Three active-gain rows show gain-squared scaling after a fixed passive filter. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Unity gain leaves the filtered budget at four
The passive low-pass stage leaves budget 4. Gain 1 keeps final budget 4.
4⋅12=4
Gain two makes sixteen output units
The passive budget is still 4. Gain 2 has squared ratio 4, so final budget is 16.
4⋅22=16
Gain three makes thirty-six output units
The third row holds the passive filter fixed and changes gain to 3. Final budget becomes 36.