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.