A voltage gain stage after a passive filter scales the squared budget by the gain squared, so it is accounted separately from the passive transmission. The low-pass passes 1/5 of the 20 input budget to give 4, then a gain of 3 scales by 9 to give 36 exactly for the ideal model; real chains add component tolerance, loading, op-amp bandwidth and slew rate, phase, source and load impedance, rail limits, noise, temperature drift, and measurement uncertainty.
Post-gain output budget is kept separate from passive transmission. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The passive filter output is separated first
The low-pass stage transmits 1/5 of the squared budget, so 20 becomes 4.
20⋅51=4
The active gain scales the squared budget afterward
A gain of 3 multiplies squared budget by 9, giving post-gain output 36.