VC) = 0

G6*(Vout - VC) + G8*(Vout - V3) = 0

G57*(VC - VB) + G4*(VC - VA) + G6*(VC - Vout) = 0

1/G1 + 1/G2 + 1/G3 = 1/K

This will give us G1, G2, G3, G4, G57, G6 and G8.  G5 and G7 can then be
determined from the following equations:

G2 = G7

1/G57 = 1/G5 + 1/G7

This is not a linear system, but it is soluble.