... why short resistor is inaccurate?
You know the resistance R ~ L/W .
The worst case (or max.)
relative L/W inaccuracy is inversely proportional to the resistor L/W ratio itself.
If we just consider L and W inaccuracies (due to lithography and etch errors), then we get
relative errors ΔL/L and ΔW/W , say e.g. ΔL/L = ΔW/W = 1% = 0.01.
Then the
relative error of the L/W ratio (which means the relative error of the resistor value) is Δ(L/W) / (L/W) = (ΔL/L ± ΔW/W) / (L/W)
The ± sign means the relative length and width errors could compensate each other (-) -- which is the best case -- or they could add (+), which is the worst case.
Of course we have to consider the worst case. In the example above, for your short resistor (L/W=1/8) the above equation results in a w.c.
relative L/W error of (0.01+0.01)/0.125 = 0.16 =
16%.
For your "long" resistor example (L/W=5), a w.c. relative L/W error of 0.02/5 = 0.004 =
0.4% would result.
With my suggestion (L/W=10), the max. relative L/W error would be 0.02/10 = 0.002 =
0.2% .
Many devices in parallel (symmetrical / common centroid layout assumed) tend to counterbalance the relative error even more.