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Optimization of Capacitance Distribution

If the total capacitance value
*C*_{tot}
is known, the individual
capacitance values can be determined such that the dynamic range is
maximized. By default FA distributes the capacitance not optimally but
equally. If the total capacitance is specified, the individual
values are shown if a `caps` item is added to an `output`
command.
The capacitance is divided optimally if `optc` is set
(see Section 9).
For example, the input

butterworth(3);
ctot = 30e-12;
umax = 1;
noisefactor = 1;
transform: scale;
output: "equally distributed capacitances:" caps dr;
set: optc;
output: "optimally distributed capacitances:" caps dr;

results in

c1 = 1.000000e-11
c2 = 1.000000e-11
c3 = 1.000000e-11
Output noise level: 4.334959e-05 V.
Scaling is L-infinity.
Maximum output level: 1.000000e+00 V.
Dynamic range: 2.306827e+04 (87.26 dB).
optimally distributed capacitances:
c1 = 9.117466e-12
c2 = 9.957500e-12
c3 = 1.092503e-11
Capacitance is divided optimally.
Output noise level: 4.323185e-05 V.
Scaling is L-infinity.
Maximum output level: 1.000000e+00 V.
Dynamic range: 2.313110e+04 (87.28 dB).

We see that at least in this case the improvement
in dynamic range by optimal redistribution of
capacitance is very small.

2009-06-03